1301 words - 6 pages

A Copula-Based EDA For a Class of Continuous Multiobjective Problems

1 Introduction

An optimisation problem consist of trying to find the optimal solution in a set of good solution, finding this optimal solution has a relation with the specific area of research problem, this kind of problem which have two or more objective function to reach are called multiobjective problem, those objectives are usually contradictory each others, the optimisation of this problems enter in Decision making of a huge industrial and research problems.

To solve this kind of problems many methods were proposed citing NSGAII [1] SPEA2 [2] Indicator-based EA [3] [4], those methods are eventually an evolutionary algorithms which start with an initial population then evaluate this population generation after generation to reach to an acceptable optimal solution .

The Evolutionary algorithm are known as one of the efficacy metaheuristics to solve the complex problem [5], there are a different type of EA ( evolutionary Algorithms): genetic algorithm, genetic programming, differential evolution and the Estimation of Distribution Algorithms (EDA) [6] , this last type was recently been the main subject of a lot of research problem in mono and multiobjective optimisation [7] [8] [9] [10] [11], this is due that those algorithms are based on estimations methods in statistics or probability sciences which give them the ability to explain the evoluvility aspect of the new populations and the convergence are usually calculated and can be guaranteed .

In this paper we will describe a new method to find the optimal in the optimisation problems using a copula-based EDA. The EDA [6] uses a different methods to estimate the new population which is primordial in this kind of algorithms, in this paper we propose to use the Copula [12] to estimate the new population, and then the evaluation process is guaranteed with the Non-Sorting Genetic Algorithm NSGAII [NSGAII]. the Copula are very strong statistical theory, used in financial and economic estimation, so the use of Copula theory to solve the Class of multiobjective optimisation which is the class of continuous one, looks like a good resolver of this kind of problems, the test applied on this algorithm exactly on the ZDT benchmarks [13] problems gives a good results in term of performance. this paper is organized as flow:

• A definition of the Multiobjective optimisation problem.

• A definition of the Estimation of Distribution Algorithm.

• A definition of the Copula theory.

• Presentation of the new proposed Algorithm.

• Used test problems.

• Experimentation and results

2 Multiobjective optimisation problem

A multiobjective problem can be viewed as well and if we consider a minimisation problem for all objectives functions:

m functions to optimize and p constraints to satisfy.

The main goal of all optimisation methods is to find an optimal solution of those problems, and we should precise that a multiobjective problem have...

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