An Improved Differential Evolution Algorithm for Numerical Optimization Problems

The differential evolution algorithm has gained popularity for solving complex optimization problems because of its simplicity and efficiency. However, it has several drawbacks, such as a slow convergence rate, high sensitivity to the values of control parameters, and the ease of getting trapped in local optima. In order to overcome these drawbacks, this paper integrates three novel strategies into the original differential evolution. First, a population improvement strategy based on a multi-level sampling mechanism is used to accelerate convergence and increase the diversity of the population. Second, a new self-adaptive mutation strategy balances the exploration and exploitation abilities of the algorithm by dynamically determining an appropriate value of the mutation parameters; this improves the search ability and helps the algorithm escape from local optima when it gets stuck. Third, a new selection strategy guides the search to avoid local optima. Twelve benchmark functions of different characteristics are used to validate the performance of the proposed algorithm. The experimental results show that the proposed algorithm performs significantly better than the original DE in terms of the ability to locate the global optimum, convergence speed, and scalability. In addition, the proposed algorithm is able to find the global optimal solutions on 8 out of 12 benchmark functions, while 7 other well-established metaheuristic algorithms, namely NBOLDE, ODE, DE, SaDE, JADE, PSO, and GA, can obtain only 6, 2, 1, 1, 1, 1, and 1 functions, respectively. Doi: 10.28991/HIJ-2023-04-02-014 Full Text: PD

Evolutionary framework with reinforcement learning-based mutation adaptation

Although several multi-operator and multi-method approaches for solving optimization problems have been proposed, their performances are not consistent for a wide range of optimization problems. Also, the task of ensuring the appropriate selection of algorithms and operators may be inefficient since their designs are undertaken mainly through trial and error. This research proposes an improved optimization framework that uses the benefits of multiple algorithms, namely, a multi-operator differential evolution algorithm and a co-variance matrix adaptation evolution strategy. In the former, reinforcement learning is used to automatically choose the best differential evolution operator. To judge the performance of the proposed framework, three benchmark sets of bound-constrained optimization problems (73 problems) with 10, 30 and 50 dimensions are solved. Further, the proposed algorithm has been tested by solving optimization problems with 100 dimensions taken from CEC2014 and CEC2017 benchmark problems. A real-world application data set has also been solved. Several experiments are designed to analyze the effects of different components of the proposed framework, with the best variant compared with a number of state-of-the-art algorithms. The experimental results show that the proposed algorithm is able to outperform all the others considered.</p

Improved Multi-Population Differential Evolution for Large-Scale Global Optimization

Differential evolution (DE) is an efficient population-based search algorithm with good robustness, however, it is challenged to deal with high-dimensional problems. In this paper, we propose an improved multi-population differential evolution with best-and-current mutation strategy (mDE-bcM). The population is divided into three subpopulations based on the fitness values, each of subpopulations uses different mutation strategy. After crossover, mutation and selection, all subpopulations are updated based on the new fitness values of their individuals. An improved mutation strategy is proposed, which uses a new approach to generate base vector that is composed of the best individual and current individual. The performance of mDE-bcM is evaluated on a set of 19 large-scale continuous optimization problems, a comparative study is carried out with other state-of-the-art optimization techniques. The results show that mDE-bcM has a competitive performance compared to the contestant algorithms and better efficiency for large-scale optimization problems

Improving the multi-objective evolutionary optimization algorithm for hydropower reservoir operations in the California Oroville-Thermalito complex

This study demonstrates the application of an improved Evolutionary optimization Algorithm (EA), titled Multi-Objective Complex Evolution Global Optimization Method with Principal Component Analysis and Crowding Distance Operator (MOSPD), for the hydropower reservoir operation of the Oroville-Thermalito Complex (OTC) - a crucial head-water resource for the California State Water Project (SWP). In the OTC's water-hydropower joint management study, the nonlinearity of hydropower generation and the reservoir's water elevation-storage relationship are explicitly formulated by polynomial function in order to closely match realistic situations and reduce linearization approximation errors. Comparison among different curve-fitting methods is conducted to understand the impact of the simplification of reservoir topography. In the optimization algorithm development, techniques of crowding distance and principal component analysis are implemented to improve the diversity and convergence of the optimal solutions towards and along the Pareto optimal set in the objective space. A comparative evaluation among the new algorithm MOSPD, the original Multi-Objective Complex Evolution Global Optimization Method (MOCOM), the Multi-Objective Differential Evolution method (MODE), the Multi-Objective Genetic Algorithm (MOGA), the Multi-Objective Simulated Annealing approach (MOSA), and the Multi-Objective Particle Swarm Optimization scheme (MOPSO) is conducted using the benchmark functions. The results show that best the MOSPD algorithm demonstrated the best and most consistent performance when compared with other algorithms on the test problems. The newly developed algorithm (MOSPD) is further applied to the OTC reservoir releasing problem during the snow melting season in 1998 (wet year), 2000 (normal year) and 2001 (dry year), in which the more spreading and converged non-dominated solutions of MOSPD provide decision makers with better operational alternatives for effectively and efficiently managing the OTC reservoirs in response to the different climates, especially drought, which has become more and more severe and frequent in California

Optimization of fed-batch fermentation processes using the Backtracking Search Algorithm

Fed-batch fermentation has gained attention in recent years due to its beneficial impact in the economy and productivity of bioprocesses. However, the complexity of these processes requires an expert system that involves swarm intelligence-based metaheuristics such as Artificial Algae Algorithm (AAA), Artificial Bee Colony (ABC), Covariance Matrix Adaptation Evolution Strategy (CMAES) and Differential Evolution (DE) for simulation and optimization of the feeding trajectories. DE traditionally performs better than other evolutionary algorithms and swarm intelligence techniques in optimization of fed-batch fermentation. In this work, an improved version of DE namely Backtracking Search Algorithm (BSA) has edged DE and other recent metaheuristics to emerge as superior optimization method. This is shown by the results obtained by comparing the performance of BSA, DE, CMAES, AAA and ABC in solving six fed batch fermentation case studies. BSA gave the best overall performance by showing improved solutions and more robust convergence in comparison with various metaheuristics used in this work. Also, there is a gap in the study of fed-batch application of wastewater and sewage sludge treatment. Thus, the fed batch fermentation problems in winery wastewater treatment and biogas generation from sewage sludge are investigated and reformulated for optimization

Memetic Differential Evolution with an Improved Contraction Criterion

Memetic algorithms with an appropriate trade-off between the exploration and exploitation can obtain very good results in continuous optimization. In this paper, we present an improved memetic differential evolution algorithm for solving global optimization problems. The proposed approach, called memetic DE (MDE), hybridizes differential evolution (DE) with a local search (LS) operator and periodic reinitialization to balance the exploration and exploitation. A new contraction criterion, which is based on the improved maximum distance in objective space, is proposed to decide when the local search starts. The proposed algorithm is compared with six well-known evolutionary algorithms on twenty-one benchmark functions, and the experimental results are analyzed with two kinds of nonparametric statistical tests. Moreover, sensitivity analyses for parameters in MDE are also made. Experimental results have demonstrated the competitive performance of the proposed method with respect to the six compared algorithms

Desenvolvimento de um Algoritmo de Decomposição Híbrido Bioinspirado Baseado em Baleias e Estratégias de Evolução Diferencial para Otimização Multiobjetivo

A Multiobjective Optimization Problem (MOP) requires the optimization of several objective functions simultaneously, usually in conflict with each other. One of the most efficient algorithms for solving MOPs is MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition), which decomposes a MOP into single-objective optimization subproblems and solves them using information from neighboring subproblems. MOEA/D variants with other evolutionary operators have emerged over the years, improving their efficiency in various MOPs. Recently, the IWOA (Improved Whale Optimization Algorithm) was proposed, an optimization algorithm bioinspired by the whale hunting method hybridized with Differential Evolution, which presented excellent results in single-objective optimization problems. This work proposes the MOEA/D-IWOA algorithm, which associates characteristics of the evolutionary operators of the IWOA to MOEA/D. Computational experiments were accomplished to analyze the performance of the MOEA/D-IWOA in benchmark MOPs suites. The results were compared with those obtained by the MOEA/D, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Third Evolution Step of Generalized Differential Evolution (GDE3), Improving the Strength Pareto Evolutionary Algorithm (SPEA2), and Indicator-Based Evolutionary Algorithm (IBEA) algorithms in the Hypervolume and Inverted Generational Distance Plus (IGD+) indicators. The MOEA/D-IWOA proved to be competitive, with a good performance profile, in addition to presenting the best results in some POMs.Um Problema de Otimização Multiobjetivo (POM) requer a otimização de várias funções objetivo simultaneamente, geralmente conflitantes entre si. Um dos algoritmos mais eficientes para resolver POMs é o MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition), que decompõe um POM em subproblemas de otimização monobjetivo, isto é, com uma única função objetivo a ser minimizada, e os resolve usando informações de subproblemas vizinhos. Variantes do MOEA/D com outros operadores evolutivos surgiram ao longo dos anos, melhorando sua eficiência em diversos POMs. Recentemente foi proposto o IWOA (Improved Whale Optimization Algorithm), um algoritmo de otimização bioinspirado no método de caça das baleias hibridizado com Evolução Diferencial que apresentou ótimos resultados em problemas de otimização monobjetivo. Esse trabalho propõe o algoritmo MOEA/D-IWOA, que extende o IWOA para resolver POMs associando características dos seus operadores evolutivos ao MOEA/D. Experimentos computacionais para analisar o desempenho do MOEA/D-IWOA em POMs benchmark foram realizados e os resultados comparados aos obtidos pelos algoritmos bem conhecidos da literatura, a saber, MOEA/D, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Third Evolution Step of Generalized Differential Evolution (GDE3), Improving the Strength Pareto Evolutionary Algorithm (SPEA2) e Indicator-Based Evolutionary Algorithm (IBEA) nos indicadores Hypervolume e Inverted Generational Distance Plus (IGD+). O MOEA/D-IWOA se mostrou competitivo, com bom perfil de desempenho, além de apresentar os melhores resultados em alguns POMs

Multi-threshold Segmentation for Color Image Based on Pyramid Evolution Strategy

In view of the fact that traditional intelligent optimization algorithms for multi-threshold segmentation of color images fall to consider the competition and cooperation between populations,which results in local optimization problems that affect the segmentation effect.In order to improve the segmentation effect,an improved pyramid evolution strategy (IPES) is proposed.The algorithm designs an adaptive search operator suitable for the multi-threshold segmentation problem of color images;expands the search space at all levels,improves the optimization ability of the algorithm;takes Otsu as the optimization goal and uses the competition and cooperation relationship between populations to solve the local optimization problem,thereby improving the accuracy of the solution and the effect of segmentation.The performance of IPES is tested on existing standard test images and compared with other eight algorithms.Experimental results show that the peak signal-to-noise ratio of the image segmented by IPES algorithm is between 28~35 dB,which is at least 10 dB higher than that of the improved tree-seed algorithm and traditional particle swarm algorithm and differential evolution algorithm;the structural similarity is between 89%~97%,increased by at least 3%.The image quality after segmentation is better and the structural similarity is higher.Therefore,the algorithm has good perfor-mance in solving multi-threshold segmentation problem of color images

Improvements of real coded genetic algorithms based on differential operators preventing premature convergence

This paper presents several types of evolutionary algorithms (EAs) used for global optimization on real domains. The interest has been focused on multimodal problems, where the difficulties of a premature convergence usually occurs. First the standard genetic algorithm (SGA) using binary encoding of real values and its unsatisfactory behavior with multimodal problems is briefly reviewed together with some improvements of fighting premature convergence. Two types of real encoded methods based on differential operators are examined in detail: the differential evolution (DE), a very modern and effective method firstly published by R. Storn and K. Price, and the simplified real-coded differential genetic algorithm SADE proposed by the authors. In addition, an improvement of the SADE method, called CERAF technology, enabling the population of solutions to escape from local extremes, is examined. All methods are tested on an identical set of objective functions and a systematic comparison based on a reliable methodology is presented. It is confirmed that real coded methods generally exhibit better behavior on real domains than the binary algorithms, even when extended by several improvements. Furthermore, the positive influence of the differential operators due to their possibility of self-adaptation is demonstrated. From the reliability point of view, it seems that the real encoded differential algorithm, improved by the technology described in this paper, is a universal and reliable method capable of solving all proposed test problems.Comment: 23 pages, 2 figures, 4 table