Evolutionary multi-objective robust optimization

Abstract

[Excerpt] 1. Introducytion. Most practical engineering optimization problems are multi-objective, i.e., their solution must consider simultaneously various performance criteria, which are often conflicting. Multi-Objective Evolutionary Algorithms (MOEAs) are particularly adequate for solving these problems, as they work with a population (of vectors or solutions) rather than with a single point (Schaffer, 1984; Fonseca & Fleming, 1993; Srinivas & Deb, 1995; Horn et al., 1994; Deb et al., 2002; Zitzler et al., 2001; Knowles & Corne, 2000; Gaspar-Cunha et al. 2004). This feature enables the creation of Pareto frontiers representing the trade-off between the criteria, simultaneously providing a link with the decision variables (Deb, 2001, Coello et al., 2002). Moreover, since in real applications small changes of the design variables or of environmental parameters may frequently occur, the performance of the optimal solution (or solutions) should be only slightly affected by these, i.e., the solutions should also be robust (Ray, 2002; Jin & Branke, 2005). The optimization problems involving unmanageable stochastic factors can be typified as (Jin & Branke, 2005): i) those where the performance is affected by noise originated by sources such as sensor measurements and/or environmental parameters (Wiesmann et al., 1998; Das, 1997); ii) those where the design variables change after the optimal solution has been found (Ray, 2002; Tsutsui & Ghosh, 1997; Chen et al., 1999); iii) problems where the process performance is estimated by an approximation to the real value; iv) and those where the performance changes with time, which implies that the optimization algorithm must be updated continuously. This text focuses exclusively problems of the second category. [...]