Which is the Best? A Statistically Correct Comparison of Heuristic Results in Structural Optimization
A. Csébfalvi · Civil-comp proceedings · 2012
The essence of this paper is very simple: to make a fair comparison between different heuristics in structural optimization we have to adapt the appropriate elements of the very rigorous protocol used to test new drugs, or compare the effects of different drugs. Naturally, the problem of fair comparison, as a fundamental requirement of the real progress is not connected only to the structural optimization [1, 2]. It is a general problem of the heuristic community without final results. When we use statistical methods in the structural optimization (namely heuristics or metaheuristics with several tunable parameters and starting seeds), then the usual presentation practice: problem - one result is extremely far from the fair comparison. From a statistical point of view, the minimal requirement is a so-called small-sample generated by independent runs and an appropriate small-sampletest according to the theory of the experimental design and evaluation and the protocol used, for example, in the drug development processes. The viability and efficiency of the proposed statistically correct methodology based on the nonparametric Kolmogorov-Smirnov test [3] is demonstrated using a well-known ten-bar truss for structural weight minimization with continuous size variables and displacement and stress constraints to investigate the effect of the hybridization in the hybrid metaheuristic ANGEL [4]. The supernatural ANGEL method combines ant colony optimization (AN), genetic algorithm (GE) and local search (L) strategy. In the algorithm, the AN and GE search alternately and cooperatively in the solution space. The powerful L algorithm, which is based on the local linearization of the constraint set, is applied to yield a better feasible or less unfeasible solution from the solution generated by the AN or GE. The statistical results, demonstrate that significant computational improvements can be obtained by hybridization and synergism may be explained by their totally different selection mechanism of the AN and GE.