Multi-Objective Memetic Algorithm using Pattern Search Filter Methods

Solving real world Multi-Objective Optimization Problems (MOOP) often involves the use of complex “black-box ”modeling routines, where the resolution of the process governing equations requires the use of expensive numerical methods [1]. Multi-Objective Evolutionary Algorithms (MOEA) is an excellent tool to deal with the multi-objective nature of these problems. They do not need the calculation of derivatives which are not available for this type of problems [2, 3]. Simultaneously, due to the fact that the MOEAs are based on the use of a population of solutions that evolves during successive generations, they are a good global search method and are particularly suitable to solve multi-objective problems [2]. The concept of non-dominance is used in MOEA in order to establish a trade-off between the solutions, i.e., the Pareto frontier [2]. The major difficulty in applying MOEAs to real optimization problems lies on the large number of evaluations of the objective functions necessary to obtain an acceptable solution. Due to the usual high computation times required by the numerical methods used, reducing the number of evaluations necessary to reach an acceptable solution is thus of major importance [4]. Different approaches have been pursued in the literature to solve this problem. One of these methods consists in using approximate objective functions, such as statistical methods or Artificial Neural Networks (ANN), to evaluate the solutions [5]. An alternative consists in coupling MOEAs with local search methods, where in each generation of the MOEA some (good) solutions using an efficient local search algorithm are generated [6].