TY - GEN

T1 - Superpolynomial lower bounds for the (1+1) EA on some easy combinatorial problems

AU - Sutton, Andrew M.

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 2014

Y1 - 2014

N2 - The (1+1) EA is a simple evolutionary algorithm that is known to be efficient on linear functions and on some combinatorial optimization problems. In this paper, we rigorously study its behavior on two easy combinatorial problems: finding the 2-coloring of a class of bipartite graphs, and constructing satisfying assignments for a class of satisfiable 2-CNF Boolean formulas. We prove that it is inefficient on both problems in the sense that the number of iterations the algorithm needs to minimize the cost functions is superpolynomial with high probability. Our motivation is to better understand the inuence of problem instance structure on the runtime character of a simple evolutionary algorithm. We are interested in what kind of structural features give rise to so-called metastable states at which, with probability 1-o(1), the (1+1) EA becomes trapped and subsequently has dificulty leaving. Finally, we show how to modify the (1+1) EA slightly in order to obtain a polynomial-time performance guarantee on both problems.

AB - The (1+1) EA is a simple evolutionary algorithm that is known to be efficient on linear functions and on some combinatorial optimization problems. In this paper, we rigorously study its behavior on two easy combinatorial problems: finding the 2-coloring of a class of bipartite graphs, and constructing satisfying assignments for a class of satisfiable 2-CNF Boolean formulas. We prove that it is inefficient on both problems in the sense that the number of iterations the algorithm needs to minimize the cost functions is superpolynomial with high probability. Our motivation is to better understand the inuence of problem instance structure on the runtime character of a simple evolutionary algorithm. We are interested in what kind of structural features give rise to so-called metastable states at which, with probability 1-o(1), the (1+1) EA becomes trapped and subsequently has dificulty leaving. Finally, we show how to modify the (1+1) EA slightly in order to obtain a polynomial-time performance guarantee on both problems.

KW - Lower bounds

KW - Runtime analysis

UR - http://www.scopus.com/inward/record.url?scp=84905694178&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905694178&partnerID=8YFLogxK

U2 - 10.1145/2576768.2598278

DO - 10.1145/2576768.2598278

M3 - Conference contribution

AN - SCOPUS:84905694178

SN - 9781450326629

T3 - GECCO 2014 - Proceedings of the 2014 Genetic and Evolutionary Computation Conference

SP - 1431

EP - 1438

BT - GECCO 2014 - Proceedings of the 2014 Genetic and Evolutionary Computation Conference

PB - Association for Computing Machinery

T2 - 16th Genetic and Evolutionary Computation Conference, GECCO 2014

Y2 - 12 July 2014 through 16 July 2014

ER -