this paper is to present an optimization algorithm, comprising a multiobjective evolutionary algorithm and a gradient--based local search. In the rest of the paper, this is referred to as memetic Pareto artificial neural network (MPANN) algorithm for training ANNs. The evolutionary approach is used to simultaneously train the network and optimize its architecture. The result is a set of networks, with each network in the set attempts to optimize both the training error and the architecture. We also present a self--adaptive version with lower computational cost. We show empirically that the proposed method is capable of reducing the training time compared to gradient--based techniques

Abstract: The success of the Particle Swarm Optimization (PSO) algorithm as a single-objective optimizer (mainly when dealing with continuous search spaces) has motivated researchers to extend the use of this bio-inspired technique to other areas. One of them is multi-objective optimization. Despite the fact that the first proposal of a Multi-Objective Particle Swarm Optimizer (MOPSO) is over six years old, a considerable number of other algorithms have been proposed since then. This paper presents a comprehensive review of the various MOPSOs reported in the specialized literature. As part of this review, we include a classification of the approaches, and we identify the main features of each proposal. In the last part of the paper, we list some of the topics within this field that we consider as promising areas of future research. I.

Abstract. This paper demonstrates that the self-adaptive technique of Differential Evolution (DE) can be simply used for solving a multiobjective optimization problem where parameters are interdependent. The real-coded crossover and mutation rates within the NSGA-II have been replaced with a simple Differential Evolution scheme, and results are reported on a rotated problem which has presented difficulties using existing Multi-objective Genetic Algorithms. The Differential Evolution variant of the NSGA-II has demonstrated rotational invariance and superior performance over the NSGA-II on this problem. 1

Abstract. Differential Evolution (DE) is a simple but powerful evolutionary optimization algorithm with many successful applications. In this paper we propose Differential Evolution for Multiobjective Optimization (DEMO) – a new approach to multiobjective optimization based on DE. DEMO combines the advantages of DE with the mechanisms of Paretobased ranking and crowding distance sorting, used by state-of-the-art evolutionary algorithms for multiobjective optimization. DEMO is implemented in three variants that achieve competitive results on five ZDT test problems. 1

Evolutionary Algorithms are a standard tool for multi-objective optimization that are able to approximate the Pareto front in a single optimization run. However, for some selection operators, the algorithm stagnates at a certain distance from the Pareto front without convergence for further iterations.

A parallel, multi--population Differential Evolution algorithm for multiobjective optimization is introduced. The algorithm is equipped with a domination selection operator to enhance its performance by favoring non--dominated individuals in the populations. Preliminary experimental results on widely used test problems are promising. Comparisons with the VEGA approach are provided and discussed.

A number of authors made the claim that a multiobjective approach preserves genetic diversity better than a single objective approach.

The field of Differential Evolution (DE) has demonstrated important advantages in single objective optimization. To date, no previous research has explored how the unique characteristics of DE can be applied to multi-objective optimization. This paper explains and demonstrates how DE can provide advantages in multi-objective optimization using directional information. We present three novel DE variants for multi-objective optimization, and a report of their performance on four multi-objective problems with different characteristics. The DE variants are compared with the NSGA-II (Non-dominated Sorting Genetic Algorithm). The results suggest that directional information yields improvements in convergence speed and spread of solutions.

Abstract. Several problems in the engineering domain are multi-objective in nature. The solution to multi-objective optimization is a set of solutions rather than a single point solution. Such a set of non-dominated solutions are called Pareto optimal solutions or non-inferior solutions. In this paper, a new algorithm, Elitist-Multi-objective Differential Evolution (E-MODE) is proposed. The proposed algorithm is applied successfully on several test functions, and the results are discussed extensively. Results obtained from the proposed algorithm are compared with those obtained using Multi-objective Differential Evolution (MODE) algorithm. E-MODE is found to give better solutions in terms of wide range of solutions, spread, and diversity of Pareto front than those obtained using MODE.

Abstract. The aim of this work is to analyze the ability of a multipopulation differential evolution to locate all optima of a multimodal function. The exploration is assured by a controlled initialization of the subpopulations while a particular differential evolution algorithm assures the exploitation. To avoid the necessity of specifying a niche radius a multi-resolution approach is proposed. All located optima are stored in an archive that plays also the role of a communication buffer between subpopulations.