Multipopulation-Based Differential Evolution with Speciation-Based Response to Dynamic Environments

Abstract

Abstract. Unlike static optimization problems, the position, height and width of the peaks may vary with time instances in dynamic optimization problems (DOPs). Many real world problems are dynamic in nature. Evolutionary Algorithms (EAs) have been considered to solve the DOPs in the recent years. This article proposes a multi-population based Differential Evolution algorithm which uses a local mutation to control the perturbation of individuals and also avoid premature convergence. An exclusion rule is used to maintain the diversity in a subpopulation to cover a larger search space. Speciation-based memory archive has been used to utilize the previously found optimal information in the new change instance. Furthermore the proposed algorithm has been compared with four other state-of-the-art EAs over the Moving Peak Benchmark (MPB) problem and a benchmarks set named Generalized Dynamic Benchmark Generator (GDBG) proposed for the 2009 IEEE Congress on Evolutionary Computation (CEC) competition.Keywords: Differential Evolution, local mutation, multi-population, dynamic optimization problems, speciation. IntroductionDifferential Evolution (DE) [1] is a very simple and popular algorithm for solving global optimization problems. It operates by means of computational steps which are similar to the EAs. However, unlike EAs, the members are perturbed by the scaled differences of the randomly taken and distinct vectors from the whole population. As it does not require any separate probability distribution, it is implicitly adaptive in this aspect. The popularity of DE is proliferating due to its simple structure, compactness, robustness and the parallel searching mechanism.Many real world problems are dynamic in nature. In case of DOPs, optimal solutions change with time. Hence we require algorithms that can detect the change in environment and should be able to track the optimum continuously [2]. A few dynamic real world problems are: price fluctuations, machine breakdown or maintenance, financial variations, stochastic arrival of new tasks etc. The main drawback of the conventional EAs under dynamic environment is loss of diversity,

A Survey of Evolutionary Continuous Dynamic Optimization Over Two Decades—Part B

“…[3], [81], [124]- [130] Moving valleys benchmark (MVB) c [131] Gaussian peaks benchmark (GPB) [15], [132] MPBs with local environmental changes d [133], [134] MPBs with cyclic and pendulum changes e [135]- [138] Multimodal MPB f [139] MPBs with varying number of peaks [140]- [143] MPBs whose peaks have different change severity g [186] Constrained MPBs h [187], [188] Modular MPBs i [144], [145], [173] DRPBG j [6], [75], [97], [106], [111], [114], [115], [146]- [148], [150]- [172], [174] Free [189]. Each peak has its own shift, height, and width severity values which result in generating peaks with different levels of robustness.…”

“…[2], [7]- [27] Moving peaks baselines b [3], [15], [18], [23], [25]- [173] Composition of basic static functions c [6], [75], [97], [106], [111], [114], [115], [146]- [148], [150]- [172], [174] Others d [24], [175]- [177] a Basic static functions include Sphere, Ackley, Rastrigin, Rosenbrock, and Griewank. b Including all baseline functions that generate a controllable number of peaks whose locations can change over time.…”

“…Best before change error [26], [27], [29], [41], [42], [51], [63], [72], [74], [75], [78], [82], [83], [87], [94], [97], [100], [106]- [108], [113]- [118], [121]- [123], [130], [134], [135], [137], [142]- [144], [147]- [162], [164]- [166], [168], [170], [172], [174], [194] Offline performance [18], [28], [35], [43], [62], [122], [126] Offline error (evaluation based) [15], [18], [22]- [25],…”

History-Driven Particle Swarm Optimization in dynamic and uncertain environments

“…Some of the presented results of the state-of-art algorithms are obtained by implementing the methods and some of them are extracted from the related references. In Tables 3-7, the efficiency of sixteen related algorithms including: mQSO [12], AmQSO [53], mPSO [54], HmPSO [55] APSO [56], FTMPSO [57], CESO [58], mNAFSA [59], PSO-AQ [60], CDEPSO [61], CellularDE [21], SFA [62], DynPopDE [25], MLDE-S [20], CbDE-wCA [23] and DPSABC [34] is compared with that of HdPSO. All simulations are performed on a PC with 2.8 GHz CPU and 8 GB memory.…”

“…In Table 8, the efficiency of the proposed algorithm on MPB with 10 peaks, shift severities of 1, 2, 3, 5, dimension of 5 and a change frequency of 5000 is compared with that of other ten algorithms including: mQSO [12], AmQSO [53], mCPSO [12], SPSO [63], rSPSO [64], PSO-CP [65], FTMPSO [57], SFA [62], MLDE-S [20], CbDE-wCA [23]. By increasing the value of shift severity, the process of tracking peaks becomes more complex, since the peaks move to further distances after each change in environment.…”