Abstract
We develop an evolutionary algorithm for multiobjective combinatorial optimization problems. The algorithm aims at converging the preferred solutions of a decision-maker. We test the performance of the algorithm on the multiobjective knapsack and multiobjective spanning tree problems. We generate the true nondominated solutions using an exact algorithm and compare the results with those of the evolutionary algorithm. We observe that the evolutionary algorithm works well in approximating the solutions in the preferred regions.
Highlights
Multiobjective combinatorial optimization (MOCO) problems have applications in a wide variety of areas such as investment and resource planning, logistics, facility location, scheduling, telecommunication and communications systems, and energy since they represent real-life situations in large organizations
In [5], Ehrgott and Gandibleux reviewed some classical metaheuristics for MOCO problems and focused on the hybrid metaheuristics that combine exact and heuristic approaches
We apply the evolutionary algorithm on the multidimensional multiobjective knapsack problem (MMOKP) and the Multiobjective spanning tree (MOST) problems with different lower or upper bound settings
Summary
Multiobjective combinatorial optimization (MOCO) problems have applications in a wide variety of areas such as investment and resource planning, logistics, facility location, scheduling, telecommunication and communications systems, and energy since they represent real-life situations in large organizations. The authors define a neighborhood relation by self-organizing maps and the evolutionary algorithm iteratively generates new points using two neighbors These approaches are designed to generate representative points, they do not incorporate the preferences of the DM into the solution process. The authors of [13] develop a genetic local search algorithm for MOCO problems and test the performance of the algorithm on MOKPs. The algorithm aims to generate a set of approximately efficient solutions from all regions of the efficient frontier in a reasonable time. The work in [14] develops a favorable weight-based evolutionary algorithm (FWEA) to obtain well-distributed solutions close to the nondominated frontier, while [15] adapts the FWEA to approximate the nondominated frontier of the multidimensional multiobjective knapsack problem (MMOKP).
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