local search for the probabilistic traveling salesman problem correction to the 2 p opt and 1 shift algorithms abstract the probabilistic traveling salesman problem concerns the best way to visit a set of customers located in some metric space where each customer requires a visit only with some known probability a solution to this problem is an a priori tour which visits all customers and the objective is to minimize the expected length of the a priori tour over all customer subsets assuming that customers in any given subset must be visited in the same order as they appear in the a priori tour this problem belongs to the class of stochastic vehicle routing problems a class which has received increasing attention in recent years and which is of major importance in real world applications several heuristics have been proposed and tested for the probabilistic traveling salesman problem many of which are a straightforward adaptation of heuristics for the classical traveling salesman problem in particular two local search algorithms 2 p opt and 1 shift were introduced by bertsimas in a previous report we have shown that the expressions for the cost evaluation of 2 p opt and 1 shift moves as proposed by bertsimas are not correct in this paper we derive the correct versions of these expressions and we show that the local search algorithms based on these expressions perform significantly better than those exploiting the incorrect expressions

a heuristic algorithm for the traveling salesman location problem on networks in this paper we present a heuristic for the traveling salesman location problem on a network each day the salesman e g a repair vehicle must visit all the calls that are registered in a service list each call is generated with a given probability and the service list contains at most n calls the heuristic requires on3 time to find the location that minimizes the expected distance traveled a worst case analysis of the heuristic indicates that it will produce a solution which is at most 50 worse than the optimal solution the paper also contains several asymptotic results for the problem in the plane

dynamic journeying under uncertainty abstract we introduce a journey planning problem in multi modal transportation networks under uncertainty the goal is to find a journey possibly involving transfers between different transport services from a given origin to a given destination within a specified time horizon due to uncertainty in travel times the arrival times of transport services at public transport stops are modeled as random variables if a transfer between two services is rendered unsuccessful the commuter has to reconsider the remaining path to the destination the problem is modeled as a markov decision process in which states are defined as paths in the transport network the main contribution is a backward induction method that generates an optimal policy for traversing the public transport network in terms of maximizing the probability of reaching the destination in time by assuming history independence and independence of successful transfers between services we obtain approximate methods for the same problem analysis and numerical experiments suggest that while solving the path dependent model requires the enumeration of all paths from the origin to the destination the proposed approximations may be useful for practical purposes due to their computational simplicity in addition to on time arrival probability we show how travel and overdue costs can be taken into account making the model applicable to freight transportation problems

an emg driven musculoskeletal model to estimate muscle forces and knee joint moments in vivo this paper examined if an electromyography emg driven musculoskeletal model of the human knee could be used to predict knee moments calculated using inverse dynamics across a varied range of dynamic contractile conditions muscle tendon lengths and moment arms of 13 muscles crossing the knee joint were determined from joint kinematics using a three dimensional anatomical model of the lower limb muscle activation was determined using a second order discrete non linear model using rectified and lowpass filtered emg as input a modified hill type muscle model was used to calculate individual muscle forces using activation and muscle tendon lengths as inputs the model was calibrated to six individuals by altering a set of physiologically based parameters using mathematical optimisation to match the net flexion extension fe muscle moment with those measured by inverse dynamics the model was calibrated for each subject using 5 different tasks including passive and active fe in an isokinetic dynamometer running and cutting manoeuvres recorded using three dimensional motion analysis once calibrated the model was used to predict the fe moments estimated via inverse dynamics from over 200 isokinetic dynamometer running and sidestepping tasks the inverse dynamics joint moments were predicted with an average r 2 of 0 91 and mean residual error of b12 nm a re calibration of only the emg to activation parameters revealed fe moments prediction across weeks of similar accuracy changing the muscle model to one that is more physiologically correct produced better predictions the modelling method presented represents a good way to estimate in vivo muscle forces during movement tasks r 2003 elsevier science ltd all rights reserved

on the one commodity pickup and delivery traveling salesman problem with stochastic demands this paper studies how to set the vehicle capacity for traveling salesman problems where some of the customer demands are stochastic the analyses are done for the one commodity pickup and delivery tsp as this problem also includes the setting of the initial load the paper first considers feasibility issues this includes finding the smallest vehicle capacity and some initial load such that a given tour is feasible for all scenarios different variants are considered as a function of the time when information becomes available the paper then analyzes the case where some penalties are paid for routing a tour unable to handle customer demands various types of penalties are considered the paper studies properties of the minimal expected penalty of a given tour which are then used to provide approaches to find near optimal tours computational results are presented

functional muscle synergies constrain force production during postural tasks abstract we recently demonstrated that a set of five functional muscle synergies were sufficient to characterize both hindlimb muscle activity and active forces during automatic postural responses in cats standing at multiple postural configurations this characterization depended critically upon the assumption that the endpoint force vector synergy force vector produced by the activation of each muscle synergy rotated with the limb axis as the hindlimb posture varied in the sagittal plane here we used a detailed 3d static model of the hindlimb to confirm that this assumption is biomechanically plausible as we varied the model posture simulated synergy force vectors rotated monotonically with the limb axis in the parasagittal plane r 2 0 94 0 08 we then tested whether a neural strategy of using these five functional muscle synergies provides the same force generating capability as controlling each of the 31 muscles individually we compared feasible force sets ffss from the model with and without a muscle synergy organization ffs volumes were significantly reduced with the muscle synergy organization f 1556 01 p 0 01 and as posture varied the synergy limited ffss changed in shape consistent with changes in experimentally measured active forces in contrast nominal ffs shapes were invariant with posture reinforcing prior findings that postural forces cannot be predicted by hindlimb biomechanics alone we propose that an internal model for postural force generation may coordinate functional muscle synergies that are invariant in intrinsic limb coordinates and this reduced dimension control scheme reduces the set of forces available for postural control

a priori optimization consider a complete graph g v e in which each node is present with probability p we are interested in solving combinatorial optimization problems on subsets of nodes which are present with a certain probability we introduce the idea of a priori optimization as a strategy competitive to the strategy of reoptimization under which the combinatorial optimization problem is solved optimally for every instance we consider four problems the traveling salesman problem tsp the minimum spanning tree vehicle routing and traveling salesman facility location we discuss the applicability of a priori optimization strategies in several areas and show that if the nodes are randomly distributed in the plane the a priori and reoptimization strategies are very close in terms of performance we characterize the complexity of a priori optimization and address the question of approximating the optimal a priori solutions with polynomial time heuristics with provable worst case guarantees finally we use the tsp as an example to find practical solutions based on ideas of local optimality

adaptive sample size and importance sampling in estimation based local search for the probabilistic traveling salesman problem the probabilistic traveling salesman problem is a paradigmatic example of a stochastic combinatorial optimization problem for this problem recently an estimation based local search algorithm using delta evaluation has been proposed in this paper we adopt two well known variance reduction procedures in the estimation based local search algorithm the first is an adaptive sampling procedure that selects the appropriate size of the sample to be used in monte carlo evaluation the second is a procedure that adopts importance sampling to reduce the variance involved in the cost estimation we investigate several possible strategies for applying these procedures to the given problem and we identify the most effective one experimental results show that a particular heuristic customization of the two procedures increases significantly the effectiveness of the estimation based local search

different initial solution generators in genetic algorithms for solving the probabilistic traveling salesman problem the probabilistic traveling salesman problem ptsp is a topic of theoretical and practical importance in the study of stochastic network problems it provides researchers with a modeling framework for exploring the stochastic effects in routing problems this paper proposed three initial solution generators nn1 nn2 ran under a genetic algorithm ga framework for solving the ptsp a set of numerical experiments based on heterogeneous and homogeneous ptsp instances were conducted to test the effectiveness and efficiency of the proposed algorithms the results from the heterogeneous ptsp show that the average e t values obtained by the three generators under a ga framework are similar to those obtained by the previous best but with an average computation time saving of 50 2 as for the homogeneous ptsp instances nn1 is a relatively better generator among the three examined while ran consistently performs worse than the other two generators in terms of average e t values additionally as compared to previously reported studies no one single algorithm consistently outperformed the others across all homogeneous ptsp instances in terms of the best e t values the fact that no one initial solution generator consistently performs best in terms of the e t value obtained across all instances in heterogeneous cases and that the performance of each examined algorithm is dependent on the number of nodes n and probability p for homogeneous cases suggest the possibility of context dependent phenomenon finally to obtain valid results researchers are advised to include at least a certain amount of test instances with the same combination of n and p when conducting ptsp experiments

probabilistic combinatorial optimization problems on graphs a new domain in operational research abstract we present a new research domain in operational research probabilistic combinatorial optimization problems we survey and comment a number of results and we discuss several problems dealing with this domain as well as future research issues

a physiologically based criterion of muscle force prediction in locomotion abstract the inversely nonlinear relationship of muscle contraction force and the possible contraction duration i e endurance is utilized in a method to mathematically predict individual muscle forces the method uses a nonlinear optimization scheme to solve the redundant distribution problem at the joints of interest the method is demonstrated at the elbow during isometric contraction and in the lower extremity during locomotion during gait the observed muscle activity pattern in the lower extremity as determined by emg shows substantial agreement with that activity pattern predicted when endurance is used as the optimization criterion the importance of selecting muscle prediction criteria based on sound physiological bases rather than on an arbitrary or mathematically convenient basis is emphasized

existence of periodic solutions for first order evolution equations without coercivity abstract in this paper we study the existence problem of periodic solutions for the following first order nonlinear evolution equation u t a t u t f t u t 0 t r u t t u t t r in a hilbert space h where a is a monotone type operator and f is a nonlinear operator existence results are obtained without assuming the coercivity condition

a priori solution of a travelling salesman problem in which a random subset of the customers are visited consider a problem of routing through a set of n points on any given instance of the problem only a subset consisting of k out of n points 0 k n has to be visited with the number k random with known probability distribution we wish to find a priori a tour through all n points on any given instance the k points present will then be visited in the same order as they appear in the a priori tour the problem of finding such a tour of minimum length in the expected value sense is defined as a probabilistic traveling salesman problem ptsp what distinguishes one ptsp from another is the probability distribution or more generally the probability law that specifies the number k and the identity of the points that need to be visited on any given instance of the problem after motivating the problem by applications we first derive closed form expressions for computing efficiently the expected length of any given tour under very general probabilistic assumptions we then provide in a unified way

diversified local search strategy under scatter search framework for the probabilistic traveling salesman problem this paper focuses on introducing a concept of diversified local search strategy under the scatter search framework for the probabilistic traveling salesman problem ptsp different combinations of three commonly used local search methods in the ptsp i e 1 shift 2 opt and 3 opt were used to investigate its effects a set of numerical experiments were conducted to test the validity of the proposed strategy based on randomly generated test instances the numerical results and the permutation test showed that the diversified local search strategy especially by combining 1 shift and 2 opt algorithms can most effectively solve the homogeneous and heterogeneous ptsp in most of the tested instances in comparison with the single local search strategy under scatter search framework

solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation abstract this paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer the solution to this vehicle routing problem with stochastic demand vrpsd involves the optimization of complete routing schedules with minimum travel distance driver remuneration and number of vehicles subject to a number of constraints such as time windows and vehicle capacity to solve such a multiobjective and multi modal combinatorial optimization problem this paper presents a multiobjective evolutionary algorithm that incorporates two vrpsd specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions a new way of assessing the quality of solutions to the vrpsd on top of comparing their expected costs is also proposed it is shown that the algorithm is capable of finding useful tradeoff solutions for the vrpsd and the solutions are robust to the stochastic nature of the problem the developed algorithm is further validated on a few vrpsd instances adapted from solomon s vehicle routing problem with time windows vrptw benchmark problems

a priori optimization of the probabilistic traveling salesman problem the probabilistic traveling salesman problem ptsp is defined on a graph g v e where v is the vertex set and e is the edge set each vertex vi has a probability pi of being present with each edge vi vj is associated a distance or cost cij in a first stage an a priori hamiltonian tour on g is designed the list of present vertices is then revealed in a second stage the a priori tour is followed by skipping the absent vertices the ptsp consists of determining a first stage solution that minimizes the expected cost of the second stage tour the problem is formulated as an integer linear stochastic program and solved by means of a branch and cut approach which relaxes some of the constraints and uses lower bounding functionals on the objective function problems involving up to 50 vertices are solved to optimality

bounds and heuristics for capacitated routing problems in a capacitated routing problem the objective is to minimize the total distance travelled by vehicles of limited capacity to serve a set of customers that are located in the euclidean plane we develop asymptotically optimal bounds and heuristics for this problem under the assumption that the capacity of a vehicle is expressed in terms of an upper bound on the number of customers that it can serve the analysis culminates in an algorithm that for a given capacity and given will find a solution with relative error at most in time polynomial in the number of customers

a biomechanical analysis of muscle strength as a limiting factor in standing posture we developed a method for studying muscular coordination and strength in multijoint movements and have applied it to standing posture the method is based on a musculoskeletal model of the human lower extremity in the sagittal plane and a technique to visualize geometrically how constraints internal and external to the body affect movement we developed an algorithm to calculate the set of all feasible accelerations i e the feasible acceleration set or fas that muscles can induce for the ankle knee and hip joints in the sagittal plane this set is a polyhedron in three dimensions using the volume of the fas as an indicator of overall mobility we found that strengthening muscles on the posterior side as opposed to the anterior of the body would cause greater increases in mobility employing the experimental observations of others we also found that acceleration constraints greatly reduce the range of feasible accelerations we then defined a set of four basic acceleration vectors which when used in various combinations can produce the repertoire of postural movements we used linear programming to find the maximum magnitudes of these vectors and the sensitivity of these magnitudes to muscle strength thereby delineating those muscles which if strengthened would cause the greatest increase in the body s ability to generate the basic acceleration vectors for our particular model those muscle groups were found to be hamstrings tibialis anterior rectus femoris and gastrocnemius these muscle groups would be of great importance in cases involving severely reduced muscle strength this methodology may therefore be useful for purposes such as design of functional electrical stimulation controllers or exercises for persons at risk for falling

characterization of the probabilistic traveling salesman problem we show that stochastic annealing can be successfully applied to gain new results on the probabilistic traveling salesman problem the probabilistic traveling salesman must decide on an a priori order in which to visit n cities randomly distributed over a unit square before learning that some cities can be omitted we find the optimized average length of the pruned tour follows e l over bar pruned rootnp 0 872 0 105p f np where p is the probability of a city needing to be visited and f np 1 as np infinity the average length of the a priori tour before omitting any cities is found to follow e l a priori rootn pbeta p where beta p 1 1 25 0 82 ln p is measured for 0 05less than or equal topless than or equal to0 6 scaling arguments and indirect measurements suggest that beta p tends towards a constant for p 0 03 our stochastic annealing algorithm is based on limited sampling of the pruned tour lengths exploiting the sampling error to provide the analog of thermal fluctuations in simulated thermal annealing the method has general application to the optimization of functions whose cost to evaluate rises with the precision required