TY - GEN
T1 - Crossover can simulate bounded tree search on a fixed-parameter tractable optimization problem
AU - Sutton, Andrew M.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - We investigate the effect of crossover in the context of parameterized complexity on a well-known fixed-parameter tractable combinatorial optimization problem known as the closest string problem. We prove that a multi-start (+1) GA solves arbitrary length-n instances of closest string in 2O(d 2+d log k) · poly(n) steps in expectation. Here, k is the number of strings in the input set, and d is the value of the optimal solution. This confirms that the multi-start (+1) GA runs in randomized fixed-parameter tractable (FPT) time with respect to the above parameterization. On the other hand, if the crossover operation is disabled, we show there exist instances that require nΩ(log(d+k)) steps in expectation. The lower bound asserts that crossover is a necessary component in the FPT running time.
AB - We investigate the effect of crossover in the context of parameterized complexity on a well-known fixed-parameter tractable combinatorial optimization problem known as the closest string problem. We prove that a multi-start (+1) GA solves arbitrary length-n instances of closest string in 2O(d 2+d log k) · poly(n) steps in expectation. Here, k is the number of strings in the input set, and d is the value of the optimal solution. This confirms that the multi-start (+1) GA runs in randomized fixed-parameter tractable (FPT) time with respect to the above parameterization. On the other hand, if the crossover operation is disabled, we show there exist instances that require nΩ(log(d+k)) steps in expectation. The lower bound asserts that crossover is a necessary component in the FPT running time.
KW - Crossover
KW - Evolutionary algorithms
KW - Fixed-parameter tractability
KW - Parameterized complexity
KW - Recombination
KW - Theory
UR - http://www.scopus.com/inward/record.url?scp=85050633760&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85050633760&partnerID=8YFLogxK
U2 - 10.1145/3205455.3205598
DO - 10.1145/3205455.3205598
M3 - Conference contribution
AN - SCOPUS:85050633760
T3 - GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference
SP - 1531
EP - 1538
BT - GECCO 2018 - Proceedings of the 2018 Genetic and Evolutionary Computation Conference
PB - Association for Computing Machinery, Inc
T2 - 2018 Genetic and Evolutionary Computation Conference, GECCO 2018
Y2 - 15 July 2018 through 19 July 2018
ER -