Runtime analysis of evolutionary algorithms for the knapsack problem with favorably correlated weights

Frank Neumann; Andrew M. Sutton

doi:10.1007/978-3-319-99259-4_12

Runtime analysis of evolutionary algorithms for the knapsack problem with favorably correlated weights

Frank Neumann, Andrew M. Sutton

Computer Science (Duluth)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

8 Scopus citations

Abstract

We rigorously analyze the runtime of evolutionary algorithms for the classical knapsack problem where the weights are favorably correlated with the profits. Our result for the (1+1) EA generalizes the one obtained in [1] for uniform constraints and shows that an optimal solution in the single-objective setting is obtained in expected time (formula presented), where (formula presented) is the largest profit of the given input. Considering the multi-objective formulation where the goal is to maximize the profit and minimize the weight of the chosen item set at the same time, we show that the Pareto front has size n+1 whereas there are sets of solutions of exponential size where all solutions are incomparable to each other. Analyzing a variant of GSEMO with a size-based parent selection mechanism motivated by these insights, we show that the whole Pareto front is computed in expected time (formula presented).

Original language	English (US)
Title of host publication	Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, 2018, Proceedings
Editors	Carlos M. Fonseca, Nuno Lourenco, Penousal Machado, Luis Paquete, Anne Auger, Darrell Whitley
Publisher	Springer Verlag
Pages	141-152
Number of pages	12
ISBN (Print)	9783319992587
DOIs	https://doi.org/10.1007/978-3-319-99259-4_12
State	Published - 2018
Event	15th International Conference on Parallel Problem Solving from Nature, PPSN 2018 - Coimbra, Portugal Duration: Sep 8 2018 → Sep 12 2018

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	11102 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	15th International Conference on Parallel Problem Solving from Nature, PPSN 2018
Country/Territory	Portugal
City	Coimbra
Period	9/8/18 → 9/12/18

Bibliographical note

Publisher Copyright:
© 2018, Springer Nature Switzerland AG.

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10.1007/978-3-319-99259-4_12

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Neumann, F., & Sutton, A. M. (2018). Runtime analysis of evolutionary algorithms for the knapsack problem with favorably correlated weights. In C. M. Fonseca, N. Lourenco, P. Machado, L. Paquete, A. Auger, & D. Whitley (Eds.), Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, 2018, Proceedings (pp. 141-152). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11102 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-99259-4_12

Runtime analysis of evolutionary algorithms for the knapsack problem with favorably correlated weights. / Neumann, Frank; Sutton, Andrew M.
Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, 2018, Proceedings. ed. / Carlos M. Fonseca; Nuno Lourenco; Penousal Machado; Luis Paquete; Anne Auger; Darrell Whitley. Springer Verlag, 2018. p. 141-152 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11102 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Neumann, F & Sutton, AM 2018, Runtime analysis of evolutionary algorithms for the knapsack problem with favorably correlated weights. in CM Fonseca, N Lourenco, P Machado, L Paquete, A Auger & D Whitley (eds), Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11102 LNCS, Springer Verlag, pp. 141-152, 15th International Conference on Parallel Problem Solving from Nature, PPSN 2018, Coimbra, Portugal, 9/8/18. https://doi.org/10.1007/978-3-319-99259-4_12

Neumann F, Sutton AM. Runtime analysis of evolutionary algorithms for the knapsack problem with favorably correlated weights. In Fonseca CM, Lourenco N, Machado P, Paquete L, Auger A, Whitley D, editors, Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, 2018, Proceedings. Springer Verlag. 2018. p. 141-152. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-99259-4_12

Neumann, Frank ; Sutton, Andrew M. / Runtime analysis of evolutionary algorithms for the knapsack problem with favorably correlated weights. Parallel Problem Solving from Nature – PPSN XV - 15th International Conference, 2018, Proceedings. editor / Carlos M. Fonseca ; Nuno Lourenco ; Penousal Machado ; Luis Paquete ; Anne Auger ; Darrell Whitley. Springer Verlag, 2018. pp. 141-152 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Runtime analysis of evolutionary algorithms for the knapsack problem with favorably correlated weights

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