An Iterated Local Search to find many solutions of the 6-states Firing Squad Synchronization Problem

Abstract : This paper proposes an optimization approach for solving a classical problem in cellular automata theory: the 6-states Firing Squad Synchronization Problem (FSSP). To this purpose, we introduce an original optimization function which quantifies the quality of solutions according only to the main goal of the problem without taking into account any side information about cellular automata computations. This function is used for a dedicated Iterated Local Search algorithm which finds several hundreds of new solutions of the FSSP. Note, that up to present only one human-designed solution was known which is optimal in time. Most of the new solutions found by our algorithm have lower complexity (in terms of number of transitions rules used). An analysis of the fitness landscape for FSSP explains why, counter-intuitively, local search strategy can achieve good results for FSSP.
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Manuel Clergue, Sébastien Verel, Enrico Formenti. An Iterated Local Search to find many solutions of the 6-states Firing Squad Synchronization Problem. Applied Soft Computing, Elsevier, 2018, 66, pp.449-461. ⟨10.1016/j.asoc.2018.01.026⟩. ⟨hal-01738330⟩

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