This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a ...

Multi-objective optimization using an evolutionary computation technique is used extensively for solving conflicting multi-objective optimization problems. In this work, an improved strategy of multi-objective differential evolution (MODE) where the mutation strategy is changed to a trigonometric mutation approach is proposed. The proposed strategy along with other well known strategies of MODE...

This article describes a set function that maps a set of Pareto optimal points to a scalar. A proof is presented that shows that the maximization of this scalar value constitutes the necessary and sufficient condition for the function’s arguments to be maximally diverse Pareto optimal solutions of a discrete, multi-objective, optimization problem. This scalar quantity, a hypervolume based on a ...

In this paper we argue that biological fitness is a multi-objective concept hence the statement "fittest" is inappropriate. The following statement is proposed "Survival is mostly for those with non-dominated fitness". Also we use some TV games to show that under the following conditions: i) There are no dominant players. ii) At each time step successful players may eliminate some of their less...

Original scientific paper Community detection in complex networks is often regarded as the problem of single-objective optimization and it is hard for single-objective optimization to identify potential community structure of meaningfulness. Thus, algorithm of multi-objective optimization is applied to the field of community detection. However, multi-objective community detection algorithm is p...

A multi-objective particle swarm optimization (MOPSO) approach is presented for generating Pareto-optimal solutions for reservoir operation problems. This method is developed by integrating Pareto dominance principles into particle swarm optimization (PSO) algorithm. In addition, a variable size external repository and an efficient elitist-mutation (EM) operator are introduced. The proposed EM-...

This paper presents a multi-objective optimal power flow technique using particle swarm optimization. Two conflicting objectives, generation cost, and environmental pollution are minimized simultaneously. A multiobjective particle swarm optimization method is used to solve this highly nonlinear and non-convex optimization problem. A diversity preserving technique is incorporated to generate eve...

Many real-world optimization problems involve several conflicting objectives that must be optimized simultaneously. Furthermore, most optimization problems have a dynamic structure and change over time. In addition to trying to establish trade-offs among conflicting objectives and explore a diverse set of solutions on a Pareto-optimal front, a dynamic multi-objective optimization (DMOO) algorit...

The optimization of multiple conflictive objectives at the same time is a hard problem. In most cases, a uniform distribution of solutions on the Pareto front is the main objective. We propose a novel evolutionary multi-objective algorithm that is based on the selection with regard to equidistant lines in the objective space. The so-called rakes can be computed efficiently in high dimensional o...