Evolutionary Algorithms and Matroid Optimization Problems

Abstract

We analyze the performance of evolutionary algorithms on various matroid optimization problems that encompass a vast number of efficiently solvable as well as NP-hard combinatorial optimization problems (including many well-known examples such as minimum spanning tree and maximum bipartite matching). We obtain very promising bounds on the expected running time and quality of the computed solution. Our results establish a better theoretical understanding of why randomized search heuristics yield empirically good results for many real-world optimization problems.

Runtime analysis of binary PSO

“…To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. GECCO'08, July [12][13][14][15][16]2008, Atlanta, Georgia, USA. Copyright 2008 ACM 978-1-60558-130-9/08/07 ...$5.00.…”

“…The runtime analysis of evolutionary algorithms can be called a success story since nowadays analyses are possible for many problems from combinatorial optimization. This includes, for example, maximum matchings [5], spanning tree problems [12], matroid optimization [14] as well as the NP-hard partition problem [17].…”

Theory of randomised search heuristics in combinatorial optimisation

“…Exemplary Results (Reichel and Skutella, 2007) The (1+1) EA and RLS solve the matroid optimisation problems min. weight basis exactly in time O(|E | 2 (log |E | + log w max )).…”

“…Exemplary Results (Reichel and Skutella, 2007) The ( Theorem (Witt, 2005) There is an instance such that the (1+1) EA needs with prob. Ω(1) at least n Ω(n) steps to find a solution with a better ratio than 4/3 − ε. Theorem (Witt, 2005) On any instance, the (1+1) EA with prob.…”

Computing Minimum Cuts by Randomized Search Heuristics

“…A lot of progress has been made in analyzing simple evolutionary algorithms with respect to their runtime behavior on artificial pseudo-boolean functions [4,10] as well as some well-known combinatorial optimization problems [8,15,18,19,21,24]. We contribute to this line of research and study the minimum s-t-cut problem in a given graph with weights on the edges.…”