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

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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…show more content…
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 many objectives to optimize these functions are mutually contradictory, so to make a comparison between solution and an other one, we should describe a relation to made this appreciation, The Pareto Dominance relation can do this. Considering a minimisation problem, lets u and v two vectors. A solution is an Pareto optimal solution if and only if it doesn’t exist an other admissible solution x where f(x) dominate . So a solution of an Multiobjective problem is a set of solutions which they are not dominated by any other solutions, we call this set the "Pareto front" 2 Related work In this

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