Focused jump-and-repair constraint handling for fixed-parameter tractable graph problems closed under induced subgraphs

Repair operators are often used for constraint handling in constrained combinatorial optimization. We investigate the (1+1) EA equipped with a tailored jump-and-repair operation that can be to probabilistically repair infeasible offspring graph problems. Instead of evolving candidate solutions entire graph, we expand genotype allow develop parallel feasible solution together growing subset instance (an induced subgraph). With this approach, prove is able simulate an iterative compression process classical fixed-parameter algorithmics obtain randomized FPT performance guarantee on three NP-hard For k-VertexCover, using focused find k-vertex cover (if one exists) O(2kn2log⁡n) iterations expectation. This leads exponential (in k) improvement over best-known parameterized bound evolutionary algorithms VertexCover. k-FeedbackVertexSet problem tournaments, finds feedback set O(2kk!n2log⁡n) expectation, and OddCycleTransversal, optimization time O(3kkmn2log⁡n). latter two problems, constitutes first result any algorithm. discuss how generalize framework other problems closed under subgraphs report experimental results illustrate behavior algorithm concrete class.