Recently, a new metaheuristic called chemical reaction optimization was proposed. This search algorithm, inspired by chemical reactions launched during collisions, inherits several features from other metaheuristics such as simulated annealing and particle swarm optimization. This fact has made it, nowadays, one of the most powerful search algorithms in solving mono-objective optimization problems. In this paper, we propose a multiobjective variant of chemical reaction optimization, called nondominated sorting chemical reaction optimization, in an attempt to exploit chemical reaction optimization features in tackling problems involving multiple conflicting criteria. Since our approach is based on nondominated sorting, one of the main contributions of this paper is the proposal of a new quasi-linear average time complexity quick nondominated sorting algorithm; thereby making our multiobjective algorithm efficient from a computational cost viewpoint. The experimental comparisons against several other multiobjective algorithms on a variety of benchmark problems involving various difficulties show the effectiveness and the efficiency of this multiobjective version in providing a well-converged and well-diversified approximation of the Pareto front.

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In this paper, we propose an Indicator-based Chemical Reaction Optimization (ICRO) algorithm for multiobjective optimization. There are two main motivations behind this work. On the one hand, CRO is a new recently proposed metaheuristic which demonstrated very good performance in solving several mono-objective problems. On the other hand, the idea of performing selection in Multi-Objective Evolutionary Algorithms (MOEAs) based on the optimization of a quality metric has shown a big promise in tackling Multi-Objective Problems (MOPs). The statistical analysis of the obtained results shows that ICRO provides competitive and better results than several other MOEAs.

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Several real world problems have two levels of optimization instead of a single one. These problems are said to be bilevel and are so computationally expensive to solve since the evaluation of each upper level solution requires finding an optimal solution at the lower level. Most existing works in this direction have focused on continuous problems. Motivated by this observation, we propose in this paper an improved version of our recently proposed algorithm CODBA (CO-evolutionary Decomposition-Based Algorithm), called CODBA-II, to tackle bi-level combinatorial problems. Differently to CODBA, CODBA-II incorporates decomposition, parallelism, and co-evolution within both levels: (1) the upper level and (2) the lower one, with the aim to further cope with the high computational cost of the overall bi-level search process. The performance of CODBA-II is assessed on a set of instances of the MDVRP (Multi-Depot Vehicle Routing Problem) and is compared against three recently proposed bi-level algorithms. The statistical analysis of the obtained results shows the merits of CODBA-II from effectiveness viewpoint.