Di-DE: Depth Information-Based Differential Evolution With Adaptive Parameter Control for Numerical Optimization

Particle Swarm Optimization or Differential Evolution—A comparison

Differential evolution (DE) is a powerful evolutionary algorithm for global optimization problems. Generally, appropriate mutation strategies and proper equilibrium between global exploration and local exploitation are significant to the performance of DE. From this consideration, in this paper, we present a novel DE variant, abbreviated to DMIE-DE, to further enhance the optimization capacity of DE by developing a dual mutations collaboration mechanism with elites guiding and inferiors eliminating techniques. More specifically, an explorative mutation strategy DE/current-to-embest with an elite individual serving as part of the difference vector and an exploitative mutation strategy DE/ebest-to-rand with selecting an elite individual as the base vector are employed simultaneously to achieve the balance between local and global performance of the whole population instead of only one mutation strategy in classical DE algorithm. The control parameters F and CR for above mutation strategies are updated adaptively to supplement the optimization ability of DMIE-DE based on a rational probability distribution model and the successful experience from the previous iterations. Moreover, an inferior solutions eliminating technique is embedded to enhance the convergence speed and compensate cost of the fitness evaluation times during the evaluation process. To evaluate the performance of DMIE-DE, experiments are conducted by comparing with five state-of-the-art DE variants on solving 29 test functions in CEC2017 benchmark set. The experimental results indicate that the performance of DMIE-DE is significantly better than, or at least comparable to the considered DE variants.

Particle swarm optimization (PSO) algorithm has shown promising performances on various benchmark functions and engineering optimization problems. However, it is still difficult to achieve a satisfying trade-off between exploration and exploitation for all the optimization problems and different evolving stages. Furthermore, control parameters of some related mechanisms need pre-experience by the requirement of trial-and-error scheme. This paper presents a novel PSO algorithm, which adaptively adopts various search strategies, called Self-adapting Hybrid Strategy PSO (SaHSPS). Unlike some other peer PSO variants, this method dynamically changes the probabilities of different strategies according to their previous successful searching memories, without any additional control parameters. The probabilities of different strategies would be re-initialized according to a proposed dynamic probabilistic model to diverse the population. Besides, particles are updated by probabilistically selected strategies after niching PSO with Ring topology. Moreover, a dynamic updating mechanism by niching PSO is proposed to guarantee the parallel searching capability during the whole evolution process. Thus, this proposed algorithm might be problem-independent and search-stage-independent, yielding more satisfying solutions on various optimization problems. A comprehensive experimental study is conducted on 28 benchmark functions of CEC 2013 special session on real-parameter optimization, including shifted, rotated, multi-modal, high conditioned, expanded and composition problems, compared with several state-of-the-art variants of PSO and differential evolution (DE) algorithms. Comparison results show that SaHSPS obtains outstanding performances on the majority of the test problems. Moreover, a practical engineering problem, real power loss minimization of IEEE 30-bus power system, is used to further evaluate SaHSPS. The numerical results, compared with other stochastic search algorithms, show that SaHSPS could find high-quality solutions with higher probability.

Differential Evolution (DE) algorithm generates a population of individuals by encoding with a floating point vector, and it is a simple and effective population-based stochastic optimization algorithm for global optimization of continuous space. Because of its excellent performance, DE variants can be applied in a wide range of applications in science and engineering. However, the performance of DE is sensitive to the choice of trial vector generation strategy and the associated control parameters. Therefore, it is necessary to choose appropriate mutation strategy and control parameters when tackling optimization applications. In this paper, an adaptive update mechanism is proposed to update control parameters F and Cr . The experimental results are verified on the CEC 2013 test suite which contains 28 benchmark functions for the evaluation of single objective real parameter optimization. The proposed algorithm is compared with jDE, iwPSO and ccPSO, and experiment results show its good performance.

This paper investigates the suitability of the Particle Swarm Optimization (PSO) and the Differential Evolution (DE) algorithms in solving expensive optimization problems. Eight PSO variants, and eight DE variants are experimentally compared among each other. The Comparing Continuous Optimizers (COCO) methodology was adopted in comparing these variants on the noiseless BBOB test bed. Based on the results, we provide useful insights regarding the algorithms' relative efficiency and effectiveness under an expensive budget of function evaluations, and draw suggestions about which algorithm should be used depending on what we know about our optimization problem in terms of evaluation budget, dimensionality, and function structure. Furthermore, we propose possible future research directions addressing the algorithms limitations. Overall, DE variants perform well in low dimensions, whereas in higher dimensions, several PSO variants surpass DE algorithms. Among the top performers, JADE and χPSO are the robust algorithms for solving expensive budget problems.

Optimisation of mooring line parameters for offshore floating structures: A review paper

Several contemporary algorithms, including cuckoo search (CS), were applied to the CEC 2017 problem set, which includes a wide variety of 120 very difficult subproblems. We found that the algorithms were ineffective, especially when the number of dimensions was high. We configured several usage patterns of Linnik flight with the inverse of the golden ratio (1/Φ) to replace Lévy flight in CS, resulting in a new search mechanism that increased the efficiency of the CS algorithm. The impacts of each Linnik flight usage pattern were evaluated using the CEC 2017. The experimental results showed that: 1) CS variants that used Linnik flight were more capable than CS variants that used Lévy flight and 2) CS variants that used a mixture of Linnik flight and quantum-behaved mechanisms were even more capable. The primary effect of Linnik flight is the strengthening of the ranking, while that of the quantum-behaved mechanisms is a decreased error. A chaotic-initialized quantum-Linnik flight CS (CQLCS) algorithm is proposed. Among the 66 competitive methods applied to the CEC 2017, CQLCS ranked first and won the contemporary competitive algorithms section, which also included several advanced variants of differential evolution (DE) and particle swarm optimization (PSO) algorithms. The CQLCS could potentially be improved further by adjusting the probability of the occurrence of Linnik flight. The processes for building improved variants were analyzed to discover how, or if, this improvement could be achieved. Finally, the CQLCS algorithm required fewer lines of code to run than did the DE and PSO variants.

In this paper, a novel hybrid intelligent algorithm, integrating with differential evolution (DE) and particle swarm optimization (PSO), is proposed. Initially, all individual in the population are divided into three groups (in increasing order of function value): inferior group, mid-group, and superior group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. The proposed method uses DE-PSO-DE, then it is denoted by DPD. At present, many mutation strategies of DE are reported. Every mutation strategy has its own pros and cons, so which one of them should be selected is critical for DE. Therefore, over 8 mutation strategies, the best one is investigated for both DEs used in DPD. Moreover, two strategies, namely elitism (to retain the best obtained values so far) and Non-redundant search (to improve the solution quality), have been employed in DPD cycle. Combination of 8 mutation strategies generated 64 different variants of DPD. Top 4 DPDs are investigated through solving a set of constrained benchmark functions. Based on the ‘performance,’ best DPD is reported and further used in solving engineering design problem.

A self-adaptive differential evolution with dynamic selecting mutation strategy (DSMSDE) is proposed to improve the performance of differential evolution algorithm by three improvements. Mutation strategies are dynamically selected, and the successfully updated individuals are stored into the archive, which is beneficial for improving the convergence performance. A mechanism that is related to the best individual at the current population is employed to help the stagnation solutions to get rid of local minima. Self-adaptive parameters control is used to accelerate the convergence speed. DSMSDE is compared with the other state-of-the-art algorithms, and they are tested on nine benchmark functions. Experimental results show that DSMSDE has higher accuracy, faster speed and better reliability.

An improved multi-population ensemble differential evolution

Differential Evolution (DE) is a simple, powerful and easy to use global optimization algorithm. DE has been studied in detail by many researchers in the past years. In DE algorithm trial vector generation strategies have a significant influence on its performance. This research studies that whether performance of DE algorithm can be improved by incorporating selection advancement in effective trial vector generation strategies. A novel advancement in DE trial vector generation strategies is proposed in this research to speeds up the convergence speed of DE algorithm. The proposed fitness proportion based random vector selection DE (FPRVDE) is based on the proportion of individual fitness mechanism. FPRVDE reduces the role of poor performing individuals to enhance it performance capability of DE algorithm. To form a trial vector using FPRVDE, individual based on the proportion of their fitness are selected. FPRVDE mechanism is applied to most commonly used set of DE variants. A comprehensive set of multidimensional function optimization problems is used to access the performance of FPRVDE. Experimental result shows that proposed approach accelerates DE algorithm.

This paper proposes a novel distributed differential evolution framework called distributed mixed variants (dynamic) differential evolution ( $$dmvD^{2}E)$$ d m v D 2 E ) . This novel framework is a heterogeneous mix of effective differential evolution (DE) and dynamic differential evolution (DDE) variants with diverse characteristics in a distributed framework to result in $$dmvD^{2}E$$ d m v D 2 E . The $$dmvD^{2}E$$ d m v D 2 E , discussed in this paper, constitute various proportions and combinations of DE/best/2/bin and DDE/best/2/bin as subpopulations with each variant evolving independently but also exchanging information amongst others to co-operatively enhance the efficacy of $$dmvD^{2}E$$ d m v D 2 E as whole. The $$dmvD^{2}E$$ d m v D 2 E variants have been run on 14 test problems of 30 dimensions to display their competitive performance over the distributed classical and dynamic versions of the constituent variants. The $$dmvD^{2}E$$ d m v D 2 E , when benchmarked on a different 13 test problems of 500 as well as 1,000 dimensions, scaled well and outperformed, on an average, five existing distributed differential evolution algorithms.

In swarm intelligence, Particle Swarm Optimization (PSO) and Differential Evolution (DE) have been successfully applied in many optimization tasks, and a large number of variants, where novel algorithm operators or components are implemented, has been introduced to boost the empirical performance. In this paper, we first propose to combine the variants of PSO or DE by modularizing each algorithm and incorporating the variants thereof as different options of the corresponding modules. Then, considering the similarity between the inner workings of PSO and DE, we hybridize the algorithms by creating two populations with variation operators of PSO and DE respectively, and selecting individuals from those two populations. The resulting novel hybridization, called PSODE, encompasses most up-to-date variants from both sides, and more importantly gives rise to an enormous number of unseen swarm algorithms via different instantiations of the modules therein. In detail, we consider 16 different variation operators originating from existing PSO- and DE algorithms, which, combined with 4 different selection operators, allow the hybridization framework to generate 800 novel algorithms. The resulting set of hybrid algorithms, along with the combined 30 PSO- and DE algorithms that can be generated with the considered operators, is tested on the 24 problems from the well-known COCO/BBOB benchmark suite, across multiple function groups and dimensionalities.

Analysis of causality-driven changes of diffusion speed in non-Markovian temporal networks generated on the basis of differential evolution dynamics

Differential evolution improved with self-adaptive control parameters based on simulated annealing