Shuffle or update parallel differential evolution for large-scale optimization

Abstract

This paper proposes a novel algorithm for large-scale optimization problems. The proposed algorithm, namely shuffle or update parallel differential evolution (SOUPDE) is a structured population algorithm characterized by sub-populations employing a Differential evolution logic. The sub-populations quickly exploit some areas of the decision space, thus drastically and quickly reducing the fitness value in the highly multi-variate fitness landscape. New search logics are introduced into the subpopulation functioning in order to avoid a diversity loss and thus premature convergence. Two simple mechanisms have been integrated in order to pursue this aim. The first, namely shuffling, consists of randomly rearranging the individuals over the sub-populations. The second consists of updating all the scale factors of the sub-populations. The proposed algorithm has been run on a set of various test problems for five levels of dimensionality and then compared with three popular meta-heuristics. Rigorous statistical and scalability analyses are reported in this article. Numerical results show that the proposed approach significantly outperforms the meta-heuristics considered in the benchmark and has a good performance despite the high dimensionality of the problems. The proposed algorithm balances well between exploitation and exploration and succeeds to have a good performance over the various dimensionality values and test problems present in the benchmark. It succeeds at outperforming the reference algorithms considered in this study. In addition, the scalability analysis proves that with respect to a standard Differential Evolution, the proposed SOUPDE algorithm enhances its performance while the dimensionality grows.

A directional mutation operator for differential evolution algorithms

“…It is well known that with the increase of problem dimension, the complexity of the problem increases exponentially [53]. The algorithms that have a good performance on relatively low dimension (D ≤ 100) maybe not applicable to high dimension problems (D ≥ 1000).…”

“…For each algorithm and each test function, 25 independent runs are executed with 5000D FEs as termination criterion. It is known that the solution space of the problem increases exponentially with the increase of the problem dimension [53]. Many algorithms suffer from the "curse of dimensionality", thus the experiment of D = 1000 can give a hint about the scalability of algorithms.…”

Multi-population differential evolution with balanced ensemble of mutation strategies for large-scale global optimization

“…They can be categorized into three main groups. The first group develops self-adaptive techniques capable of choosing appropriate mutation strategies and/or suitable population topologies and/or the best values for the control parameters [24][25][26][27]. The second group is to merge the DE technique with other types of evolutionary algorithms or local search [28][29][30].…”

“…Seven DE-based algorithms [24][25][26]31,[33][34][35] among thirteen were published in the special issue on scalability of evolutionary and other metaheuristic algorithms for large-scale continuous optimization problems. This is an indication of the usefulness of the DE algorithm for solving LSGO problems.…”

Benchmarking NLopt and state-of-the-art algorithms for continuous global optimization via IACOR

“…0e+08 A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A11 A12 A13 A14 A15 A16 A17 A18 A19 A20 A21 A22 A23 A24 A25 A26 A28 A29 A30 A31 A32 A33 A34 A35 A36 A37 A38 A39 A40 A41 Figure 4: Ranking of all algorithms based upon the sum of average and median errors on SOCO benchmarks coded CHC algorithm (CHC) [15], Shuffle Or Update Parallel Differential Evolution (SOUPDE) [65], DE − D 4 0 + M m [18], Generalized Opposition-based Differential Evolution (GODE) [64], Generalized Adaptive Differential Evolution (GADE) [70], jDElscop [4], Self-adaptive Differential Evolution with Multi-Trajectory Search (SaDE-MMTS) [74], MOS-DE [31], MA-SSW-Chains [40], Restart Particle Swarm Optimization with Velocity Modulation (RPSO-VM) [19], Tuned IPSOLS [10] EVO-PROpt [12], EM323 [20] and VXQR [42] among others.…”