Parameterized Complexity Analysis of Randomized Search Heuristics
This work offers incremental improvements in theoretical analysis for researchers in evolutionary algorithms and combinatorial optimization.
The chapter applies parameterized complexity theory to analyze the running time of randomized search heuristics on NP-hard problems like minimum vertex cover, maximum leaf spanning tree, and traveling salesperson, providing finer-grained insights than classical complexity approaches.
This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms. The parameterized approach articulates the running time of algorithms solving combinatorial problems in finer detail than traditional approaches from classical complexity theory. We outline the main results and proof techniques for a collection of randomized search heuristics tasked to solve NP-hard combinatorial optimization problems such as finding a minimum vertex cover in a graph, finding a maximum leaf spanning tree in a graph, and the traveling salesperson problem.