In this paper, we review the development of studies on multiobjective noncooperative games, and particularly we focus on nondominated equilibrium solutions in multiobjective two-person nonzero-sum games in normal and extensive forms. After outlining studies related to multiobjective noncooperative games, we treat multiobjective two-person nonzero-sum games in normal form, and a mathematical pro...

The relationship between bilevel optimization and multiobjective optimization has been studied by several authors and there have been repeated attempts to establish a link between the two. We unify the results from the literature and generalize them for bilevel multiobjective optimization. We formulate sufficient conditions for an arbitrary binary relation to guarantee equality between the effi...

The Protein Structure Prediction problem, which involves correctly predicting the geometrical conformation of a fully folded protein, is extremely difficult to solve and there currently is no “best” method of generating solutions. This paper focuses on an energy minimization technique and the use of a multiobjective genetic algorithm, the multiobjective fast messy genetic algorithm (fmGA) to ob...

In the first part of this study we have introduced six different multiobjective dual problems to a general multiobjective optimization problem, for which we presented weak as well as strong duality assertions. Afterwards, we derived some inclusion results for the image sets of three of these problems. The aim of this second part is to complete our investigations by studying the relations betwee...

Very large-scale neighborhood search (VLSNS) is a technique intensively used in single-objective optimization. However, there is almost no study of VLSNS for multiobjective optimization. We show in this paper that this technique is very efficient for the resolution of multiobjective combinatorial optimization problems. Two problems are considered: the multiobjective multidimensional knapsack pr...

As multiobjective optimization problems have many solutions, evolutionary algorithms have been widely used for complex multiobjective problems instead of simulated annealing. However, simulated annealing also has favorable characteristics in the multimodal search. We developed several simulated annealing schemes for the multiobjective optimization based on this fact. Simulated annealing and evo...

In this paper, we present the first proposal to use a cultural algorithm to solve multiobjective optimization problems. Our proposal uses evolutionary programming, Pareto ranking and elitism (i.e., an external population). The approach proposed is validated using several examples taken from the specialized literature. Our results are compared with respect to the NSGA-II, which is an algorithm r...

This paper presents the methodology used for finding the optimal set of foot trajectories for a quadruped robot using manual tuning and multiobjective genetic algorithm optimization that provide energy efficient and fast locomotion. Manual trajectory tuning is used to obtain initial set of trajectories for the multiobjective GA optimization. The multiobjective optimization evaluates the energy ...

In the field of evolutionary multiobjective optimization, the hypervolume indicator is the only single set quality measure that is known to be strictly monotonic with regard to Pareto dominance. This property is of high interest and relevance for multiobjective search involving a large number of objective functions. However, the high computational effort required for calculating the indicator v...

This paper presents a new multiobjective evolutionary algorithm for Environmental/Economic power Dispatch (EED) problem. The EED problem is formulated as a nonlinear constrained multiobjective optimization problem. A new Strength Pareto Evolutionary Algorithm (SPEA) based approach is proposed to handle the problem as a true multiobjective problem with competing and non-commensurable objectives....