Differential evolution with orthogonal array‐based initialization and a novel selection strategy

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.

Enhancing the search ability of differential evolution through orthogonal crossover

Differential evolution with dynamic combination based mutation operator and two-level parameter adaptation strategy

Differential evolution using homeostasis adaption based mutation operator and its application for software cost estimation

Differential Evolution (DE) is a very simple but powerful Evolutionary Algorithm (EA) for real-world applications. There are two aspects affecting the overall optimization performance significantly, one is parameter control scheme and the other is trial vector generation strategy. As all the control parameters are employed in generating trial vectors, from this perspective of view, the trial vector generation strategy dominates the overall optimization performance. Therefore, trial vector generation strategies are often designed first, and then the corresponding parameter control schemes are well-tuned thereafter. Both of them constitute the main body of a new DE variant. Here in the paper, a novel DE variant with a new designed trial vector generation strategy as well as novel parameter control scheme is proposed to tackle freight trains scheduling problem. By incorporating both a time-stamp mechanism of the external archive and a novel parameter control scheme, the new algorithm can secure better optimization performance not only on man-made benchmarks but also on real-world applications. Both the man-made benchmarks from Congress on Evolutionary Computation (CEC) test suite and the real-world freight train scheduling problem are employed in the validation of the new DE variant. The experiment results show that it is competitive with other state-of-the-art DE techniques for these optimization problems.

Differential Evolution with exponential crossover can be also competitive on numerical optimization

Differential evolution (DE) is one of the most successful evolutionary algorithms (EAs) for global numerical optimization. Like other EAs, maintaining population diversity is important for DE to escape from local optima and locate a near-global optimum. Using a multi-population algorithm is a representative method to avoid early loss of population diversity. In this paper, we propose a multi-population DE algorithm (MPDE) which manipulates multiple sub-populations. Different sub-populations in MPDE exchange information via a novel mutation operation instead of migration used in most multi-population EAs. The mutation operation is helpful to balance the fast convergence and population diversity of the proposed algorithm. Moreover, the performance of MPDE is further improved by an adaptive parameter control scheme designed based on the multi-population approach. Each sub-population in MPDE evolves with its own set of control parameters, and a learning strategy is used to adaptively adjust the parameter values. A set of benchmark functions is used to test the proposed MPDE algorithm. The experimental results show that MPDE performs better than, or at least comparably, to the classical single population DE with fixed parameter values and three existing state-of-the-art DE variants.

Chapter Ten - Differential evolution

In recent years, many new variants of Differential Evolution (DE) have been proposed for real number function optimization, and most of these variants employ binomial recombination as their crossover operators. By contrast, another classical crossover operator, exponential recombination, received less attention. This paper examines the explorative ability of exponential recombination in handling high-dimensional multimodal problems. Based on the analysis, a new variant of DE with a hybrid crossover operation is proposed. DE/best/1, a greedy mutation strategy rarely used in tackling multimodal problems, is utilized in our algorithm to help combine the two basic recombination operators. Empirical results demonstrate that the proposed algorithm is powerful in solving high-dimensional multimodal problems.

Improved random selection strategy, self-adaptive crossover and mutation operators, population co-evolution algorithm are adopted in this paper to set up a new genetic algorithm(GA), guaranteeing the universality of population, the thoroughness of solution and the execution efficiency of algorithm in solving multi-process, process crossover, work-piece flow and other condition based scheduling problem of flexible manufacturing system(FMS). The problem of GA in solving FMS scheduling is summarized in this paper, reasons and countermeasures for GA's pre-maturing are studied, longitudinal and transverse comprehensive state-based correlative self-adaptive crossover and mutation operators are raised according to the analysis on GA to avoid local optimization and pre-maturity, the co-evolutionary GA is designed to solve the scheduling model for FMS, and the algorithm is validated for the scheduling of box-type parts for precise machine tools.

Differential evolution (DE) is well known for its simple structure and excellent performance among various evolutionary algorithms. Difference vectors have a dominant effect on the evolution progress. But the difference vectors in mutation operators for the conventional DE are simply generated by selecting individuals from the current population without any selective pressure. Besides, the directional information only depends on the existing individuals and hardly exploits the interaction between individuals. Therefore, a novel interactive information scheme called IIN is proposed to overcome this weakness. It attempts to provide more effective directional information during the evolution process and achieve a good balance between exploration and exploitation. In IIN, both the ranking information based on fitness and the interactive information between individuals is fully considered. The interaction between individuals is implemented by the mathematically weight-based combination according to ranking information. Hence, the interactive information inherited from existing individuals acts as a directional vector. In this way, IIN-DE utilizes the directional information to speed up convergence. The proposed scheme can be easily incorporated into different mutation strategies to provide useful directional information. To verify the effectiveness, the proposed IIN is incorporated into the original DEs based on several mutation operators as well as several state-of-art DE variants. With the incorporation of IIN, significant improvements can be achieved for most of the compared DEs, as demonstrated by the experimental results.

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

Differential Evolution (DE) is perhaps one of the most efficient and versatile evolutionary techniques and its different variants have been proposed in the recent past. However, all these variants often suffer from the shortcomings of slow and/or premature convergence. Further, nearest neighbour (NN) is a frequently used classifier in the domain of data mining but its primitive version is noise sensitive and shows low accuracy. Different data reduction methods such as prototype selection, prototype generation, and DE are widely used to mitigate these drawbacks of NN. However, none of the methods substantially avoids all these shortcomings. This paper proposes a new variant of DE that is based on the biological phenomenon of the centromeric location of chromosomes. The proposed ‘Chromosomes Identification based Differential Evolution (CIDE)’ extracts the knowledge from databases and constructs effective and reliable decision rules for classification. In this paper, the performance of the proposed CIDE technique is computed and compared with 1-NN classifier optimized by fourteen state-of-art variants of DE, and 1-R classifier using six-real datasets as well as KDDCup’99 dataset to illustrate its superiority over the 1-NN and 1-R classifier. Finally, the performance of CIDE is also compared with Naïve Bayes, support vector machine, Neural Network, and Random Forest for the KDDCup’99 dataset using different performance metrics.

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.

Differential evolution (DE), as a class of biologically inspired and meta-heuristic techniques, has attained increasing popularity in solving many real world optimization problems. However, DE is not always successful. It can easily get stuck in a local optimum or an undesired stagnation condition. This paper proposes a new DE algorithm Differential Evolution with Alopex-Based Local Search (DEALS), for enhancing DE performance. Alopex uses local correlations between changes in individual parameters and changes in function values to estimate the gradient of the landscape. It also contains the idea of simulated annealing that uses temperature to control the probability of move directions during the search process. The results from experiments demonstrate that the use of Alopex as local search in DE brings substantial performance improvement over the standard DE algorithm. The proposed DEALS algorithm has also been shown to be strongly competitive (best rank) against several other DE variants with local search.