Linked interpolation-optimization strategies for multicriteria optimization problems

Abstract

Despite the huge amount of methods available in literature, the practical use of multiobjective optimization tools in industry is still an open issue. A strategy to reduce objective function evaluations is essential, at a fixed degree of Pareto optimal front (F P ) approximation accuracy. To this aim, an extension of single objective Generalized response surface (GRS) methods to F P approximation is proposed. Such an extension is not at all straightforward due to the usually complex shape of the Pareto optimal set (S P ) as well as the non-linear relation between the F P and the S P . As a consequence of such complexity, it is extremely difficult to identify a multiobjective analogue of single objective current optimum region. Consequently, the design domain search space zooming strategy around the current optimum region, which is the core of a GRS method, has to be carefully reconsidered when F P approximation is concerned. In this paper, a GRS strategy for multiobjective optimization is proposed. This strategy links the optimization (based on evolutionary computation) to the interpolation (based on Neural Networks). The strategy is explained in detail and tested on various test cases. Moreover, a detailed analysis of approximation errors and computational cost is given together with a description of real-life applications.Keywords Evolutionary multiobjective optimization, Neural networks interpolation, Response surface methods IntroductionEvolutionary multiobjective optimization has now come to full maturity, both in terms of methodologies [1, 2] and algorithm development [3][4][5][6][7][8][9].Nevertheless, the application of the wide variety of available methods to problems arising from industrial design (in particular electromagnetic devices shape design [10-15] and optimal controllers design), is still not completely straightforward, due to the computational cost needed to evaluate the objective function. In fact, it is often either a (non-linear or coupled) Finite Element Method, or a long time-domain full-system simulation.Two alternative (to available MOEAs) approaches have been considered by the authors and colleagues in previous papers, being specifically devoted to the reduction of objective function calls. They are useful and meaningful when the following constraint and requirement hold.-On one hand (the constraint), the number of objective function calls that can be afforded from the point of view of an industrially practical computational cost is much smaller than the threshold number required for convergence of available powerful MOEAs. -On the other hand (the requirement) the few affordable solutions should converge towards the F P and be diverse each other. In other words this means that solutions are to be few (due to the computational cost) but distributed all along the F P (in order to me meaningful).The two approaches can be summarized as follows:-Build specific MOEAs for tiny populations.-Reconsider a particular preference function method with hybrid global-evolutionary and local-determinist...

Design of a motorcycle frame using neuroacceleration strategies in MOEAs

“…In recent years, some authors have proposed algorithms that incorporate approximate fitness functions in MOEAs (Nain and Deb 2002;Farina and Amato 2005;Lagaros et al 2005;Chafekar et al 2005;Knowles 2006;Voutchkov and Keane 2006). These algorithms, which use different control methods intended to reduce the MOEA's computational cost without affecting convergence to the POF, share two characteristics that are key to high performance.…”

“…According to Farina and Amato (2005), designing such an algorithm is justified only when C(f) C(f) and T (f) T (f), where C(f) and C(f) are the number of evaluations of the approximated and real objective functions, respectively; and T (f) and T (f) are the computational times needed to evaluate the approximated and real objective functions, respectively. In other words, the strategy is to evaluate the low computational cost functionf as many times as needed, but evaluate the high computational cost function f (like the FE simulation described in this work) as few times as possible.…”

“…The proposed algorithm, NN-MOEA, is based on the GRS-MOEA proposed by Farina and Amato (2005), which is an extension of the generalized response surface metaheuristic (GRS) for multiobjective optimization problems. According to Farina and Amato (2005), designing such an algorithm is justified only when C(f) C(f) and T (f) T (f), where C(f) and C(f) are the number of evaluations of the approximated and real objective functions, respectively; and T (f) and T (f) are the computational times needed to evaluate the approximated and real objective functions, respectively.…”

Prediction-Based Population Re-initialization for Evolutionary Dynamic Multi-objective Optimization

“…Stationary multi-objective evolutionary algorithms such as NSGA-II [7], SPEA2 [8], MSOPS [9] and OMOEA-II [10] have been directly applied to DMOPs [6,11]. A few evolutionary algorithms for solving dynamic single objective optimization problems have also been extended to the case of multiobjective problems [12]. Several strategies have been proposed to add to stationary multi-objective evolutionary algorithms problems for tracking the movement of the PS [13][14][15].…”

“…It is natural to draw the PF for stationary multi-objective optimization, but it is no longer practical to plot the changing PFs in dynamic environment. In [12], two convergence performance measures have been suggested. In [6], the generational distance with time was plotted to show the convergence.…”