2014/04/11 by Chotard, Alexandre, Auger, Anne, Nikolaus Hansen +3
Computer Science · Mathematics · #Advanced Multi-Objective Optimization Algorithms #Constraint Satisfaction and Optimization #FOS: Computer and information sciences #FOS: Mathematics #Metaheuristic Optimization Algorithms Research #Neural and Evolutionary Computing (cs.NE) #Optimization and Control (math.OC) #cs.NE #math.OC
paper · pdf · doi:10.48550/arxiv.1404.3023
Amir Hussain; Zhigang Zeng; Nian Zhang. IEEE Congress on Evolutionary Computation, Jul 2014, Beijing, China
openalex publication_date 2014/04/11 · arxiv created 2014/12/06 · arxiv updated 2014/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper analyses a (1,λ)-Evolution Strategy, a randomised comparison-based adaptive search algorithm, on a simple constraint optimisation problem. The algorithm uses resampling to handle the constraint and optimizes a linear function with a linear constraint. Two cases are investigated: first the case where the step-size is constant, and second the case where the step-size is adapted using path length control. We exhibit for each case a Markov chain whose stability analysis would allow us to deduce the divergence of the algorithm depending on its internal parameters. We show divergence at a constant rate when the step-size is constant. We sketch that with step-size adaptation geometric divergence takes place. Our results complement previous studies where stability was assumed.