This paper studies a novel approach to analysis of switched dynamical systems in perspective of bifurcation and multiobjective optimization. As a first step, we analyze a simple switched dynamical system based on a boost converter with photovoltaic input. First, in a bifurcation phenomenon perspective, we consider period doubling bifurcation sets in the parameter space. Second, in a multiobjective optimization perspective, we consider a trade-off between maximum input power and stability. The trade-off is represented by a Pareto front in the objective space. Performing numerical experiments, relationship between the bifurcation sets and the Pareto front is investigated.

This paper presents an approach for improving proximity and diversity in multiobjective evolutionary algorithms (MOEAs). The idea is to discover new nondominated solutions in the promising area of search space. It can be achieved by applying mutation only to the most converged and the least crowded individuals. In other words, the proximity and diversity can be improved because new nondominated solutions are found in the vicinity of the individuals highly converged and less crowded. Empirical results on multiobjective knapsack problems (MKPs) demonstrate that the proposed approach discovers a set of nondominated solutions much closer to the global Pareto front while maintaining a better distribution of the solutions.

When we try to solve Multiobjective Optimization Problems (MOPs) using an evolutionary algorithm, the Pareto Genetic Algorithm (Pareto GA) introduced by Goldberg in 1989 has now become a sort of standard. After the first introduction, this approach was further developed and lead to many applications. All of these approaches are based on Pareto ranking and use the fitness sharing function to maintain diversity. On the other hand in the early 50's another scheme was presented by Nash. This approach introduced the notion of Nash Equilibrium and aimed at solving optimization problems having multiobjective functions that are originated from Game Theory and Economics. Since the concept of Nash Equilibrium as a solution of these problems was introduced, game theorists have attempted to formalize aspects of the equilibrium solution. The Nash Genetic Algorithm (Nash GA), which is introduced by Sefrioui, is the idea to bring together genetic algorithms and Nash strategy. The aim of this algorithm is to find the Nash Equilibrium of MOPs through the genetic process. Another central achievement of evolutionary game theory is the introduction of a method by which agents can play optimal strategies in the absence of rationality. Not the rationality but through the process of Darwinian selection, a population of agents can evolve to an Evolutionary Stable Strategy (ESS) introduced by Maynard Smith in 1982. In this paper, we propose Game theory based Co-Evolutionary Algorithm (GCEA) and try to find the ESS as a solution of MOPs. By applying newly designed co-evolutionary algorithm to several MOPs, the first we will confirm that evolutionary game can be embodied by co-evolutionary algorithm and this co-evolutionary algorithm can find ESSs as a solutions of MOPs. The second, we show optimization performance of GCEA by applying this model to several test MOPs and comparing with the solutions of previously introduced evolutionary optimization algorithms.

A halftoning technique that uses a simple GA has proven to be very effective to generate high quality halftone images. Recently, the two major drawbacks of this conventional halftoning technique with GAs, i.e. it uses a substantial amount of computer memory and processing time, have been overcome by using an improved GA (GA-SRM) that applies genetic operators in parallel putting them in a cooperative-competitive stand with each other. The halftoning problem is a true multiobjective optimization problem. However, so far, the GA based halftoning techniques have treated the problem as a single objective optimization problem. In this work, the improved GA-SRM is extended to a multiobjective optimization GA to simultaneously generate halftone images with various combinations of gray level precision and spatial resolution. Simulation results verify that the proposed scheme can effectively generate several high quality images simultaneously in a single run reducing even further the overall processing time.