memetic algorithm based on improved inver over operator and lin kernighan local search for the euclidean traveling salesman problem in this study an improved inver over operator is proposed to solve the euclidean traveling salesman problem tsp problem the improved inver over operator is tested on 14 different tsp examples selected from tsplib the application of the improved inver over operator gives much more effective results regarding to the best and average error values than the basic inver over operator then an effective memetic algorithm based on improved inver over operator and lin kernighan local search is implemented to speed up the convergence capability of the presented algorithm a restart technique is employed we evaluate the proposed algorithm based on standard tsp test problems and show that the proposed algorithm performs better than other memetic algorithm in terms of solution quality and computational effort

a milnor condition for nonatomic lipschitz games and its applications one of milnor s reasonable axioms is generalized to nonatomic games several uses of this generalization are discussed in particular the general form of values and semivalues on subspaces of pna is derived

nonsymmetric values of nonatomic and mixed games this paper presents a new unifying approach to the study of nonsymmetric or quasi values of nonatomic and mixed games a family ofpath values is defined using an appropriate generalization of mertens diagonal formula a path value possesses the following intuitive description consider a function path attaching to each player a distribution function on 0 1 we think of players as arriving randomly and independently to a meeting when the arrival time of a player is distributed according to each player s payoff is defined as his marginal contribution to the coalition of players that have arrived earlier under certain conditions on a path different subspaces of mixed games pna pm bv fl are shown to be in the domain of the path value the family of path values turns out to be very wide we show that onpna pm and their subspaces the path values are essentially the basic construction blocks extreme points of quasi values

on the landscape ruggedness of the quadratic assignment problem local search based heuristics have been demonstrated to give very good results to approximately solve the quadratic assignment problem qap in this paper following the works of weinberger and stadler we introduce a parameter called the ruggedness coeffcient which measures the ruggedness of the qap landscape which is the union of a cost function and a neighborhood we give an exact expression and a sharp lower bound for this parameter we are able toderive from it that the landscape of the qap is rather flat and so it gives a theoretical justification of the effectiveness of local search based heuristics for this problem experimental results with simulated annealing are presented which con8rm this conclusion and also the influence of the ruggedness coe5cient on the quality of results obtained

two dimensional packing problems a survey we consider problems requiring to allocate a set of rectangular items to larger rectangular standardized units by minimizing the waste in two dimensional bin packing problems these units are finite rectangles and the objective is to pack all the items into the minimum number of units while in two dimensional strip packing problems there is a single standardized unit of given width and the objective is to pack all the items within the minimum height we discuss mathematical models and survey lower bounds classical approximation algorithms recent heuristic and metaheuristic methods and exact enumerative approaches the relevant special cases where the items have to be packed into rows forming levels are also discussed in detail

guided local search and its application to the traveling salesman problem abstract the traveling salesman problem tsp is one of the most famous problems in combinatorial optimization in this paper we are going to examine how the techniques of guided local search gls and fast local search fls can be applied to the problem gls sits on top of local search heuristics and has as a main aim to guide these procedures in exploring efficiently and effectively the vast search spaces of combinatorial optimization problems gls can be combined with the neighborhood reduction scheme of fls which significantly speeds up the operations of the algorithm the combination of gls and fls with tsp local search heuristics of different eiciency and effectiveness is studied in an effort to determine the dependence of gls on the underlying local search heuristic used comparisons are made with some of the best tsp heuristic algorithms and general optimization techniques which demonstrate the advantages of gls over alternative heuristic approaches suggested for the problem

ordered weighted average optimization in multiobjective spanning tree problem abstract multiobjective spanning tree problems are studied in this paper the ordered median objective function is used as an averaging operator to aggregate the vector of objective values of feasible solutions this leads to the ordered weighted average spanning tree problem a nonlinear combinatorial optimization problem different mixed integer linear programs are proposed based on the most relevant minimum cost spanning tree models in the literature these formulations are analyzed and several enhancements presented their empirical performance is tested over a set of randomly generated benchmark instances the results of the computational experiments show that the choice of an appropriate formulation allows to solve larger instances with more objectives than those previously solved in the literature

experimental analysis of simulated annealing based algorithms for the layout problem abstract in this paper results from an experimental analysis involving the 2 way and 3 way exchange algorithms a modified penalty algorithm the simulated annealing algorithm and a hybrid simulated annealing algorithm are presented the hybrid simulated annealing algorithm uses the modified penalty algorithm to generate an initial solution and then improves it using simulated annealing it is tested on single row layout problems with facilities of unequal area and multi row layout problems with facilities of equal area the algorithm produced solutions better than those previously reported in the literature for two of the larger single row problems and five multi row layout problems for all the other single row problems and eight of ten multi row layout test problems it produced the best known solutions the hybrid simulated annealing algorithm appears to produce better quality solutions than the simulated annealing and tabu navigation algorithms but requires more computation time than simulated annealing

facet identification for the symmetric traveling salesman polytope several procedures for the identification of facet inducing inequalities for the symmetric traveling salesman polytope are given an identification procedure accepts as input the support graph of a point which does not belong to the polytope and returns as output some of the facet inducing inequalities violated by the point a procedure which always accomplishes this task is calledexact otherwise it is calledheuristic we give exact procedures for the subtour elimination and the 2 matching constraints based on the gomory hu and padberg rao algorithms respectively efficient reduction procedures for the input graph are proposed which accelerate these two algorithms substantially exact and heuristic shrinking conditions for the input graph are also given that yield efficient procedures for the identification of simple and general comb inequalities and of some elementary clique tree inequalities these procedures constitute the core of a polytopal cutting plane algorithm that we have devised and programmed to solve a substantial number of large scale problem instances with sizes up to 2392 nodes to optimality

an efficient transformation of the generalized traveling salesman problem into the traveling salesman problem on digraphs abstract the generalized traveling salesman problem gtsp is a generalization of the traveling salesman problem tsp one of the outstanding intractable combinatorial optimization problems in the gtsp problem we are given n cities that are grouped into mutually disjoint districts clusters and nonnegative distances between the cities in different districts a traveling salesman has to find the shortest tour that visits exactly one city in each district in this paper we study the asymmetric version of this problem and describe a transformation by which an instance of the gtsp can be transformed into an instance of the asymmetric tsp with 2 n cities this compares favorably with the transformation proposed by lien and ma in 5 in which the resulting tsp has more than 3 n vertices we show that any optimal solution of the tsp instance corresponds to a unique optimal solution of the gtsp instance of no greater length thus the described transformation enables to solve the gtsp by applying some of the numerous tsp s heuristics or optimal approaches

a restricted lagrangean approach to the traveling salesman problem we describe an algorithm for the asymmetric traveling salesman problem tsp using a new restricted lagrangean relaxation based on the assignment problem ap the lagrange multipliers are constrained so as to guarantee the continued optimality of the initial ap solution thus eliminating the need for repeatedly solving ap in the process of computing multipliers we give several polynomially bounded procedures for generating valid inequalities and taking them into the lagrangean function with a positive multiplier without violating the constraints so as to strengthen the current lower bound upper bounds are generated by a fast tour building heuristic when the bound strengthening techniques are exhausted without matching the upper with the lower bound we branch by using two different rules according to the situation the usual subtour breaking disjunction and a new disjunction based on conditional bounds we discuss computational experience on 120 randomly generated asymmetric tsp s with up to 325 cities the maximum time used for any single problem being 82 seconds this is a considerable improvement upon earlier methods though the algorithm discussed here is for the asymmetric tsp the approach can be adapted to the symmetric tsp by using the 2 matching problem instead of ap

using logical surrogate information in lagrangean relaxation an application to symmetric traveling salesman problems abstract the traveling salesman problem tsp is a classical combinatorial optimization problem which has been intensively studied the lagrangean relaxation was first applied to the tsp in 1970 the lagrangean relaxation limit approximates what is known today as held and karp hk bound a very good bound less than 1 from optimal for a large class of symmetric instances it became a reference bound for new heuristics mainly for the very large scale instances where the use of exact methods is prohibitive a known problem for the lagrangean relaxation application is the definition of a convenient step size control in subgradient like methods even preserving theoretical convergence properties a wrong defined control can affect the performance and increase computational times we show in this work how to accelerate a classical subgradient method while conserving good approximations to the hk bounds the surrogate and lagrangean relaxations are combined using the local information of the relaxed constraints it results in a one dimensional search that corrects the possibly wrong step size and is independent of the used step size control comparing with the ordinary subgradient method and beginning with the same initial multiplier the computational times are almost twice as fast for medium instances and greatly improved for some large scale tsplib instances

an improved annealing scheme for the qap abstract recently there has been some interest in the use of simulated annealing to obtain good solutions to a number of combinatorial problems this paper reports on the use of this method applied to the quadratic assignment problem i e the assignment of inter communicating objects to locations to minimize the total cost of communication between them the result is a much improved annealing scheme for this problem which performs well on a range of examples finding improved solutions for several of the largest problems available in the literature and requiring only modest amounts of computational effort

potentials and weighted values of nonatomic games the potential approach to value theory for finite games was introduced by hart and mas colell hart s a mas colell 1989 potential value and consistency econometrica57 589 614 here this approach is extended to non atomic games on appropriate spaces of differentiable games there is a unique potential operator that generates the aumann and shapley aumann r j l s shapley 1974 values of nonatomic games princeton university press princeton new jersey value as a corollary we obtain the uniqueness of the aumann shapley value on certain subspaces of games next the potential approach is applied to the weighted case leading to weighted non atomic values it is further shown that the asymptotic weighted value is well defined and that it coincides with the weighted value generated by the potential

optimization by simulated annealing an experimental evaluation part ii graph coloring and number partitioning this is the second in a series of three papers that empirically examine the competitiveness of simulated annealing in certain well studied domains of combinatorial optimization simulated annealing is a randomized technique proposed by s kirkpatrick c d gelatt and m p vecchi for improving local optimization algorithms here we report on experiments at adapting simulated annealing to graph coloring and number partitioning two problems for which local optimization had not previously been thought suitable for graph coloring we report on three simulated annealing schemes all of which can dominate traditional techniques for certain types of graphs at least when large amounts of computing time are available for number partitioning simulated annealing is not competitive with the differencing algorithm of n karmarkar and r m karp except on relatively small instances moreover if running time is taken into account natural annealing schemes cannot even outperform multiple random runs of the local optimization algorithms on which they are based in sharp contrast to the observed performance of annealing on other problems

measure based values of non atomic games a complete characterization of symmetric linear continuous operators from pna to fa is given this is used to prove the existence of a unique value on pna and to deduce the general form of a semivalue and the general form of a degenerate value

simulated annealing for the qap optimal tradeoff between simulation time and solution quality abstract this paper reports on the optimization of solution quality for a simulated annealing algorithm applied to the quadratic assignment problem the optimization is performed by varying two of the parameters in the algorithm the size of the ensemble i e the number of simulations and the length of each simulation the variation is performed in such a way that the algorithm always uses the same amount of time for a given problem size it is found that the simulation length is indeed optimizable but also that a rather broad spectrum of values produce a near optimal solution quality generally it seems that the optimal simulation length is rather short compared to results found for other optimization problems

the n city travelling salesman problem statistical mechanics and the metropolis algorithm in any n city travelling salesman problem there are n 1 mathord left vphantom 2 right kern nulldelimiterspace 2 possible tours we use the metropolis algorithm to generate a sequence of such tours this sequence may be viewed as the random evolution of a physical system in contact with a heat bath as the temperature is lowered the tours generated approach the optimal tour it appears that for large n one arrives within a few percent of the optimal solution in better than quadratic time

some experiments with simulated annealing techniques for packing problems abstract experiments with a variety of combinatorial optimisation problems have shown that the simulated annealing algorithm is an effective local search heuristic method the basic requirements of the algorithm are a neighbourhood structure on the set of feasible solutions and a number of parameters which govern the acceptance or rejection of new solutions generated during the search the quality of the solution is very sensitive to both these factors this paper is concerned with the application of the simulated annealing approach to packing problems and describes a series of experiments carried out to ascertain the effectiveness of the method for such problems and the most appropriate neighbourhood structure to use and the best parameters to apply

application of the simulated annealing algorithm to the combinatorial optimisation problem with permutation property an investigation of generation mechanism focusing on the generation mechanism of random permutation solutions this paper investigates the application of the simulated annealing sa algorithm to the combinatorial optimisation problems with permutation property six types of perturbation scheme for generating random permutation solutions are introduced they are proved to satisfy the asymptotical convergence requirements the results of experimental evaluations on traveling salesman problem tsp flow shop scheduling problem fsp and quadratic assignment problem qap reveal that the efficiencies of the perturbation schemes are different in searching a solution space by adopting a proper perturbation scheme the sa algorithm has shown to produce very efficient solutions to different combinatorial optimisation problems with permutation property

an additive bounding procedure for the asymmetric travelling salesman problem in this paper new lower bounds for the asymmetric travelling salesman problem are presented based on spanning arborescences the new bounds are combined in an additive procedure whose theoretical performance is compared with that of the balas and christofides procedure 1981 both procedures have been imbedded in a simple branch and bound algorithm and experimentally evaluated on hard test problems

exploring variants of 2 opt and 3 opt for the general routing problem the general routing problem grp is the problem of finding a minimum length tour visiting a number of specified vertices and edges in an undirected graph in this paper we describe how the well known 2 opt and 3 opt local search procedures for node routing problems can be adapted to solve arc and general routing problems successfully two forms of the 2 opt and 3 opt approaches are applied to the grp the first version is similar to the conventional approach for the traveling salesman problem the second version includes a dynamic programming procedure and explores a larger neighborhood at the expense of higher running times extensive computational tests including ones on larger instances than previously reported in the arc routing literature are performed with variants of both algorithms in combination with the guided local search metaheuristic and the mechanisms of marking and neighbor lists the procedures systematically detect optimal or high quality solutions within limited computation time

a braided yang baxter algebra in a theory of two coupled lattice quantum kdv algebraic properties and aba representations a generalization of the yang baxter algebra is found in quantizing the monodromy matrix of two m kdv equations discretized on a space lattice this braided yang baxter equation still ensures that the transfer matrix generates operators in involution which form the cartan sub algebra of the braided quantum group representations diagonalizing these operators are described through relying on an easy generalization of algebraic bethe ansatz techniques the conjecture that this monodromy matrix algebra leads in the cylinder continuum limit to a perturbed minimal conformal field theory description is analysed and supported

the quadratic assignment problem an experimental evaluation of solution strategies since procedures for producing optimal solutions to a quadratic assignment problem are computationally infeasible for any but small problems heuristic techniques for producing approximate solutions must be employed for the solution of real practical problems this paper presents the results of experimentation that demonstrates that a solution procedure which couples a constructive initial placement technique with simple and inexpensive improvement procedures produces good solutions with very reasonable computation requirements the results indicate that such an approach would make the solution of large scale quadratic assignment problems feasible

genetic algorithm for asymmetric traveling salesman problem with imprecise travel times this paper presents a variant of the asymmetric traveling salesman problem atsp in which the traveling time between each pair of cities is represented by an interval of values wherein the actual travel time is expected to lie instead of a fixed deterministic value as in the classical atsp here the atsp with interval objective is formulated using the usual interval arithmetic to solve the interval atsp i atsp a genetic algorithm with interval valued fitness function is proposed for this purpose the existing revised definition of order relations between interval numbers for the case of pessimistic decision making is used the proposed algorithm is based on a previously published work and includes some new features of the basic genetic operators to analyze the performance and effectiveness of the proposed algorithm and different genetic operators computational studies of the proposed algorithm on some randomly generated test problems are reported

formulating and solving production planning problems production planning problems frequently involve the assignment of jobs or operations to machines the simplest model of this problem is the well known assignment problem ap however due to simplifying assumptions this model does not provide implementable solutions for many actual production planning problems extensions of the simple assignment model known as the generalized assignment problem gap and the multi resource generalized assignment problem mrgap have been developed to overcome this difficulty this paper presents an extension of the mrgap to allow splitting individual batches across multiple machines while considering the effect of setup times and setup costs the extension is important for many actual production planning problems including ones in the injection molding industry and in the metal cutting industry we formulate models which are logical extensions of previous models which ignored batch splitting for the problem we address we then give different formulations and suggest adaptations of a genetic algorithm ga and simulated annealing sa a systematic evaluation of these algorithms as well as a lagrangian relaxation lr approach is presented

exact and approximation algorithms for the min max k traveling salesmen problem on a tree abstract given k identical salesmen where k 2 is a constant independent of the input size the min max k traveling salesmen problem on a tree is to determine a set of k tours for the salesmen to serve all customers that are located on a tree shaped network so that each tour starts from and returns to the root of the tree with the maximum total edge weight of the tours minimized the problem is known to be np hard even when k 2 in this paper we have developed a pseudo polynomial time exact algorithm for this problem with any constant k 2 closing a question that has remained open for a decade along with this we have further developed a 1 approximation algorithm for any 0

a polyhedral approach to the asymmetric traveling salesman problem several branch and bound algorithms for the exact solution of the asymmetric traveling salesman problem atsp based on the assignment problem ap relaxation have been proposed in the literature these algorithms perform very well for some instances e g those with uniformly random integer costs but very poorly for others the aim of this paper is to evaluate the effectiveness of a branch and cut algorithm exploiting atsp specific facet defining cuts to be used to attack hard instances that cannot be solved by the ap based procedures from the literature we present new separation algorithms for some classes of facet defining cuts and a new variable pricing technique for dealing with highly degenerate primal lp problems a branch and cut algorithm based on these new results is designed and evaluated through computational analysis on several classes of both random and real world instances the outcome of the research is that on hard instances the branch and cut algorithm clearly outperforms the best ap based algorithms from the literature

heuristics for biquadratic assignment problems and their computational comparison abstract the biquadratic assignment problem biqap is a generalization of the quadratic assignment problem qap as for any hard optimization problem also for biqap a reasonable effort to cope with the problem is trying to derive heuristics which solve it suboptimally and which possibly yield a good trade off between the solution quality and the time and memory requirements in this paper we describe several heuristics for biqaps in particular pair exchange algorithms improvement methods and variants of simulated annealing and taboo search we implement these heuristics as c codes and analyze their performances

applying the attribute based hill climber heuristic to the vehicle routing problem abstract the attribute based hill climber abhc is a variant of the general tabu search principle which has shown to be competitive with respect to quality as well as efficiency to other local search heuristics for the two corner stone problems in combinatorial optimization the travelling salesman problem and the quadratic assignment problem abhc is completely parameter free and its generic logic depends on the concept of partitioning the solution space based on solution attributes which is the problem specific choice in this paper we analyze the effectiveness of this concept and the efficiency of the abhc heuristic for the general vehicle routing problem

asymptotic expected performance of some tsp heuristics an empirical evaluation abstract this paper presents an empirical study on the performance of some heuristics for the travelling salesman problem our study indicates that the expected tour lengths through n points in a unit square produced by these heuristics are all proportional to sqrt n asymptotically in this study the average tour lengths generated by each heuristic are approximated by a linear function of sqrt n the model parameters are estimated by the linear regression method the possible effect of different random number generators which are used to perform the statistical analysis is also investigated

performance characteristics of alternative genetic algorithmic approaches to the traveling salesman problem using path representation an empirical study abstract the potential of genetic algorithmic ga approaches for solving order based problems including the traveling salesman problem tsp is recognized in a number of recent studies by applying various gas these studies developed a set of unresolved ga design and configuration issues the purpose of this study is to resolve the conflicting ga design and configuration issues by 1 concentrating on the classical tsp and 2 developing implementing and testing a complete set of alternative ga configurations 144 gas are developed and evaluated by solvinh 5000 tsps a carefully designed statistical experimental plan accompanied by rigorous statistical analysis isolate the most promising configurations and identify their effect on solution time and quality although the emphasis is on the tsp the final results are applicable to other order based problems that use sequence encoding

genetic algorithms and traveling salesman problems abstract a genetic algorithm ga with an asexual reproduction plan through a generalized mutation for an evolutionary operator is developed that can be directly applied to a permutation of n numbers for an approximate global optimal solution of a traveling salesman problem tsp schema analysis of the algorithm shows that a sexual reproduction with the generalized mutation operator preserves the global convergence property of a genetic algorithm thus establishing the fundamental theorem of the ga for the algorithm avoiding an intermediate step of encoding through random keys to preserve crossover or permuting n and using fixing states for legal crossover are the chief benefits of the innovations reported in this paper the algorithm has been applied to a number of natural and artificial problems and the results are encouraging

new lower bounds for the symmetric travelling salesman problem in this paper new lower bounds for the symmetric travelling salesman problem are proposed and combined in additive bounding procedures efficient implementations of the algorithms are given in particular fast procedures for computing the linear programming reduced costs of the shortest spanning tree sst problem and for finding all ther sst of a given graph are presented computational results on randomly generated test problems are reported

improving the performance guarantee for approximate graph coloring the performance guarantee of a graph coloring algorithm is the worst case ratio between the number of colors it uses on the input graph and the chromauc number of this graph the previous best known polynomial time algorithm had a performance guarantee o n logn for graphs on n vertices this result stood unchallenged for eight years this paper presents an efficient algorithm with performance guarantee of o n loglog n 2 logn 2

extensions to the generalised assignment heuristic for vehicle routing abstract although tabu search has generally given the best results for benchmark vehicle routing problems it has been observed that such heuristics require substantial computing times and several parameter settings thus when good quality solutions are required quickly there is still a need for relatively fast and effective heuristics the generalised assignment heuristic for the basic vehicle routing problem vrp can be extended by adjusting seed positions to reduce the optimal objective value for the generalised assignment problem gap combined with a simple lagrangean heuristic this gives a relatively straightforward method for obtaining solutions within a few percent of the best known values for benchmark problems

some experiments with simulated annealing for coloring graphs abstract methods of thermodynamical simulation have been used for several famous combinatorial optimization problems for graph coloring i e partition of the node set into as few independent sets as possible we describe a method of simulation such an approach is combined with other techniques for graph coloring experiments on random graphs show evidence that this combination gives better results than anyone of the original non combined methods

partially symmetric values we consider spaces of differentiable nonatomic and mixed vector measure games pna andpm with finitely or countably many types of players type symmetric values on these spaces of games are investigated all aumann and shapley conditions except symmetry are assumed the latter being replaced by a weaker assumption of covariance under automorphisms of the space of players that preserve each type we show that if the types are uncountable then type symmetric values are random path values in particular the symmetric values onpm are characterized as mixtures of values defined in hart 1973

formulations and benders decomposition algorithms for multidepot salesmen problems with load balancing this paper describes new models and exact solution algorithms for the fixed destination multidepot salesmen problem defined on a graph with n nodes where the number of nodes each salesman is to visit is restricted to be in a predefined range such problems arise when the time to visit a node takes considerably longer as compared to the time of travel between nodes in which case the number of nodes visited in a salesman s tour is the determinant of their load the new models are novel multicommodity flow formulations with o n 2 binary variables which is contrary to the existing formulations for the same and similar problems that typically include o n 3 binary variables the paper also describes benders decomposition algorithms based on the new formulations for solving the problem exactly results of the computational experiments on instances derived from tsplib show that some of the proposed algorithms perform remarkably well in cases where formulations solved by a state of the art optimization code fail to yield optimal solutions within reasonable computation time

the quadratic three dimensional assignment problem exact and approximate solution methods abstract this paper reports on algorithm development for solving the quadratic three dimensional assignment problem q3ap the q3ap arises for example in the implementation of a hybrid arq automatic repeat request scheme for enriching diversity among multiple packet re transmissions by optimizing the mapping of data bits to modulation symbols typical practical problem sizes would be 8 16 32 and 64 we present an exact solution method based upon a reformulation linearization technique that is one of the best available for solving the quadratic assignment problem qap our current exact algorithm is useful for q3ap instances of size 13 or smaller we also investigate four stochastic local search algorithms that provide optimum or near optimum solutions for large and difficult qap instances and adapt them for solving the q3ap the results of our experiments make it possible to get good solutions to signal mapping problems of size 8 and 16

an algorithm for quadratic assignment problems abstract facility layout and location problems with stochastic congestion in the traffic circulation system have been studied in a previous paper in this paper we present a heuristic algorithm to solve these complex problems with its straight forward approach the algorithm can solve large scale quadratic assignment problems with reasonable computing times and efficient performance computational experience for solving many test examples is also presented

a guided local search metaheuristic for the team orienteering problem in the team orienteering problem top a set of locations is given each with a score the goal is to determine a fixed number of routes limited in length that visit some locations and maximise the sum of the collected scores this paper describes an algorithm that combines different local search heuristics to solve the top guided local search gls is used to improve two of the proposed heuristics an extra heuristic is added to regularly diversify the search in order to explore more areas of the solution space the algorithm is compared with the best known heuristics of the literature and applied on a large problem set the obtained results are almost of the same quality as the results of these heuristics but the computational time is reduced significantly applying gls to solve the top appears to be a very promising technique furthermore the usefulness of exploring more areas of the solution space is clearly demonstrated

generation of the exact pareto set in multi objective traveling salesman and set covering problems abstract the calculation of the exact set in multi objective combinatorial optimization moco problems is one of the most computationally demanding tasks as most of the problems are np hard in the present work we use augmecon2 a multi objective mathematical programming momp method which is capable of generating the exact pareto set in multi objective integer programming moip problems for producing all the pareto optimal solutions in two popular moco problems the multi objective traveling salesman problem motsp and the multi objective set covering problem moscp the computational experiment is confined to two objective problems that are found in the literature the performance of the algorithm is slightly better to what is already found from previous works and it goes one step further generating the exact pareto set to till now unsolved problems the results are provided in a dedicated site and can be useful for benchmarking with other momp methods or even multi objective meta heuristics momh that can check the performance of their approximate solution against the exact solution in motsp and moscp problems

a branch and bound algorithm for the symmetric traveling salesman problem based on the 1 tree relaxation abstract in 1970 held and karp introduced the lagrangean approach to the symmetric traveling salesman problem we use this 1 tree relaxation in a new branch and bound algorithm it differs from other algorithms not only in the branching scheme but also in the ascent method to calculate the 1 tree bounds urthermore we determine heuristic solutions throughout the computations to provide upperbounds we present computational results for both a depth first and a breadth first version of our algorithm on the average our results on a number of euclidean problems from the literature are obtained in about 60 less 1 trees than the best known algorithm based on the 1 tree relaxation for random table problems up to 100 cities the average results are also satisfactory

new edges not used in shortest tours of tsp abstract for the symmetric traveling salesman problem in an euclidian plane a geometrical method for finding edges not used in shortest tours of a complete graph is shown the edges are obtained as pairs like edges crossing each other in special cases the number of these pairs is six times the number of crossing pairs relations between the method introduced here and the shortest spanning tree are discussed

a node current based 2 index formulation for the fixed destination multi depot travelling salesman problem abstract the travelling salesman problem forms a basis for many optimisation problems in logistics finance and engineering several variants exist to accommodate for different problem types in this paper we discuss the fixed destination multi depot travelling salesman problem where several salesmen will start from different depots and they are required to return to the depot they originated from we propose a novel formulation for this problem using 2 index binary variables and node currents and compare it to other 2 index formulations from the literature this novel formulation requires less binary variables and continuous variables to formulate a problem resulting in lower computation times using a large benchmark the effectiveness of the new formulation is demonstrated

path planning on a cuboid using genetic algorithms the traveling salesman problem tsp is one of the most extensively studied problems in the fields of combinatorial optimization and global search heuristics a variety of heuristic algorithms are available for solving euclidean tsp and planar tsps however optimization on a cuboid has potential applications for areas like path planning on the faces of buildings rooms furniture books and products or simulating the behaviors of insects in this paper we address a variant of the tsp in which all points cities and paths solution are on the faces of a cuboid we develop an effective hybrid method based on genetic algorithms and 2 opt to adapt the euclidean tsp to the surface of a cuboid the method was tested on some benchmark problems from tsplib with satisfactory results a web based interactive visualization tool has also been developed using java 3d and optimization results for different point densities on the cuboid are presented

simulated annealing with an optimal fixed temperature contrary to conventional belief it turns out that in some problem instances of moderate size fixed temperature simulated annealing algorithms based on a heuristic formula for determining the optimal temperature can be superior to algorithms based on cooling such a heuristic formula however often seems elusive in practical cases considered we include instances of traveling salesman quadratic assignment and graph partitioning problems where we obtain results that compare favorably to the ones known in the literature

simulated annealing searching for an optimal temperature schedule a sizable part of the theoretical literature on simulated annealing deals with a property called convergence which asserts that the simulated annealing chain is in the set of global minimum states of the objective function with probability tending to 1 however in practice the convergent algorithms are considered too slow whereas a number of nonconvergent ones are usually preferred we attempt a detailed analysis of various temperature schedules examples will be given of when it is both practically and theoretically justified to use boiling fixed temperature or even fast cooling schedules which have a small probability of reaching global minima applications to traveling salesman problems of various sizes are also given

value theory without efficiency a semivalue is a symmetric positive linear operator on a space of games which leaves the additive games fixed such an operator satisfies all of the axioms defining the shapley value with the possible exception of the efficiency axiom the class of semivalues is completely characterized for the space of finite player games and for the space pna of nonatomic games

iterated local search for the quadratic assignment problem iterated local search ils is a simple and powerful stochastic local search method this article presents and analyzes the application of ils to the quadratic assignment problem qap we justify the potential usefulness of an ils approach to this problem by an analysis of the qap search space however an analysis of the run time behavior of a basic ils algorithm reveals a stagnation behavior which strongly compromises its performance to avoid this stagnation behavior we enhance the ils algorithm using acceptance criteria that allow moves to worse local optima and we propose population based ils extensions an experimental evaluation of the enhanced ils algorithms shows their excellent performance when compared to other state of the art algorithms for the qap

new insertion and postoptimization procedures for the traveling salesman problem this paper describes a new insertion procedure and a new postoptimization routine for the traveling salesman problem the combination of the two methods results in an efficient algorithm genius which outperforms known alternative heuristics in terms of solution quality and computing time

a survey for the quadratic assignment problem the quadratic assignment problem qap one of the most difficult problems in the np hard class models many real life problems in several areas such as facilities location parallel and distributed computing and combinatorial data analysis combinatorial optimization problems such as the traveling salesman problem maximal clique and graph partitioning can be formulated as a qap in this paper we present some of the most important qap formulations and classify them according to their mathematical sources we also present a discussion on the theoretical resources used to define lower bounds for exact and heuristic algorithms we then give a detailed discussion of the progress made in both exact and heuristic solution methods including those formulated according to metaheuristic strategies finally we analyze the contributions brought about by the study of different approaches

fast neighborhood search for two and three dimensional nesting problems abstract in this paper we present a new heuristic solution method for two dimensional nesting problems it is based on a simple local search scheme in which the neighborhood is any horizontal or vertical translation of a given polygon from its current position to escape local minima we apply the meta heuristic method guided local search the strength of our solution method comes from a new algorithm which is capable of searching the neighborhood in polynomial time more precisely given a single polygon with m edges and a set of polygons with n edges the algorithm can find a translation with minimum overlap in time o mn log mn solutions for standard test instances are generated by an implementation and a comparison is done with recent results from the literature the solution method is very robust and most of the best solutions found are also the currently best results published our approach to the problem is very flexible regarding problem variations and special constraints and as an example we describe how it can handle materials with quality regions finally we generalize the algorithm for the fast neighborhood search and present a solution method for three dimensional nesting problems

algodesk an experimental comparison of eight evolutionary heuristics applied to the quadratic assignment problem abstract this work compares the effectiveness of eight evolutionary heuristic algorithms applied to the quadratic assignment problem qap reputedly one of the most difficult combinatorial optimization problems qap is merely used as a carrier for the comparison we do not attempt to compare any heuristics with solving algorithms specific for it results are given both with respect to the best result achieved by each algorithm in a limited time span and to its speed of convergence to that result

recent advances in the solution of quadratic assignment problems the quadratic assignment problem qap is notoriously difficult for exact solution methods in the past few years a number of long open qaps including those posed by steinberg 1961 nugent et al 1968 and krarup 1972 were solved to optimality for the first time the solution of these problems has utilized both new algorithms and novel computing structures we describe these developments as well as recent work which is likely to result in the solution of even more difficult instances

approximate optimal periodic scheduling of multiple sensors with constraints a constrained periodic multiple sensor scheduling problem is considered in this paper for each sensor constraints on dwell time and activation times are imposed at each time instant only one sensor can update its measurement with the estimator and the objective is to minimize the average state estimation error an approximation framework is proposed to calculate the objective function which transforms the original scheduling problem into an approximate optimal scheduling problem aosp an upper bound on the approximation error is presented to evaluate the performance of the framework to solve the aosp a necessary condition is first proposed on the optimal schedules when no constraints on activation times exist a dynamic programming based algorithm is devised to identify the optimal schedule with polynomial computational complexity when activation time constraints exist we show that the aosps can be solved by solving traveling salesman problems examples are provided to illustrate the proposed results

a new table of constant weight codes a table of binary constant weight codes of length nl28 is presented explicit constructions are given for most of the 600 codes in the table the majority of these codes are new the known techniques for constructing constant weight codes are surveyed and a table of unrestricted binary codes of length nl28 is given

optimization engineering techniques for the exact solution of np hard combinatorial optimization problems abstract the design of effective exact enumerative algorithms for finding the optimal solution of a given np hard combinatorial optimization problem whose mathematical model is given by an integer linear program is considered the commonly used approaches i e dynamic programming branch and bound branch and cut and branch and price are shortly described since the most effective algorithm to be used for finding the optimal solution of a given problem strongly depends on the specific instance to be solved then the best results are often obtained by using hybrid algorithms i e by combining different approaches according to what can be called an optimization engineering technique to illustrate the above mentioned approach the well known 0 1 knapsack problem asymmetric travelling salesman problem and 2 constraint bin packing problem are considered

the traveling salesman problem an overview of exact and approximate algorithms in this paper some of the main known algorithms for the traveling salesman problem are surveyed the paper is organized as follows 1 definition 2 applications 3 complexity analysis 4 exact algorithms 5 heuristic algorithms 6 conclusion

clustering data that are graph connected abstract a new combinatorial model for clustering is proposed for all applications in which individual and relational data are available individual data refer to the intrinsic features of units they are stored in a matrix d and are the typical input of all clustering algorithms proposed so far relational data refer to the observed links between units representing social ties such as friendship joint participation to social events and so on relational data are stored in the graph g v e and the data available for clustering are the triplet g v e d called attributed graph known clustering algorithms can take advantage of the relational structure of g to redefine and refine the units membership for example uncertain membership of units to groups can be resolved using the sociological principle that ties are more likely to form between similar units the model proposed here shows how to take into account the graph information combining the clique partitioning objective function a known clustering methodology with connectivity as the structural constraint of the resulting clusters the model can be formulated and solved using integer linear programming and a new family of cutting planes moderate size problems are solved and heuristic procedures are developed for instances in which the optimal solution can only be approximated finally tests conducted on simulated data show that the clusters quality is greatly improved through this methodology

upper and lower bounding strategies for the generalized minimum spanning tree problem abstract we address the generalized minimum spanning tree problem gmst which requires spanning at least one vertex out of every set of disjoint vertices in a graph we show that the geometric version of this problem is np hard and we propose two stochastic heuristics the first one is a very fast randomized greedy search algorithm and the second one being a genetic algorithm also we investigate some existing integer programming formulations and present an new one a new lagrangian based lower bound is proposed and implemented to assess the performance of the heuristics computational experiments performed on a large set of randomly generated instances with up to 1000 vertices and 10 000 edges provide evidence of the good performance of the proposed heuristics

the hardest constraint problems a double phase transition abstract the distribution of hard graph coloring problems as a function of graph connectivity is shown to have two distinct transition behaviors the first previously recognized is a peak in the median search cost near the connectivity at which half the graphs have solutions this region contains a high proportion of relatively hard problem instances however the hardest instances are in fact concentrated at a second lower transition point near this point most problems are quite easy but there are also a few very hard cases this region of exceptionally hard problems corresponds to the transition between polynomial and exponential scaling of the average search cost whose location we also estimate theoretically these behaviors also appear to arise in other constraint problems this work also shows the limitations of simple measures of the cost distribution such as mean or median for identifying outlying cases

solution of large scale symmetric travelling salesman problems in this paper we report on a cutting plane procedure with which we solved symmetric travelling salesman problems of up to 1000 cities to optimality our implementation is based on a fast lp solver ibm s mpsx and makes effective use of polyhedral results on the symmetric travelling salesman polytope we describe the important ingredients of our code and give an extensive documentation of its computational performance

a new subtour elimination constraint for the vehicle routing problem abstract vehicle routing problems vrp are concerned with the delivery of a single commodity from a centralized depot to a number of specified customer locations with known demands in this paper we consider the vrp characterized by fixed or variable number of vehicles common vehicle capacity distance restrictions and minimization of total distance travelled by all vehicles as the objective we develop an exact algorithm based on a new subtour elimination constraint the algorithm is implemented using the cplex package for solving the relaxed subproblems computational results on 1590 simulated problems and 10 literature problems without distance restrictions are reported and a comparative analysis is carried out

optimization of the quadratic assignment problem using an ant colony algorithm ant algorithm is a multi agent systems inspired by the behaviors of real ant colonies function to solve optimization problems in this paper an ant colony optimization algorithm is developed to solve the quadratic assignment problem the local search process of the algorithm is simulated annealing in the exploration of the search space the evaluation of pheromones which are laid on the ground by ants is used in this work the algorithm is analyzed by using current problems in the literature and is compared with other metaheuristics

an optimal solution method for large scale multiple traveling salesmen problems we develop an efficient branch and bound based method for solving the multiple traveling salesman problem and develop lower bounds through a lagrangean relaxation that requires computing a degree constrained minimal spanning tree a subgradient optimization procedure updates the lagrange multipliers we use fast sensitivity analysis techniques to increase the underlying graph sparsity and reduce the problem size the algorithm was tested on 416 problems with up to 500 cities and 10 salesmen we also present computational results on different data sets and parameters in order to identify the major factors that influence the performance of the developed code

convergence of an annealing algorithm the annealing algorithm is a stochastic optimization method which has attracted attention because of its success with certain difficult problems including np hard combinatorial problems such as the travelling salesman steiner trees and others there is an appealing physical analogy for its operation but a more formal model seems desirable in this paper we present such a model and prove that the algorithm converges with probability arbitrarily close to 1 we also show that there are cases where convergence takes exponentially long that is it is no better than a deterministic method we study how the convergence rate is affected by the form of the problem finally we describe a version of the algorithm that terminates in polynomial time and allows a good deal of practical confidence in the solution

a heuristic for quadratic boolean programs with applications to quadratic assignment problems abstract a heuristic for quadratic boolean programs is presented computational tests with quadratic assignment problems qap showed that it finds very good suboptimal solutions in moderate time and behaves computationally stable in the appendix a fortran program for qap is listed which improves an earlier code published by burkard and derigs

a thermodynamically motivated simulation procedure for combinatorial optimization problems abstract exchange algorithms are an important class of heuristics for hard combinatorial optimization problems as e g salesman problems or quadratic assignment problems in kirkpatrick s and cerny s exchange algorithms for the travelling salesman problem and placement problem they propose to perform an exchange not only if the objective function value decreases by this exchange but also in certain cases if the objective function value increases an exchange increasing the objective function value is performed stochastically depending on the size of the increment computational tests with quadratic assignment problems revealed an excellent behaviour in such an approach suboptimal solutions differing 1 2 from the best known solutions are obtained by a simple program in short time by starting this program several times with different starting values all known minimal objective function values were reached thus this approach is well suited also for smaller computers and leads in short time to acceptable solutions

from the braided to the usual yang baxter relation quantum monodromy matrices coming from a theory of two coupled m kdv equations are modified in order to satisfy the usual yang baxter relation as a consequence a general connection between braided and unbraided usual yang baxter algebras is derived and also analysed

heuristic algorithms for the 2 period balanced travelling salesman problem in euclidean graphs in the 2 period travelling salesman problem some nodes called double nodes are visited in both of two periods while the remaining ones called single nodes are visited in either one of the periods in this paper we study the case in which a balance constraint is also introduced we require that the difference between the number of visited nodes in the two periods must be below a fixed threshold moreover we suppose that distances between nodes are euclidean the problem is np hard and exact methods now available appear inadequate here we propose three heuristics computational experiences and a comparison between the algorithms are also given

integrable structure of conformal field theory ii q operator and ddv equation this paper is a direct continuation of 1 where we began the study of the integrable structures in conformal field theory we show here how to construct the operators bf q pm lambda which act in the highest weight virasoro module and commute for different values of the parameter these operators appear to be the cft analogs of the q matrix of baxter 2 in particular they satisfy baxter s famous t q equation we also show that under natural assumptions about analytic properties of the operators as the functions of the baxter s relation allows one to derive the nonlinear integral equations of destri de vega ddv 3 for the eigenvalues of the q operators we then use the ddv equation to obtain the asymptotic expansions of the q operators at large it is remarkable that unlike the expansions of the t operators of 1 the asymptotic series for q contains the dual nonlocal integrals of motion along with the local ones we also discuss an intriguing relation between the vacuum eigenvalues of the q operators and the stationary transport properties in the boundary sine gordon model on this basis we propose a number of new exact results about finite voltage charge transport through the point contact in the quantum hall system

quantized braided groups algebras that represent a generalization of both quantum groups quantum supergroups and braided groups are defined they are given by a pair of solutions of the yang baxter equation that satisfy some additional conditions several examples are presented

a general variable neighborhood search for the one commodity pickup and delivery travelling salesman problem abstract we present a variable neighborhood search approach for solving the one commodity pickup and delivery travelling salesman problem it is characterized by a set of customers such that each of the customers either supplies pickup customers or demands delivery customers a given amount of a single product and by a vehicle whose given capacity must not be exceeded that starts at the depot and must visit each customer only once the objective is to minimize the total length of the tour thus the considered problem includes checking the existence of a feasible travelling salesman s tour and designing the optimal travelling salesman s tour which are both np hard problems we adapt a collection of neighborhood structures k opt double bridge and insertion operators mainly used for solving the classical travelling salesman problem a binary indexed tree data structure is used which enables efficient feasibility checking and updating of solutions in these neighborhoods our extensive computational analysis shows that the proposed variable neighborhood search based heuristics outperforms the best known algorithms in terms of both the solution quality and computational efforts moreover we improve the best known solutions of all benchmark instances from the literature with 200 to 500 customers we are also able to solve instances with up to 1000 customers

an effective implementation of the lin kernighan traveling salesman heuristic abstract this paper describes an implementation of the lin kernighan heuristic one of the most successful methods for generating optimal or near optimal solutions for the symmetric traveling salesman problem tsp computational tests show that the implementation is highly effective it has found optimal solutions for all solved problem instances we have been able to obtain including a 13 509 city problem the largest non trivial problem instance solved to optimality today

instance specific multi objective parameter tuning based on fuzzy logic abstract finding good parameter values for meta heuristics is known as the parameter setting problem a new parameter tuning strategy called ipts is proposed that is a novel instance specific method to take the trade off between solution quality and computational time into consideration two important steps in the method are an a priori statistical analysis to identify the factors that determine heuristic performance in both quality and time for a specific type of problem and the transformation of these insights into a fuzzy inference system rule base which aims to return parameter values on the pareto front with respect to a decision maker s preference applied to the symmetric travelling salesman problem and the meta heuristic guided local search the approach is consistently faster than a traditional non instance specific parameter tuning strategy without significantly affecting solution quality optimised for speed computational times are shown to be on average 20 times faster while producing solutions of similar quality a number of interesting areas for further research are discussed

an iterated local search algorithm for the vehicle routing problem with backhauls abstract the vehicle routing problem with backhauls vrpb is an extension of the vrp that deals with two types of customers the consumers linehaul that request goods from the depot and the suppliers backhaul that send goods to the depot in this paper we propose a simple yet effective iterated local search algorithm for the vrpb its main component is an oscillating local search heuristic that has two main features first it explores a broad neighborhood structure at each iteration this is efficiently done using a data structure that stores information about the set of neighboring solutions second the heuristic performs constant transitions between feasible and infeasible portions of the solution space these transitions are regulated by a dynamic adjustment of the penalty applied to infeasible solutions an extensive statistical analysis was carried out in order to identify the most important components of the algorithm and to properly tune the values of their parameters the results of the computational experiments carried out show that this algorithm is very competitive in comparison to the best metaheuristic algorithms for the vrpb additionally new best solutions have been found for two instances in one of the benchmark sets these results show that the performance of existing metaheuristic algorithms can be considerably improved by carrying out a thorough statistical analysis of their components in particular it shows that by expanding the exploration area and improving the efficiency of the local search heuristic it is possible to develop simpler and faster metaheuristic algorithms without compromising the quality of the solutions obtained

a guided local search heuristic for the capacitated arc routing problem abstract this paper presents a new local search algorithm for the capacitated arc routing problem carp the procedure uses single vehicle moves and moves that operate on two routes both derived from a node routing context but properly adapted to work well for arc routing problems we combine the algorithm with the meta heuristic guided local search and further use the mechanisms of neighbor lists and edge marking to improve the solution quality and to save computation time experiments on standard benchmark problems from the literature show that our algorithm outperforms the existing heuristics for the carp on a set of new test problems the local search approach consistently produces high quality solutions and often detects an optimal solution within limited computation time

quadratic assignment problems abstract this paper surveys quadratic assignment problems qap at first several applications of this problem class are described and mathematical formulations of qaps are given then some exact solution methods and good heuristics are outlined their computational behaviour is illustrated by numerical results further recent results on the asymptotic probabilistic behaviour of qaps are outlined