Abstract
We present several technologies recommended for making 2-dimensional (2D) or 3-dimensional (3D) representations of selected discrete solution spaces as well as features of the solution algorithms occurring in combinatorial optimization (CO) tasks. We provide some results of theoretical as well as experimental investigations of so called landscape of the space with reference to some exemplary hard CO problems. Theoretical analysis starts from various measures of the distance between solutions represented by typical combinatorial objects, namely permutations, composition of permutations, set partition and so forth. Then, we propose some mapping of n-dimensional space of permutations into 2- or 3 dimensional Euclidean space to extract factors responsible for hardness of the problem and to illustrate behavior of approximation algorithms.
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Notes
- 1.
Paper is supported by funds of National Science Centre, grant OPUS no. DEC 2017/25/B/ST7/02181.
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Smutnicki, C. (2020). Visualization of Solution Spaces for the Needs of Metaheuristics. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2019. EUROCAST 2019. Lecture Notes in Computer Science(), vol 12013. Springer, Cham. https://doi.org/10.1007/978-3-030-45093-9_37
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