Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. However...
详细信息
Connectedness of efficient solutions is a powerful property in multiple objective combinatorial optimization since it allows the construction of the complete efficient set using neighborhood search techniques. However, we show that many classical multiple objective combinatorial optimization problems do not possess the connectedness property in general, including, among others, knapsack problems (and even several special cases) and linear assignment problems. We also extend known non-connectedness results for several optimization problems on graphs like shortest path, spanning tree and minimum cost flow problems. Different concepts of connectedness are discussed in a formal setting, and numerical tests are performed for two variants of the knapsack problem to analyze the likelihood with which non-connected adjacency graphs occur in randomly generated instances.
Solving the Tchebycheff program means optimizing a particular scalarizing function. When dealing with combinatorial problems, however, it is due to computational intractability often necessary to apply heuristics and ...
详细信息
Solving the Tchebycheff program means optimizing a particular scalarizing function. When dealing with combinatorial problems, however, it is due to computational intractability often necessary to apply heuristics and settle for approximations to the optimal solution. The experiments in this paper suggest that for the multiobjective traveling salesman problem (moTSP) instances considered, heuristic optimization of the Tchebycheff program gives better results when using a substitute scalarizing function instead of the Tchebycheff based one to guide the local search path. Two families of substitute scalarizing functions are considered.
This paper focuses on branching strategies that are involved in branch and bound algorithms when solving multi-objectiveoptimization problems. The choice of the branching variable at each node of the search tree cons...
详细信息
This paper focuses on branching strategies that are involved in branch and bound algorithms when solving multi-objectiveoptimization problems. The choice of the branching variable at each node of the search tree constitutes indeed an important component of these algorithms. In this work we focus on multi-objective knapsack problems. In the literature, branching heuristics used for these problems are static, i.e., the order on the variables is determined prior to the execution. This study investigates the benefit of defining more sophisticated branching strategies. We first analyze and compare a representative set of classic branching heuristics and conclude that none can be identified as the best overall heuristic. Using an oracle, we highlight that combining branching heuristics within the same branch and bound algorithm leads to considerably reduced search trees but induces high computational costs. Based on learning adaptive techniques, we propose then dynamic adaptive branching strategies that are able to select the suitable heuristic to apply at each node of the search tree. Experiments are conducted on the bi-objective 0/1 unidimensional knapsack problem.
An approach to solve the multipleobjectives problem for optimal choice of circuit elements parameters among a set of possible alternatives is proposed in this paper. The presented approach is based on the PROMETHEE I...
详细信息
ISBN:
(纸本)9783319086729;9783319086712
An approach to solve the multipleobjectives problem for optimal choice of circuit elements parameters among a set of possible alternatives is proposed in this paper. The presented approach is based on the PROMETHEE I method. The considered combinatorial problem is decomposed in sub-problems to reduce considerably the number of investigated alternatives. The approach is illustrated on two voltage regulator circuits. The results obtained are encouraging and the efficiency of the approach increases when the number of circuit elements and the alternatives set cardinality is larger.
暂无评论