The success of the Particle Swarm Optimiza- tion (PSO) algorithm as a single-objective optimizer (mainly when dealing with continuous search spaces) has motivated re- searchers to extend the use of this bio-inspired technique to other areas. One of them is multi-objective optimization. De- spite the fact that the first proposal of a Multi-Objective Par- ticle Swarm Optimizer (MOPSO) is over six years old, a con- siderable number of other algorithms have been proposed since then. This paper presents a comprehensive review of the vari- ous 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.

/pdf/multi-objective-particle-swarm-optimizers-a-survey-of-the-2siwlm7s84.pdf

Multi-Objective Particle Swarm Optimizers: A Survey of the State-of-the-Art

Surrogate-assisted, or meta-model based evolutionary computation uses efficient computational models, often known as surrogates or meta-models, for approximating the fitness function in evolutionary algorithms. Research on surrogate-assisted evolutionary computation began over a decade ago and has received considerably increasing interest in recent years. Very interestingly, surrogate-assisted evolutionary computation has found successful applications not only in solving computationally expensive single- or multi-objective optimization problems, but also in addressing dynamic optimization problems, constrained optimization problems and multi-modal optimization problems. This paper provides a concise overview of the history and recent developments in surrogate-assisted evolutionary computation and suggests a few future trends in this research area.

http://www.soft-computing.de/SECPublished.pdf

Surrogate-assisted evolutionary computation: Recent advances and future challenges

This article provides a general overview of the field now known as "evolutionary multi-objective optimization," which refers to the use of evolutionary algorithms to solve problems with two or more (often conflicting) objective functions. Using as a framework the history of this discipline, we discuss some of the most representative algorithms that have been developed so far, as well as some of their applications. Also, we discuss some of the methodological issues related to the use of multi-objective evolutionary algorithms, as well as some of the current and future research trends in the area.

Evolutionary multi-objective optimization: a historical view of the field

This paper concerns multiobjective optimization in scenarios where each solution evaluation is financially and/or temporally expensive. We make use of nine relatively low-dimensional, nonpathological, real-valued functions, such as arise in many applications, and assess the performance of two algorithms after just 100 and 250 (or 260) function evaluations. The results show that NSGA-II, a popular multiobjective evolutionary algorithm, performs well compared with random search, even within the restricted number of evaluations used. A significantly better performance (particularly, in the worst case) is, however, achieved on our test set by an algorithm proposed herein-ParEGO-which is an extension of the single-objective efficient global optimization (EGO) algorithm of Jones et al. ParEGO uses a design-of-experiments inspired initialization procedure and learns a Gaussian processes model of the search landscape, which is updated after every function evaluation. Overall, ParEGO exhibits a promising performance for multiobjective optimization problems where evaluations are expensive or otherwise restricted in number.

ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems

The covariancematrix adaptation evolution strategy (CMA-ES) is one of themost powerful evolutionary algorithms for real-valued single-objective optimization. In this paper, we develop a variant of the CMA-ES for multi-objective optimization (MOO). We first introduce a single-objective, elitist CMA-ES using plus-selection and step size control based on a success rule. This algorithm is compared to the standard CMA-ES. The elitist CMA-ES turns out to be slightly faster on unimodal functions, but is more prone to getting stuck in sub-optimal local minima. In the new multi-objective CMAES (MO-CMA-ES) a population of individuals that adapt their search strategy as in the elitist CMA-ES is maintained. These are subject to multi-objective selection. The selection is based on non-dominated sorting using either the crowding-distance or the contributing hypervolume as second sorting criterion. Both the elitist single-objective CMA-ES and the MO-CMA-ES inherit important invariance properties, in particular invariance against rotation of the search space, from the original CMA-ES. The benefits of the new MO-CMA-ES in comparison to the well-known NSGA-II and to NSDE, a multi-objective differential evolution algorithm, are experimentally shown.

Covariance Matrix Adaptation for Multi-objective Optimization

We present an overview of evolutionary algorithms that use empirical models of the fitness function to accelerate convergence, distinguishing between evolution control and the surrogate approach. We describe the Gaussian process model and propose using it as an inexpensive fitness function surrogate. Implementation issues such as efficient and numerically stable computation, exploration versus exploitation, local modeling, multiple objectives and constraints, and failed evaluations are addressed. Our resulting Gaussian process optimization procedure clearly outperforms other evolutionary strategies on standard test functions as well as on a real-world problem: the optimization of stationary gas turbine compressor profiles.

Accelerating evolutionary algorithms with Gaussian process fitness function models

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.

We analyze this observation for different multi-objective selection operators. We derive a simple analytical estimate of the stagnation distance for several selection operators, that use the dominance criterion for the fitness assignment. Two of the examined operators are shown to converge with arbitrary precision to the Pareto front. We exploit this property and propose a novel algorithm to increase their convergence speed by introducing suitable self-adaptive mutation. This adaptive mutation takes into account the distance to the Pareto front. All algorithms are analyzed on a 2- and 3-objective test function.

Self-adaptation for multi-objective evolutionary algorithms

Evolutionary Algorithms have been applied to single and mul- tiple objectives optimization problems, with a strong emphasis on problems, solved through numerical simulations. However in several engineering problems, there is limited availability of suitable models and there is need for optimization of realistic or experimental configurations. The multi- objective optimization of an experimental set-up is addressed in this work. Experimental setups present a number of challenges to any optimization technique including: availability only of pointwise information, experimen- tal noise in the objective function, uncontrolled changing of environmental conditions and measurement failure. This work introduces a multi-objective evolutionary algorithm capable of handling noisy problems with a particular emphasis on robustness against unexpected measurements (outliers). The algorithm is based on the Strength Pareto Evolutionary Algorithm (SPEA) of Zitzler and Thiele and includes the new concepts of domination dependent lifetime, re-evaluation of solutions and modifications in the update of the archive population. Sev- eral tests on prototypical functions underline the improvements in conver- gence speed and robustness of the extended algorithm. The proposed algorithm is implemented to the Pareto optimization of the combustion process of a stationary gas turbine in an industrial setup. The Pareto front is constructed for the objectives of minimization of NOx emis- sions and reduction of the pressure fluctuations (pulsation) of the flame. Both objectives are conflicting affecting the environment and the lifetime of the turbine, respectively. The optimization leads a Pareto front corre- sponding to reduced emissions and pulsation of the burner. The physical implications of the solutions are discussed and the algorithm is evaluated. Keywords—evolutionary algorithms, multi-objective optimization, noisy objective functions, gas turbine combustion, emission reduction, combus- tion instabilities

Preprint: Multi-objective Evolutionary Algorithm for the Optimization of Noisy Combustion Processes

Selon l'invention, chaque bruleur gyrostabilise a premelange (1) d'une unite de bruleurs presente en amont un dispositif de distribution reglable (5) a soupapes de reglage (V 1, ..., V8) et/ou soupapes d'entree et de sortie (V'1, ..., V'16) qui permet de definir differentes distributions axiales de flux massique du combustible introduit. On choisira de preference des elements de ce type presentant des valeurs particulierement avantageuses en termes de caracteristiques telles que les emissions de NOx et les amplitudes maximales des pulsations presentes. Des solutions de Pareto sont determinees relativement aux caracteristiques mentionnees de la maniere suivante : un dispositif de distribution (5) est represente par une arborescence comprenant des parametres de distribution et des valeurs iteratives sont produites pour ces parametres de distribution dans une unite de traitement de donnees au moyen d'un algorithme evolutif, ces valeurs permettant de regler le dispositif de distribution (5) au moyen d'une unite de commande.

Unite de bruleurs et son procede de fonctionnement

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. We analyze this observation for different multi-objective selection operators. We derive a simple analytical estimate of the stagnation distance for several selection operators, that use the dominance criterion for the fitness assignment. Two of the examined operators are shown to converge with arbitrary precision to the Pareto front. We exploit this property and propose a novel algorithm to increase their convergence speed by introducing suitable self-adaptive mutation. This adaptive mutation takes into account the distance to the Pareto front. All algorithms are analyzed on a 2- and 3-objective test function.

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Accelerating evolutionary algorithms with Gaussian process fitness function models

Self-adaptation for multi-objective evolutionary algorithms

Preprint: Multi-objective Evolutionary Algorithm for the Optimization of Noisy Combustion Processes

Unite de bruleurs et son procede de fonctionnement

Self-adaptation for multi-objective evolutionary algorithms