Keywords: statistical comparison, Kolmogorov-Smirnov test, nonparametric test, heuristics, meta-heuristics, structural optimization, hybridization.

The essence of this paper is very simple: the appropriate elements of the very rigorous protocol, as used to test new drugs, or compare the effects of different drugs, must be adapted to make a fair comparison between different heuristics in structural optimization. Naturally, the problem of fair comparison, is a fundamental requirement of real judgment of the progress and is not connected only to structural optimization. It is a general problem of the heuristic community without final results [1,2].

When statistical methods are used in the structural optimization (namely heuristics or meta-heuristics with several tunable parameters and starting seeds), then the usual presentation practice: "one 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-sample-test" 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 method [4].

The "supernatural" ANGEL method combines ant colony optimization (AN), genetic algorithm (GE) and a local search (L) strategy. In the ANGEL 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 AN or GE.

The statistical results demonstrate that significant computational improvements can be obtained by hybridization and synergism may be explained by the totally different selection mechanisms of the AN and the GE.

1

J.N. Hooker, "Testing Heuristics: We Have It All Wrong", Journal of Heuristics, 1, 33-42, 1995. doi:10.1007/BF02430364

2

R.S. Barr, B.L. Golden, J.P. Kelly, M.G.C. Resende, W.R. Stewart, "Design and Reporting on Computational Experiments with Heuristic Methods", Journal of Heuristics, 1, 9-32, 1995. doi:10.1007/BF02430363

3

A. Csébfalvi, "Kolmogorov-Smirnov test to tackle fair comparison of heuristic approaches in structural optimization", International Journal of Optimization in Civil Engineering, 2(1), 135-150, 2012.

4

A. Csébfalvi, "Angel method for discrete optimization problems", Periodica Polytechnica Civil Engineering, 51/2, 37-46, 2007. doi:10.3311/pp.ci.2007-2.06

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