Reoptimization Time Analysis of Evolutionary Algorithms on Linear Functions Under Dynamic Uniform Constraints

Feng Shi, Martin Schirneck, Tobias Friedrich, Timo Kötzing, Frank Neumann

Abstract: Rigorous runtime analysis is a major approach towards understanding evolutionary computing techniques, and in this area linear pseudo-Boolean objective functions play a central role. Having an additional linear constraint is then equivalent to the NP-hard Knapsack problem, certain classes thereof have been studied in recent works. In this article, we present a dynamic model of optimizing linear functions under uniform constraints. Starting from an optimal solution with respect to a given constraint bound, we investigate the runtimes that different evolutionary algorithms need to recompute an optimal solution when the constraint bound changes by a certain amount. The classical $$(1{+}1)$$ ( 1 + 1 ) EA and several population-based algorithms are designed for that purpose, and are shown to recompute efficiently. Furthermore, a variant of the $$(1{+}(\lambda ,\lambda ) )$$ ( 1 + ( λ , λ ) ) GA for the dynamic optimization problem is studied, whose performance is better when the change of the constraint bound is small.