Abstract
In this paper we propose a new metaheuristic algorithm for solving stochastic multiobjective combinatorial optimization(SMOCO) problems. Indeed, we find that the various initiatives that have been launched recently on this subject, they propose the classical metaheuristics to solve a stochastic multi-objective problems,but when the stochasticity effects is not taken into account, the choice of an arbitrary value leading to a particular configuration and a high loss of information. To conserve the stochastic nature of SMOCO problems,the pareto ranking should be defined on the random objectives functions directly rather than converted deterministic objectives. From these considerations, the scope of this research should consist of: (i)Proposed novel methodology of stochastic optimality for ranking objective functions characterized by non-continuous and no closed form expression. This novel approach is based on combinatorial probability and can be incorporated in a multiobjective evolutionary algorithm. (ii)Provide probabilistic approaches to elitism and diversification in multiobjective evolutionary algorithms. Finally, The behavior of the resulting Probabilistic Multi-objective Evolutionary Algorithms (PrMOEAs) is empirically investigated on the multi-objective stochastic VRP problem.
Highlights
Many real-life optimization problems encountered in logistics, transportation, and Markets finance have several conflicts objectives under aleatory uncertainty to be satisfied, traditionally such problems were handled by converting the stochastic multiple objectives to deterministic multiple objectives using statistical aggregation: mean value, extreme value, variance..., applying the classical metaheuristics [1], such as pareto evolutionary algorithms for generate a set of well-distributed pareto-optimal solutions [13]
The remainder of this paper is organized as follows: In section 2, we investigate the formula of stochastic multiobjective optimization problems and we discusse the main concepts in multiobjective evolutionary algorithms that can be extended in stochastic context
From this formulation of SMOCO problems, each objective function can yield different values for the same individual from time to time (Figure.1), concerning the multiobjective part, we focus on the solution concept of determining pareto-optimal solutions, under this approach there are three possible relationships between the exact solutions: Definition.1 (Weak Dominance) x weakly dominates x
Summary
Many real-life optimization problems encountered in logistics, transportation, and Markets finance have several conflicts objectives under aleatory uncertainty to be satisfied, traditionally such problems were handled by converting the stochastic multiple objectives to deterministic multiple objectives using statistical aggregation: mean value, extreme value, variance..., applying the classical metaheuristics [1], such as pareto evolutionary algorithms for generate a set of well-distributed pareto-optimal solutions [13]. Such an approach has many problems, the including the loss of significant trade-off information and the inability to search the true objective space because it is incapable to describe the relationship among stochastic(random) objectives.
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