Abstract
Evolutionary algorithms (EAs) evaluate many candidate solutions but use them mainly to rank individuals. This paper treats the evaluated solutions as the spot heights of a topographic survey and draws the contour lines they imply. The contour map decomposes the evaluated region into peaks: in two dimensions a contour tree with persistence separates significant peaks from interpolation ripples, and in more dimensions hill climbing on the interpolated surface locates the peaks and ray-cast level sets describe them. A memory of the explored peaks directs the search to new ones. The data-supported contours of each peak are extrapolated to zero size by an area law, exact for quadratic peaks and second-order accurate for smooth ones, that estimates a peak's location, height and shape before it is sampled. A contour-assisted EA (CA-EA) inserts contour steps with local search and peak memory into a genetic algorithm (GA), differential evolution or particle swarm optimization. A contour-assisted surrogate-assisted EA (CA-SAEA), for expensive problems, spends each evaluation on surrogate-screened offspring or on sampling around a peak, entered at the maximum of the interpolated surface. On 2-D benchmarks, CA-EA reduces the evaluations a plain GA needs by factors of 12 to 112; controls attribute its gain over classical memetic search to restarting local search on distinct peaks. On the CEC 2015 expensive suite in 10 and 30 dimensions, CA-SAEA has the second-best average rank, behind DYCORS and ahead of lq-CMA-ES and the competition winner MVMO, although in 30 dimensions MVMO wins significantly on 9 functions and loses on 6; there the map beats sampling around the best point on 5 of 15 functions and loses on 3. Entering the peaks at their extrapolated locations brought no gain at these budgets, although, with enough samples, it improves the estimated heights on most two-dimensional functions.
Abstract (translated)
URL
https://arxiv.org/abs/2611.15641
