DGA and Pareto Elitism : Improving Pareto

Previous works have shown the eeciency of a new approach for the Genetic Algorithms, the Dual Genetic Algorithms, in the multiobjective optimization context. Dual Genetic Algorithms make use of a meta level to enhance the expressiveness of schemata, entities implicitly handle by Genetic Algorithms. In this paper, we show that this approach, coupled with a new method, Pareto Elitism, leads to very interesting results, in particular on an adaptation for multi-objective optimization of Royal Road Functions, the Multi Royal Road Functions. We begin with a quick reminder on multiobjective optimization , on what makes it diierent from single objective optimization and what has been done in this context. After this, the Dual Genetic Algorithm principles are brieey exposed, as well as previous results obtained. Then, we present Pareto Elitism, combining steady state and sharing techniques for Pareto optimization, and its behavior on Multi Royal Road Functions. 1 Pareto Optimization Many problems can be seen as optimization over a cost function. In such a problem, we are given a mapping f : X ! Y, where X is the space being searched. For that f , we seek one x 2 X or a subset X X, which gives rise to a particular y 2 Y or a particular subset Y Y. The most studied case is the one where Y = R. In this context, we seek the x 's that extremize the given f. Many methods, as Simulated Annealing, Hill Climbing or Genetic Algorithms, were developed and each have particular advantages or disadvantages that make them well suited for a particular class of such single objective functions. However, engineers are very often faced with problems expressed in terms of many criteria, or objectives , often competitive, which should be satissed simultaneously. In this case, Y = R n , where n is the number of criteria in the problem. The mapping f is now a vector function, with n components f k ; k = 1:::n, where each component has to be optimized. This mapping associates for each x 2 X a vector y 2 Y, such that y = f (x) = (f 1 (x); :::; f n (x)). The goal is still to nd particular x 's which give rise to optimal y. But the diiculty in the multiobjective context is that there is no trivial way to say that one y is better than another one …