In this paper, we propose a multiobjective Genetic Algorithm (mo-GA) for solving a multiobjective reliability optimization problem. In order to obtain high efficiency of searching non-dominated solutions, we combine the Improved Saving Pareto solutions Strategy (ISPS) and the adoptive Local Search (LS) with the multiobjective Genetic Algorithm. Through some numerical experiments, we evaluate th...

In this paper we provide a duality theory for multiobjective optimization problems with convex objective functions and finitely many D.C. constraints. In order to do this, we study first the duality for a scalar convex optimization problem with inequality constraints defined by extended real-valued convex functions. For a family of multiobjective problems associated to the initial one we determ...

This chapter aims to review the state of the art in algorithms of multiobjective optimization with artificial immune systems (MOAIS). As it will be focused in the chapter, Artificial Immune Systems (AIS) have some intrinsic characteristics which make them well suited as multiobjective optimization algorithms. Following this basic idea, different implementations have been proposed in the literat...

A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational-like inequalities is established under some suitable conditions. Nonemptiness and compactness of the solutions set for the n...

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...

This chapter provides a description of multiobjective optimization software with a general overview of selected few available tools developed in the last decade. This chapter can be considered a revision of previous valid papers and chapters on nonlinear multiobjective optimization software such as the ones written by Weistroffer et al. (2005) and Miettinen (1999) that lists existing software p...

Financial portfolio optimization is a challenging problem. First, the problem is multiobjective (i.e.: minimize risk and maximize profit) and the objective functions are often multimodal and non smooth (e.g.: value at risk). Second, managers have often to face real-world constraints, which are typically non-linear. Hence, conventional optimization techniques, such as quadratic programming, cann...

Real world engineering design problems are usually characterized by the presence of many conflicting objectives. Therefore, it is natural to look at the engineering design problem as a multiobjective optimization problem. This report summarizes a survey of techniques to conduct multiobjective optimization in an engineering design context. The report starts with discussing some of the difficulti...

Many design problems in engineering are typically multiobjective, under complex nonlinear constraints. The algorithms needed to solve multiobjective problems can be significantly different from the methods for single objective optimization. Computing effort and the number of function evaluations may often increase significantly for multiobjective problems. Metaheuristic algorithms start to show...

Almost all approaches to multiobjective optimization are based on Genetic Algorithms, and implementations based on Evolution Strategies (ESs) are very rare. In this paper, a new approach to multiobjective optimization, based on ESs, is presented. The comparisons with other algorithms indicate a good performance of the Multiobjective Elitist