Differential Evolution with wavelet basis function based parameter control and dimensional interchange for diversity enhancement

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 (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.

An adaptive differential evolution with opposition-learning based diversity enhancement

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.

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

Differential evolution (DE) is a simple and efficient technique for real parameter optimization over continuous spaces. Its success is highly dependent on the choice of correct trial vector generation strategies and control parameters. Choosing appropriate trial vector generation strategies and control parameters for new problems by trial and error method can be computationally costly and inefficient. This paper proposes a hybrid approach, incorporating genetic programming (GP) with DE, where GP generates trial vector generation strategies based on the problem specification and the state of the population using a simple learning method. Trial vector generation strategies are chosen from this pool of strategies generated by GP. The choice of a particular strategy depends on the type of the problem, initialization values and state of evolution. Consequently, the strategies chosen for different run of the same problem are different. However, it allows self-adaptation to be completely problem dependent and as a result for a unknown problem domain the method is expected to perform better than other state-of-the-art self-adaptive evolutionary techniques. In this method, the control parameter F is eliminated and crossover ratio Cr is evolved with the population and population size NP is still fixed empirically. The performance of this method is extensively evaluated using the CEC2005 contest test instances. Experimental results show that, self-adaptive genetically programmed differential evolution (SaGPDE) leads to quick convergence and produce very competitive results.

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.

The differential evolution, one of the most powerful nature inspired algorithm is used to solve the real world problems. This algorithm takes minimum number of function evaluations to reach near to global optimum solution. Although its performance is very good, yet it suffers from the problem of st agnation. In this paper, some new mutation strategies are proposed to improve the performance of differential evolution (DE). The proposed method adds one more vector named as Homeostasis mutation vector in the existing mutation vectors to provide more bandwidth for selecting effective mutant solutions. The proposed approach provides more promising solutions to guide the evolution and helps DE escaping the situation of stagnation. Performance of proposed algorithm is compared with other state-of-the-art algorithms on COCO (Comparing Continuous Optimizers) framework. The result verifies that our proposed Homeostasis mutation strategy outperform most of the state-of-the-art DE variants and other state-of-the-art population based optimization algorithms.

Differential Evolution (DE) is a simple and effective stochastic algorithm for optimization problems, and it became much more popular in recent year because of its easy-implementation and excellent performance. Nevertheless, the performance of DE algorithm is greatly affected by the trial vector generation strategy including mutation strategy and parameter control, both of which still exist some weaknesses, e.g. the premature convergence to some local optima of a mutation strategy and the misleading interaction among control parameters. Therefore in this paper, a novel Di-DE algorithm is proposed to tackle these weaknesses. A depth information based external archive was advanced in our novel mutation strategy, which can get a better perception of the landscape of objective in an optimization. Moreover, a novel grouping strategy was also employed in Di-DE and parameters were updated separately so as to avoid the misleading among parameters. Moreover, a cooperative strategy for information interchange was also advanced aiming at improving the efficiency of the exploration behavior. By absorbing these advancements, the novel Di-DE algorithm can secure better performance in comparison with other famous optimization algorithms. The algorithm validation was conducted on CEC2013 and CEC2017 test suites, and the results revealed the competitiveness of our Di-DE algorithm in comparison with those famous optimization algorithms including Particle Swarm Optimization (PSO) variants, QUasi-Affine TRansformation Evolution (QUATRE) variants and Differential Evolution (DE) variants.

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

Memetic algorithms (MAs) are population-based meta-heuristic search algorithms that combine the composite benefits of natural and cultural evolutions. An adaptive MA (AMA) incorporates an adaptive selection of memes (units of cultural transmission) from a meme pool to improve the cultural characteristics of the individual member of a population-based search algorithm. This paper presents a novel approach to design an AMA by utilizing the composite benefits of differential evolution (DE) for global search and Q-learning for local refinement. Four variants of DE, including the currently best self-adaptive DE algorithm, have been used here to study the relative performance of the proposed AMA with respect to runtime, cost function evaluation, and accuracy (offset in cost function from the theoretical optimum after termination of the algorithm). Computer simulations performed on a well-known set of 25 benchmark functions reveal that incorporation of Q-learning in one popular and one outstanding variants of DE makes the corresponding algorithm more efficient in both runtime and accuracy. The performance of the proposed AMA has been studied on a real-time multirobot path-planning problem. Experimental results obtained for both simulation and real frameworks indicate that the proposed algorithm-based path-planning scheme outperforms the real-coded genetic algorithm, particle swarm optimization, and DE, particularly its currently best version with respect two standard metrics defined in the literature.

Differential Evolution (DE) proved to be one of the most successful evolutionary algorithms for global optimization purposes in continuous problems. The core operator in DE is a mutation which can provide the algorithm with both exploration and exploitation. In this article, a new notation for DE is proposed which has a formula that can be utilized for generating and extracting novel mutations and by applying this new notation, four novel mutations are proposed. More importantly, by combining these novel trial vector generation strategies and four other well-known ones, we proposed Generalized Differential Evolution (GDE) that takes advantage of two mutation pools that have both explorative and exploitative strategies inside them. Results and experimental analysis are performed on CEC2005 benchmarks and the results stated that GDE is surprisingly competitive and significantly improved the performance of this algorithm.

Enhancing the search ability of differential evolution through orthogonal crossover

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

In artificial intelligence, evolutionary algorithms (EAs) have shown to be effective and robust in solving difficult optimization problems. EAs are generic populationbased metaheuristic optimization algorithms. The mechanisms used in EAs are inspired by biological evolution: reproduction, mutation, recombination, and selection. The development of EAs can be classified into two categories: single objective and multi-objective optimization. In this thesis, both single objective and multi-objective evolutionary algorithms have been studied. For single objective optimization, various niching techniques are integrated with differential evolution (DE) and particle swarm optimization (PSO) for multi-modal optimization. Multi-modal optimization deals with optimization tasks that involve finding all or most of the global/local peaks in one single run. EAs in their original forms are usually designed for locating one single global solution. To promote and maintain formation of multiple stable subpopulations within a single population, we introduced a neighborhood mutation technique to enhance DE with ability of handling multi-modal problems. We also proposed a locally informed PSO to tackle multi-modal optimization. Beside these, several existing niching techniques from the literature were modified and improved by us.