×

On the statistical evaluation of algorithmic’s computational experimentation with infeasible solutions. (English) Zbl 1478.68467

Summary: The experimental evaluation of algorithms results in a large set of data which generally do not follow a normal distribution or are not heteroscedastic. Besides, some of its entries may be missing, due to the inability of an algorithm to find a feasible solution until a time limit is met. Those characteristics restrict the statistical evaluation of computational experiments. This work proposes a bi-objective lexicographical ranking scheme to evaluate datasets with such characteristics. The output ranking can be used as input to any desired statistical test. We used the proposed ranking scheme to assess the results obtained by the Iterative Rounding heuristic (IR). A Friedman’s test and a subsequent post-hoc test carried out on the ranked data demonstrated that IR performed significantly better than the Feasibility Pump heuristic when solving 152 benchmark problems of Nonconvex Mixed-Integer Nonlinear Problems. However, is also showed that the RECIPE heuristic was significantly better than IR when solving the same benchmark problems.

MSC:

68W99 Algorithms in computer science
62J15 Paired and multiple comparisons; multiple testing
90C59 Approximation methods and heuristics in mathematical programming

Software:

FEASPUMP; ASlib
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Zhang, T.; Yin, Y., The minimum spanning tree problem with non-terminal set, Inf. Process. Lett., 112, 17-18, 688-690 (2012) · Zbl 1248.68226
[2] Papadopoulos, K.; Christofides, D., A fast algorithm for the gas station problem, Inf. Process. Lett., 131, 55-59 (2018) · Zbl 1425.90015
[3] Box, G. E.; Hunter, J. S.; Hunter, W. G., Statistics for Experimenters: Design, Innovation, and Discovery, vol. 2 (2005), Wiley-Interscience: Wiley-Interscience New York · Zbl 1082.62063
[4] García, S.; Molina, D.; Lozano, M.; Herrera, F., A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the cec’2005 special session on real parameter optimization, J. Heuristics, 15, 6, 617 (2009) · Zbl 1191.68828
[5] García, S.; Fernández, A.; Luengo, J.; Herrera, F., A study of statistical techniques and performance measures for genetics-based machine learning: accuracy and interpretability, Soft Comput., 13, 10, 959 (2009)
[6] Weaver, K. F.; Morales, V.; Dunn, S. L.; Godde, K.; Weaver, P. F., Parametric versus nonparametric tests, (An Introduction to Statistical Analysis in Research: With Applications in the Biological and Life Sciences (2017), John Wiley & Sons: John Wiley & Sons Hoboken, NJ, USA), 191-194, Ch. 4
[7] Pavlikov, K., Improved formulations for minimum connectivity network interdiction problems, Comput. Oper. Res., 97, 48-57 (2018) · Zbl 1391.90122
[8] Melo, W.; Fampa, M.; Raupp, F., Integrality gap minimization heuristics for binary mixed integer nonlinear programming, J. Glob. Optim., 71, 3, 593-612 (2018) · Zbl 1402.90101
[9] Fortz, B.; Oliveira, O.; Requejo, C., Compact mixed integer linear programming models to the minimum weighted tree reconstruction problem, Eur. J. Oper. Res., 256, 1, 242-251 (2017) · Zbl 1394.90435
[10] Nannicini, G.; Belotti, P., Rounding-based heuristics for nonconvex MINLPs, Math. Program. Comput., 4, 1, 1-31 (2012) · Zbl 1257.90059
[11] Kerschke, P.; Kotthoff, L.; Bossek, J.; Hoos, H. H.; Trautmann, H., Leveraging tsp solver complementarity through machine learning, Evol. Comput., 1-24 (2017)
[12] Bischl, B.; Kerschke, P.; Kotthoff, L.; Lindauer, M.; Malitsky, Y.; Fréchette, A.; Hoos, H.; Hutter, F.; Leyton-Brown, K.; Tierney, K., Aslib: a benchmark library for algorithm selection, Artif. Intell., 237, 41-58 (2016) · Zbl 1357.68202
[13] Hansen, N.; Auger, A.; Finck, S.; Ros, R., Real-Parameter Black-Box Optimization Benchmarking 2010: Experimental Setup (2010), INRIA, Tech. Rep. RR-7215
[14] Price, K., Differential evolution vs. the functions of the 2nd ICEC, (Proceeding of 1997 IEEE International Conference on Evolutionary Computation (1997)), 153-157
[15] de Campos, C. P.; Benavoli, A., Joint analysis of multiple algorithms and performance measures, New Gener. Comput., 35, 1, 69-86 (2017) · Zbl 1450.62090
[16] D’Ambrosio, C.; Frangioni, A.; Liberti, L.; Lodi, A., Experiments with a feasibility pump approach for nonconvex minlps, (International Symposium on Experimental Algorithms (2010), Springer), 350-360
[17] Liberti, L.; Mladenović, N.; Nannicini, G., A recipe for finding good solutions to minlps, Math. Program. Comput., 3, 4, 349-390 (2011) · Zbl 1276.90041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.