conormal problem of higher order parabolic systems with time irregular coefficients the paper is a comprehensive study of lp and schauder estimates for higher order divergence type parabolic systems with discontinuous coefficients on a half space and cylindrical domains with the conormal derivative boundary conditions for the lp estimates we assume that the leading coefficients are only bounded and measurable in the t variable and have vanishing mean oscillations vmox with respect to x we also prove the schauder estimates in two situations the coefficients are holder continuous only in the x variable the coefficients are holder continuous in the t variable as well on the lateral boundary

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

active constraint variable ordering for faster feasibility of mixed integer linear programs the selection of the branching variable can greatly affect the speed of the branch and bound solution of a mixed integer or integer linear program traditional approaches to branching variable selection rely on estimating the effect of the candidate variables on the objective function we present a new approach that relies on estimating the impact of the candidate variables on the active constraints in the current lp relaxation we apply this method to the problem of finding the first feasible solution as quickly as possible empirical experiments demonstrate a significant improvement compared to a state of the art commercial mip solver

gradient estimates of mean curvature equations with neumann boundary value problems abstract in this paper we use the maximum principle to get the gradient estimate for the solutions of the prescribed mean curvature equation with neumann boundary value problem which gives a positive answer for the question raised by lieberman in 2013 as a consequence we obtain the corresponding existence theorem for a class of mean curvature equations

an integer linear programming based heuristic for the capacitated m ring star problem abstract we address the capacitated m ring star problem in which the aim is to find m rings simple cycles visiting a central depot a subset of customers and a subset of potential steiner nodes while customers not belonging to any ring must be allocated to a visited customer or steiner node moreover the rings must be node disjoint and the number of customers allocated or visited in a ring cannot be greater than a given capacity q the objective is to minimize the total visiting and allocation costs the capacitated m ring star problem is np hard since it generalizes the traveling salesman problem in this paper we propose a new heuristic algorithm which combines both heuristic and exact ideas to solve the problem following the general variable neighborhood search scheme the algorithm incorporates an integer linear programming based improvement method which is applied whenever the heuristic algorithm is not able to improve the quality of the current solution extensive computational experiments on benchmark instances of the literature and on a new set of instances have been performed to compare the proposed algorithm with the most effective methods from the literature the results show that the proposed algorithm outperforms the other methods

nonlinear oblique boundary value problems for nonlinear elliptic equations on considere le probleme aux valeurs limites a derivee oblique non lineaire pour des equations uniformement elliptiques quasi lineaires et totalement non lineaires d ordre 2 les operateurs elliptiques satisfont des conditions de structure naturelle on donne des theoremes d existence pour les solutions

adaptive kernel search a heuristic for solving mixed integer linear programs abstract we introduce adaptive kernel search aks a heuristic framework for the solution of general mixed integer linear programs mips aks extends and enhances kernel search a heuristic framework that has been shown to produce high quality solutions for a number of specific combinatorial optimization problems in a short amount of time aks solves a sequence of carefully constructed restricted mips using a commercial mip solver the computational effort required to solve the first restricted mip guides the construction of the subsequent mips the restricted mips are constructed around a kernel which contains the variables that are presumably non zero in an optimal solution computational results for a set of 137 instances show that aks significantly outperforms other state of the art heuristics for solving mips aks also compares favorably to cplex and offers more flexibility to trade off solution quality and computing time

a new class of functions for measuring solution integrality in the feasibility pump approach mixed integer optimization is a powerful tool for modeling many optimization problems arising from real world applications finding a first feasible solution represents the first step for several mixed integer programming mip solvers the feasibility pump is a heuristic for finding feasible solutions to mixed integer linear programming milp problems which is effective even when dealing with hard mip instances in this work we start by interpreting the feasibility pump as a frank wolfe method applied to a nonsmooth concave merit function then we define a general class of functions that can be included in the feasibility pump scheme for measuring solution integrality and we identify some merit functions belonging to this class we further extend our approach by dynamically combining two different merit functions finally we define a new version of the feasibility pump algorithm which includes the original version of the feasibility pump as a special case and we present computational results on bi

uniqueness of the critical point of the solutions to some semilinear elliptic boundary value problems in we consider some two dimensional semilinear elliptic boundary value problems over a bounded convex domain in r2 and show the uniqueness of the critical point of the solutions

a hybrid adaptive large neighborhood search heuristic for lot sizing with setup times abstract this paper presents a hybrid of a general heuristic framework and a general purpose mixed integer programming mip solver the framework is based on local search and an adaptive procedure which chooses between a set of large neighborhoods to be searched a mixed integer programming solver and its built in feasibility heuristics is used to search a neighborhood for improving solutions the general reoptimization approach used for repairing solutions is specifically suited for combinatorial problems where it may be hard to otherwise design suitable repair neighborhoods the hybrid heuristic framework is applied to the multi item capacitated lot sizing problem with setup times where experiments have been conducted on a series of instances from the literature and a newly generated extension of these on average the presented heuristic outperforms the best heuristics from the literature and the upper bounds found by the commercial mip solver ilog cplex using state of the art mip formulations furthermore we improve the best known solutions on 60 out of 100 and improve the lower bound on all 100 instances from the literature

vanishing of rabinowitz floer homology on negative line bundles following frauenfelder rabinowitz action functional on very negative line bundles habilitationsschrift munich munchen 2008 albers and frauenfelder bubbles and onis 2014 arxiv 1412 4360 we construct rabinowitz floer homology for negative line bundles over symplectic manifolds and prove a vanishing result ritter adv math 262 1035 1106 2014 showed that symplectic homology of these spaces does not vanish in general thus the theorem mathrm sh 0 leftrightarrow mathrm rfh 0 ritter in j topol 6 2 391 489 2013 does not extend beyond the symplectically aspherical situation we give a conjectural explanation in terms of the cieliebak frauenfelder oancea long exact sequence cieliebak et al ann sci ec norm super 4 43 6 957 1015 2010

octane a new heuristic for pure 0 1 programs we propose a new heuristic for pure 0 1 programs which finds feasible integer points by enumerating extended facets of the octahedron the outer polar of the unit hypercube we give efficient algorithms to carry out the enumeration and we explain how our heuristic can be embedded in a branch and cut framework finally we present computational results on a set of pure 0 1 programs taken from miplib and other sources

fatcop a fault tolerant condor pvm mixed integer programming solver we describe fatcop a new parallel mixed integer program solver written in pvm the implementation uses the condor resource management system to provide a virtual machine composed of otherwise idle computers the solver differs from previous parallel branch and bound codes by implementing a general purpose parallel mixed integer programming algorithm in an opportunistic multiple processor environment as opposed to a conventional dedicated environment it shows how to make effective use of resources as they become available while ensuring the program tolerates resource retreat the solver performs well on test problems arising from real applications and is particularly useful for solving long running hard mixed integer programming problems

the nonlinear oblique derivative problem for quasilinear elliptic equations on considere des problemes aux valeurs limites pour une equation elliptique quasilineaire d ordre 2 qu 0 dans ou est un domaine borne de r n n 2 et q est donne sur c 2 par qu x a ij x u x du x d ij u x a x u x du x

local search with constraint propagation and conflict based heuristics search algorithms for solving csp constraint satisfaction problems usually fall into one of two main families local search algorithms and systematic algorithms both families have their advantages designing hybrid approaches seems promising since those advantages may be combined into a single approach in this paper we present a new hybrid technique it performs a local search over partial assignments instead of complete assignments and uses filtering techniques and conflict based techniques to efficiently guide the search this new technique benefits from both classical approaches a priori pruning of the search space from filtering based search and possible repair of early mistakes from local search we focus on a specific version of this technique tabu decision repair experiments done on open shop scheduling problems show that our approach competes well with the best highly specialized algorithms

the conormal derivative problem for elliptic equations of variational type on considere des solutions du probleme qu 0 dans nu 0 sur ou est un domaine borne dans r n et q et n sont definis par qu x div a x u x du x b x u x du x x nu x a x u x du x x x x

new convergent heuristics for 0 1 mixed integer programming abstract several hybrid methods have recently been proposed for solving 0 1 mixed integer programming problems some of these methods are based on the complete exploration of small neighborhoods in this paper we present several convergent algorithms that solve a series of small sub problems generated by exploiting information obtained from a series of relaxations these algorithms generate a sequence of upper bounds and a sequence of lower bounds around the optimal value first the principle of a linear programming based algorithm is summarized and several enhancements of this algorithm are presented next new hybrid heuristics that use linear programming and or mixed integer programming relaxations are proposed the mixed integer programming mip relaxation diversifies the search process and introduces new constraints in the problem this mip relaxation also helps to reduce the gap between the final upper bound and lower bound our algorithms improved 14 best known solutions from a set of 108 available and correlated instances of the 0 1 multidimensional knapsack problem other encouraging results obtained for 0 1 mip problems are also presented

floer theory for negative line bundles via gromov witten invariants abstract we prove that the gw theory of negative line bundles m tot l b determines the symplectic cohomology indeed s h m is the quotient of q h m by the kernel of a power of quantum cup product by c 1 l we prove this also for negative vector bundles and the top chern class we calculate s h and q h for o n c p m for example for o 1 m is the blow up of c m 1 at the origin and s h m has rank m we prove kodaira vanishing for very negative l s h 0 and serre vanishing if we twist a complex vector bundle by a large power of l s h 0 observe s h m 0 iff c 1 l is nilpotent in q h m this implies oancea s result b 2 b 0 s h m 0 we prove the weinstein conjecture for any contact hypersurface surrounding the zero section of a negative line bundle for symplectic manifolds x conical at infinity we build a homomorphism from 1 ham l x to invertibles in s h x this is similar to seidel s representation for closed x except now they are not invertibles in q h x

a branch and cut algorithm for the resolution of large scale symmetric traveling salesman problems an algorithm is described for solving large scale instances of the symmetric traveling salesman problem stsp to optimality the core of the algorithm is a polyhedral cutting plane procedure that exploits a subset of the system of linear inequalities defining the convex hull of the incidence vectors of the hamiltonian cycles of a complete graph the cuts are generated by several identification procedures that have been described in a companion paper whenever the cutting plane procedure does not terminate with an optimal solution the algorithm uses a tree search strategy that as opposed to branch and bound keeps on producing cuts after branching the algorithm has been implemented in fortran two different linear programming lp packages have been used as the lp solver the implementation of the algorithm and the interface with one of the lp solvers is described in sufficient detail to permit the replication of our experiments computational results are reported with up to 42 stsps with sizes rangin

a hybrid tabu search branch bound approach to solving the generalized assignment problem a new approach for solving the generalized assignment problem gap is proposed that combines the exact branch bound approach with the heuristic strategy of tabu search ts to produce a hybrid algorithm for solving gap the algorithm described uses commercial software to solve sub problems generated by the ts guiding strategy the ts approach makes use of the concept of referent domain optimisation and introduces novel add drop strategies in addition the linear programming relaxation of gap that forms part of the branch bound approach is itself helpful in suggesting which variables might take binary values computational results on benchmark test instances are presented and compared with results obtained by the standard branch bound approach and also several other heuristic approaches from the literature the results show the new algorithm performs competitively against the alternatives and is able to find some new best solutions for several benchmark instances

transversality in elliptic morse theory for the symplectic action our goal in this paper is to settle some transversality question for the perturbed nonlinear cauchy riemann equations on the cylinder these results play a central role in the denition of symplectic floer homology and hence in the proof of the arnold conjecture there is currently no other reference to these transversality results in the open literature our approach does not require aronszajn s theorem instead we derive the unique continuation theorem from a generalization of the carleman similarity principle

minimizing conflicts a heuristic repair method for constraint satisfaction and scheduling problems abstract the paper describes a simple heuristic approach to solving large scale constraint satisfaction and scheduling problems in this approach one starts with an inconsistent assignment for a set of variables and searches through the space of possible repairs the search can be guided by a value ordering heuristic the min conflicts heuristic that attempts to minimize the number of constraint violations after each step the heuristic can be used with a variety of different search strategies we demonstrate empirically that on the n queens problem a technique based on this approach performs orders of magnitude better than traditional backtracking techniques we also describe a scheduling application where the approach has been used successfully a theoretical analysis is presented both to explain why this method works well on certain types of problems and to predict when it is likely to be most effective

genetic algorithms for a supply management problem mip recombination vs greedy decoder two variants of genetic algorithm ga for solving the supply management problem with lower bounded demands smpld are proposed and experimentally tested the smpld problem consists in planning the shipments from a set of suppliers to a set of customers minimizing the total cost given lower and upper bounds on shipment sizes lower bounded consumption and linear costs for opened deliveries the first variant of ga uses the standard binary representation of solutions and a new recombination operator based on the mixed integer programming mip techniques the second ga is based on the permutation representation and a greedy decoder our experiments indicate that the ga with mip recombination compares favorably to the other ga and to the mip solver cplex 9 0 in terms of cost of obtained solutions the ga based on greedy decoder is shown to be the most robust in finding feasible solutions

on the complexity of selecting disjunctions in integer programming the imposition of general disjunctions of the form pi x leq pi 0 vee pi x geq pi 0 1 where pi pi 0 are integer valued is a fundamental operation in both the branch and bound and cutting plane algorithms for solving mixed integer linear programs such disjunctions can be used for branching at each iteration of the branch and bound algorithm or to generate split inequalities for the cutting plane algorithm we first consider the problem of selecting a general disjunction and show that the problem of selecting an optimal such disjunction according to specific criteria described herein is mathcal np hard we further show that the problem remains mathcal np hard even for binary programs or when considering certain restricted classes of disjunctions we observe that the problem of deciding whether a given inequality is a split inequality can be reduced to one of the above problems which leads to a proof that the problem is mathcal np complete

elliptic equations in divergence form with partially bmo coefficients the solvability in sobolev spaces is proved for divergence form second order elliptic equations in the whole space a half space and a bounded lipschitz domain for equations in the whole space or a half space the leading coefficients aij are assumed to be only measurable in one direction and have locally small bmo semi norms in the other directions for equations in a bounded domain additionally we assume that aij have small bmo semi norms in a neighborhood of the boundary of the domain we give a unified approach of both the dirichlet boundary problem and the conormal derivative problem we also investigate elliptic equations in sobolev spaces with mixed norms under the same assumptions on the coefficients

solvability of quasilinear elliptic equations with nonlinear boundary conditions ii abstract it is shown that solvability of the second order quasilinear elliptic equation qu 0 in with first order nonlinear boundary condition nu 0 on can be inferred from appropriate estimates on solutions of the problem qu in nu 0 on as varies over a suitable function class this result improves previous work of the author where estimates were required on solutions of qu in nu on as varies over some function space the value of this improvement is demonstrated by some examples

random dispersal versus fitness dependent dispersal abstract this work extends previous work cantrell et al 2008 9 on fitness dependent dispersal for a single species to a two species competition model both species have the same population dynamics but one species adopts a combination of random and fitness dependent dispersal and the other adopts random dispersal global existence of smooth solutions to the time dependent quasilinear parabolic system is studied when a single species has a strong tendency to move up its fitness gradient it results in a stable equilibrium that can approximate the spatial distribution predicted by the ideal free distribution cantrell et al 2008 9 for the two species competition model if one species has strong tendency to move up its fitness gradient such approximately ideal free dispersal is advantageous relative to random dispersal bifurcation analysis shows that two competing species can coexist when one species has only an intermediate tendency to move up its fitness gradient and the other species has a smaller random dispersal rate

computational study of a family of mixed integer quadratic programming problems we present computational experience with a branch and cut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables such problems arise in financial applications the algorithm solves the largest real life problems in a few minutes of run time

a heuristic for bilp problems the single source capacitated facility location problem abstract in the single source capacitated facility location problem sscflp each customer has to be assigned to one facility that supplies its whole demand the total demand of customers assigned to each facility cannot exceed its capacity an opening cost is associated with each facility and is paid if at least one customer is assigned to it the objective is to minimize the total cost of opening the facilities and supply all the customers in this paper we extend the kernel search heuristic framework to general binary integer linear programming bilp problems and apply it to the sscflp the heuristic is based on the solution to optimality of a sequence of subproblems where each subproblem is restricted to a subset of the decision variables the subsets of decision variables are constructed starting from the optimal values of the linear relaxation variants based on variable fixing are proposed to improve the efficiency of the kernel search framework the algorithms are tested on benchmark instances and new very large scale test problems computational results demonstrate the effectiveness of the approach the kernel search algorithm outperforms the best heuristics for the sscflp available in the literature it found the optimal solution for 165 out of the 170 instances with a proven optimum the error achieved in the remaining instances is negligible moreover it achieved on 100 new very large scale instances an average gap equal to 0 64 computed with respect to a lower bound or the optimum when available the variants based on variable fixing improved the efficiency of the algorithm with minor deteriorations of the solution quality

undercover a primal minlp heuristic exploring a largest sub mip we present undercover a primal heuristic for nonconvex mixed integer nonlinear programs minlps that explores a mixed integer linear subproblem sub mip of a given minlp we solve a vertex covering problem to identify a smallest set of variables to fix a so called cover such that each constraint is linearized subsequently these variables are fixed to values obtained from a reference point e g an optimal solution of a linear relaxation each feasible solution of the sub mip corresponds to a feasible solution of the original problem we apply domain propagation to try to avoid infeasibilities and conflict analysis to learn additional constraints from infeasibilities that are nonetheless encountered we present computational results on a test set of mixed integer quadratically constrained programs miqcps and minlps it turns out that the majority of these instances allows for small covers although general in nature we show that the heuristic is most successful on miqcps it nicely complements existing root node heuristics in different state of the art solvers and helps to significantly improve the overall performance of the minlp solver scip

exploring relaxation induced neighborhoods to improve mip solutions given a feasible solution to a mixed integer programming mip model a natural question is whether that solution can be improved using local search techniques local search has been applied very successfully in a variety of other combinatorial optimization domains unfortunately local search relies extensively on the notion of a solution neighborhood and this neighborhood is almost always tailored to the structure of the particular problem being solved a mip model typically conveys little information about the underlying problem structure this paper considers two new approaches to exploring interesting domain independent neighborhoods in mip the more effective of the two which we call relaxation induced neighborhood search rins constructs a promising neighborhood using information contained in the continuous relaxation of the mip model neighborhood exploration is then formulated as a mip model itself and solved recursively the second which we call guided dives is a simple modification of the mip tree traversal order loosely speaking it guides the search towards nodes that are close neighbors of the best known feasible solution extensive computational experiments on very difficult mip models show that both approaches outperform default cplex mip and a previously described approach for exploring mip neighborhoods local branching with respect to several different metrics the metrics we consider are quality of the best integer solution produced within a time limit ability to improve a given integer solution of both good and poor quality and time required to diversify the search in order to find a new solution

multiple positive solutions for a quasilinear elliptic equation with critical exponential nonlinearity abstract let be a bounded domain in r n n 2 with c 2 boundary in this work we study the existence of multiple positive solutions of the following problem p div u 2 n 2 1 u 2 n u u 2 n 2 1 u 2 n u u p e u n n 1 u 0 in u 2 n 2 1 u 2 n u u q on where 0 p 2 n 1 q 0 n 1 and is a non negative holder continuous function we show that there exists 0 such that p admits at least two solutions in w 1 n for 0 and no solution for

the feasibility pump in this paper we consider the np hard problem of finding a feasible solution if any exists for a generic mip problem of the form min ctx ax b xj integer j trivially a feasible solution can be defined as a point x p x ax b that is equal to its rounding where the rounded point is defined by x j if j and x j otherwise and represents scalar rounding to the nearest integer replacing equal with as close as possible relative to a suitable distance function x suggests the following feasibility pump fp heuristic for finding a feasible solution of a given mip we start from any x p and define its rounding at each fp iteration we look for a point x p that is as close as possible to the current by solving the problem min x x p assuming x is chosen appropriately this is an easily solvable lp problem if x 0 then x is a feasible mip solution and we are done otherwise we replace by the rounding of x and repeat we report computational results on a set of 83 difficult 0 1 mips using the commercial software ilog cplex 8 1 as a benchmark the outcome is that fp in spite of its simple foundation proves competitive with ilog cplex both in terms of speed and quality of the first solution delivered interestingly ilog cplex could not find any feasible solution at the root node for 19 problems in our test bed whereas fp was unsuccessful in just 3 cases

a heuristic approach for big bucket multi level production planning problems multi level production planning problems in which multiple items compete for the same resources frequently occur in practice yet remain daunting in their difficulty to solve in this paper we propose a heuristic framework that can generate high quality feasible solutions quickly for various kinds of lot sizing problems in addition unlike many other heuristics it generates high quality lower bounds using strong formulations and its simple scheme allows it to be easily implemented in the xpress mosel modeling language extensive computational results from widely used test sets that include a variety of problems demonstrate the efficiency of the heuristic particularly for challenging problems

a hierarchical method for discrete structural topology design problems with local stress and displacement constraints in this paper we present a hierarchical optimization method for finding feasible true 0 1 solutions to finite element based topology design problems the topology design problems are initially modelled as non convex mixed 0 1 programs the hierarchical optimization method is applied to the problem of minimizing the weight of a structure subject to displacement and local design dependent stress constraints the method iteratively treats a sequence of problems of increasing size of the same type as the original problem the problems are defined on a design mesh which is initially coarse and then successively refined as needed at each level of design mesh refinement a neighbourhood optimization method is used to treat the problem considered the non convex topology design problems are equivalently reformulated as convex all quadratic mixed 0 1 programs this reformulation enables the use of methods from global optimization which have only recently become available for solving the problems in the sequence numerical examples of topology design problems of continuum structures with local stress and displacement constraints are presented copyright 2006 john wiley sons ltd

mir closures of polyhedral sets we study the mixed integer rounding mir closures of polyhedral sets the mir closure of a polyhedral set is equal to its split closure and the associated separation problem is np hard we describe a mixed integer programming mip model with linear constraints and a non linear objective for separating an arbitrary point from the mir closure of a given mixed integer set we linearize the objective using additional variables to produce a linear mip model that solves the separation problem exactly using a subset of these additional variables yields an mip model which solves the separation problem approximately with an accuracy that depends on the number of additional variables used our analysis yields an alternative proof of the result of cook et al 1990 that the split closure of a polyhedral set is again a polyhedron we also discuss a heuristic to obtain mir cuts based on our approximate separation model and present some computational results

zero duality gap in surrogate constraint optimization a concise review of models abstract surrogate constraint relaxation was proposed in the 1960s as an alternative to the lagrangian relaxation for solving difficult optimization problems the duality gap in the surrogate relaxation is always as good as the duality gap in the lagrangian relaxation over the years researchers have proposed procedures to reduce the gap in the surrogate constraint our aim is to review models that close the surrogate duality gap five research streams that provide procedures with zero duality gap are identified and discussed in each research stream we will review major results discuss limitations and suggest possible future research opportunities in addition relationships between models if they exist are also discussed

gradient bounds for solutions of nonuniformly elliptic oblique derivative problems introduction in the theory of quasilinear elliptic equations there are three archetypical forms which seem to embody the various possible behaviors of solutions laplace s equation or more generally a uniformly elliptic equation the minimal surface equation and a sort of false minimal surface equation sii diudiu d u 0 for each of these equations the behavior of solutions to the dirichlet problem is wellunderstood see for example 3 5 10 11 additionally uniformly elliptic conormal problems were studied in 5 chapter lo and minimal surface type conormal problems xvere studied in l 13 61 the class of equations considered in 6 was much broader than those in l 131 but did not include the false minimal surface equation finally uniformly elliptic oblique derivative problems were studied in 7 91 while minimal surface type oblique derivative problems are the subject of 4 here we examine the oblique derivative problem on a smooth domain q c 2

an iterative variable based fixation heuristic for the 0 1 multidimensional knapsack problem an iterative scheme which is based on a dynamic fixation of the variables is developed to solve the 0 1 multidimensional knapsack problem such a scheme has the advantage of generating memory information which is used on the one hand to choose the variables to fix either permanently or temporarily and on the other hand to construct feasible solutions of the problem adaptations of this mechanism are proposed to explore different parts of the search space and to enhance the behaviour of the algorithm encouraging results are presented when tested on the correlated instances of the 0 1 multidimensional knapsack problem

the conormal derivative problem for equations of variational type in nonsmooth domains it is well known that elliptic boundary value problems in smooth domains have smooth solutions but if the domain is say c 1 the solutions need not be lipschitz recently korevaar has identified a class of lipschitz domains in which solutions of the capillary problem are lipschitz assuming the contact angle relates correctly to the geometry of the domain lipschitz bounds for more general boundary value problems in the same class of domains are proved applications to variational inequalities are also considered

parallel branch and bound algorithms for general mixed integer programming on the cm 5 this proof of concept paper describes parallel solution of general mixed integer programs by a branch and bound algorithm on the cm 5 multiprocessing system it goes beyond prior parallel branch and bound work by implementing a reasonably realistic general purpose mixed integer programming algorithm as opposed to a specialized method for a narrow class of problems it shows how to use the capabilities of the cm 5 to produce an efficient parallel implementation employing centrally controlled search achieving near linear speedups using 64 128 processors on a variety of difficult problems derived from real applications in concrete terms a problem requiring half an hour to solve on a sparc 2 workstation might be solved in 15 20 seconds and a problem originally taking a week might be reduced to about an hour central search control does have limitations and some final computational experiments begin to address the merits of more decentralized options

a new approach to the feasibility pump in mixed integer programming the feasibility pump is a recent highly successful heuristic for general mixed integer linear programming problems we show that the feasibility pump heuristic can be interpreted as a discrete ver

existence and optimal convergence rates of multi dimensional subsonic potential flows through an infinitely long nozzle with an obstacle inside in this paper the well posedness and optimal convergence rates of subsonic irrotational flows through a three dimensional infinitely long nozzle with a smooth obstacle inside are established more precisely the global existence and uniqueness of the uniformly subsonic flow are obtained via variational formulation as long as the incoming mass flux is less than a critical value furthermore with the aid of delicate choice of weight functions we prove the optimal convergence rates of the flow at far fields via weighted energy estimates and nash moser iteration

a trust branching path heuristic for zero one programming abstract for 0 1 problems we propose an exact branch and bound procedure where branching strategy is based on empirical distribution of each variable within three intervals 0 1 1 1 under the linear relaxation model we compare the strategy on multiknapsack and maximum clique problems with other heuristics