Abstract
Local search algorithms and iterated local search algorithms are a basic technique. Local search can be a stand-alone search method, but it can also be hybridized with evolutionary algorithms. Recently, it has been shown that it is possible to identify improving moves in Hamming neighborhoods for k-bounded pseudo-Boolean optimization problems in constant time. This means that local search does not need to enumerate neighborhoods to find improving moves. It also means that evolutionary algorithms do not need to use random mutation as a operator, except perhaps as a way to escape local optima. In this paper, we show how improving moves can be identified in constant time for multiobjective problems that are expressed as k-bounded pseudo-Boolean functions. In particular, multiobjective forms of NK Landscapes and Mk Landscapes are considered.
F. Chicano—This research was partially funded by the Fulbright program, the Spanish Ministry of Education (CAS12/00274), the University of Málaga, Andalucía Tech, and the Spanish Ministry of Science and Innovation and FEDER (TIN2014-57341-R).
D. Whitley—It was also sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant number FA9550-11-1-0088. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon.
R. Tinós—Would like to thank FAPESP (under grant 2015/06462-1) and CNPq for the financial support.
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Notes
- 1.
In general, we will use boldface to denote vectors in \(\mathbb {R}^d\), as \(\mathbf{f}\), but we will use normal weight for vectors in \(\mathbb {B}^n\), like x.
- 2.
What we call Score here is also named \(\varDelta \)-evaluation by other authors [13].
- 3.
Distinguishing the weak, but not strong, improving moves from the strong disimproving moves in the implementation would reduce the runtime here, since only weak improving moves need to be re-classified.
- 4.
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Chicano, F., Whitley, D., Tinós, R. (2016). Efficient Hill Climber for Multi-Objective Pseudo-Boolean Optimization. In: Chicano, F., Hu, B., García-Sánchez, P. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2016. Lecture Notes in Computer Science(), vol 9595. Springer, Cham. https://doi.org/10.1007/978-3-319-30698-8_7
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