Network problems & algorythms

Special structure linear programming problems have received considerable attention during the last two decades and among them network problems are of particular importance and have found numerous applications in manage- ment science and technology. The mathematical models of the shortest route, maximal flow, and pure minimum cost flow problems are presented and various interrelationships among them are investigated. Finally three algorithms due to Dijkstra and Ford and Fulkerson which deal with the solution of the above three network problems are discussed

Some useful cost allocation strategies for the shortest route relaxation of the set covering problem

Shortest route relaxation (SRR) of the Set Covering Problem (S C P ) is away of relaxing the problem to nd quick lower boundson the value of the objective function. A number of useful cost allocation strategies for the SRR are introduced which are applied to a number of test problems and computational results are presented.Sociedad Argentina de Informática e Investigación Operativ

Some useful cost allocation strategies for the shortest route relaxation of the set covering problem

Shortest route relaxation (SRR) of the Set Covering Problem (S C P ) is away of relaxing the problem to nd quick lower boundson the value of the objective function. A number of useful cost allocation strategies for the SRR are introduced which are applied to a number of test problems and computational results are presented.Sociedad Argentina de Informática e Investigación Operativ

Improved binary artificial fish swarm algorithm for the 0–1 multidimensional knapsack problems

The 0–1 multidimensional knapsack problem (MKP) arises in many fields of optimization and is NP-hard. Several exact as well as heuristic methods exist. Recently, an artificial fish swarm algorithm has been developed in continuous global optimization. The algorithm uses a population of points in space to represent the position of fish in the school. In this paper, a binary version of the artificial fish swarm algorithm is proposed for solving the 0–1 MKP. In the proposed method, a point is represented by a binary string of 0/1 bits. Each bit of a trial point is generated by copying the corresponding bit from the current point or from some other specified point, with equal probability. Occasionally, some randomly chosen bits of a selected point are changed from 0 to 1, or 1 to 0, with an user defined probability. The infeasible solutions are made feasible by a decoding algorithm. A simple heuristic add_item is implemented to each feasible point aiming to improve the quality of that solution. A periodic reinitialization of the population greatly improves the quality of the solutions obtained by the algorithm. The proposed method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method gives a competitive performance when solving this kind of problems.Fundação para a Ciência e a Tecnologia (FCT

Solving large 0–1 multidimensional knapsack problems by a new simplified binary artificial fish swarm algorithm

The artificial fish swarm algorithm has recently been emerged in continuous global optimization. It uses points of a population in space to identify the position of fish in the school. Many real-world optimization problems are described by 0-1 multidimensional knapsack problems that are NP-hard. In the last decades several exact as well as heuristic methods have been proposed for solving these problems. In this paper, a new simpli ed binary version of the artificial fish swarm algorithm is presented, where a point/ fish is represented by a binary string of 0/1 bits. Trial points are created by using crossover and mutation in the different fi sh behavior that are randomly selected by using two user de ned probability values. In order to make the points feasible the presented algorithm uses a random heuristic drop item procedure followed by an add item procedure aiming to increase the profit throughout the adding of more items in the knapsack. A cyclic reinitialization of 50% of the population, and a simple local search that allows the progress of a small percentage of points towards optimality and after that refines the best point in the population greatly improve the quality of the solutions. The presented method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method can be an alternative method for solving these problems.The authors wish to thank three anonymous referees for their comments and valuable suggestions to improve the paper. The first author acknowledges Ciˆencia 2007 of FCT (Foundation for Science and Technology) Portugal for the fellowship grant C2007-UMINHO-ALGORITMI-04. Financial support from FEDER COMPETE (Operational Programme Thematic Factors of Competitiveness) and FCT under project FCOMP-01-0124-FEDER-022674 is also acknowledged

Some useful cost allocation strategies for the shortest route relaxation of the set covering problem

Shortest route relaxation (SRR) of the Set Covering Problem (S C P ) is away of relaxing the problem to nd quick lower boundson the value of the objective function. A number of useful cost allocation strategies for the SRR are introduced which are applied to a number of test problems and computational results are presented.Shortest route relaxation (SRR) of the Set Covering Problem (S C P ) is away of relaxing the problem to nd quick lower boundson the value of the objective function. A number of useful cost allocation strategies for the SRR are introduced which are applied to a number of test problems and computational results are presented

Memetic Algorithm for Solving the 0-1 Multidimensional Knapsack Problem

In this paper, we propose a memetic algorithm for the Multidimensional Knapsack Problem (MKP). First, we propose to combine a genetic algorithm with a stochastic local search (GA-SLS), then with a simulated annealing (GA-SA). The two proposed versions of our approach (GA-SLS and GA-SA) are implemented and evaluated on benchmarks to measure their performance. The experiments show that both GA-SLS and GA-SA are able to find competitive results compared to other well-known hybrid GA based approaches