**Balanced Explore-Exploit clustering based Distributed Evolutionary Algorithm for Multi-objective Optimisation**

**Mariem GZARA**

Multimedia Information systems and Advanced Computing Laboratory (MIRACL)

route Tunis Km 3; B.P. 1030, Sfax, 3018

**Abdelbasset ESSABRI**

Laboratoire de Gestion Industrielle et d’Aide à la Décision (GIAD)

route de l’aérodrome Km 4.5 BP 1088, Sfax, 3018

**Abstract**: Most parallel evolutionary algorithms for single and multi-objective optimisation are motivated by the reduction of the computation time and the resolution of larger problems. Another promising alternative is to create new distributed schemes that improve the behaviour of the search process of such algorithms. In multi-objective optimisation problems, more exploration of the search space is required to obtain the whole or the best approximation of the Pareto Optimal Front. In this paper, we present a new clustering-based parallel multi-objective evolutionary algorithm that balances between the two main concepts in metaheuristics, which are exploration and exploitation of the search space. The proposed algorithm is implemented and tested on several standard multi-objective test functions using a network of multiple computers.

**Keywords**: Parallel computing, multi-objective optimisation, evolutionary algorithms.

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**CITE THIS PAPER AS**:

Mariem GZARA, Abdelbasset ESSABRI, **Balanced Explore-Exploit clustering based Distributed Evolutionary Algorithm for Multi-objective Optimisation**, *Studies in Informatics and Control*, ISSN 1220-1766, vol. 20 (2), pp. 97-106, 2011.

**1. Introduction**

Evolutionary Algorithms (EAs) are stochastic search metaheuristics that have been used successfully to solve many optimisation problems such as scheduling, routing, etc [2, 17, 23, 14, 15]. EAs are population based metaheuristics that perform well global search by exploring simultaneously different regions of the search space. They are therefore less attracted to local optima and are suitable to solve Multi-Objective Optimisation problems (MOP) where a set of non-dominated solutions is sought. This is in contrast to the single-objective optimisation problems where a unique optimum is sought. Several algorithms are proposed to adapt EAs to MOPs, including NSGA-II [9, 25], SPEA-II [28], NPGA-II [20]. These algorithms can be divided into two categories: the non-Pareto and the Pareto Multi-Objective Evolutionary Algorithms (MOEAs). The concept of Pareto dominance is used to rank the population in such a way that all non-dominated individuals in the population are assigned the same cost. Pareto elitist MOEAs maintain another population than the current one, which permits to keep the Pareto-optimal solutions found during the search. This external population participates in the process of selection. Thus, elitism permits a better intensification of the search. Among these algorithms, SPEA-II [28] and NSGA-II [25] have powerful search mechanisms and obtained good results. SPEA-II [28] and NSGA-II [25] use similar concepts; such as Pareto selection, elitism and diversification techniques that are proved to be efficient to characterise the Pareto Optimal Front (POF). A state of the art on MOEAs is given in [13, 8, 7].

Despite their success in solving several real-world MOPs [11, 16], these algorithms require large computational times and memory. Several parallel schemes are proposed to overcome this problem. Another motivation is to exploit parallelism to best explore the search space and to discover new ways to direct the search. In the single-objective case, parallel EAs exploit the inherent parallelism in evolutionary computation where crossover, mutation, selection and fitness evaluation can be easily distributed. Whereas, in the multi-objective case, many parallel schemes focus on how to divide the population on the objective or/and the decision space where each process will concentrate on a specific region of the search space.

One of the most difficult issues in designing metaheuristics for the resolution of both single-objective and multi-objective problems is how to balance between exploration and exploitation of the search space. For example, in evolutionary computation a high rate of conventional mutation (high diversification) makes the search process looks like a random exploration. While a high rate of crossover without mutation leads to a premature convergence. In Parallel Multi-Objective Evolutionary Algorithms (PMOEAs), the parallelism can be exploited to direct the search toward more exploration or more exploitation through the mechanisms of collecting, dividing and redistributing the global population or a subset of individuals among the available processors. In this paper, we propose a new parallel evolutionary algorithm for multi-objective optimisation that is called “Balanced Explore Exploit clustering based Distributed Evolutionary Algorithm for multi-objective optimisation” (BEEDEA). This algorithm is based on dividing the search space by clustering algorithms then redistributing the individuals such that both global search and local search will be performed. To test the BEEDEA, we use the benchmark functions of Zitzler [27] on a network of several computers. Experimental results have shown that the BEEDEA performs a good balance between exploration and exploitation of the search space and it is more efficient to characterise the POF than a classic island model parallel MOEA without migration.

The paper is organised as follows. Section 2 reviews the literature on existing PMOEAs. Section 3 describes the proposed parallel MOEA. Section 4 presents numerical results. Section 5 concludes the paper and outlines future research directions.

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