A Multi-objective Differential Evolutionary Algorithm Based on Spacial Distance

The Differential Evolution (DE) algorithm, under the family of Evolutionary Algorithms (EAs), is one of the powerful algorithms used for solving continuous parameter optimization challenges. The simplistic nature and robustness of the classical DE algorithm have drawn researchers' attention towards its progressive enhancement. This work reports on an investigation of the behavioral changes of the classical DE algorithm, evoked when its mutation and crossover components are fine tuned for enhancement of DE's performance. The scope of this study covers the implementation of a mutation level enhancement and a crossover level enhancement, followed by their integration. The mutation and the crossover components are augmented by incorporation of Centroid DE and Superior-Superior & Superior-Inferior DE logics, respectively. The algorithms appraised in this inquiry were classical DE, Centroid based DE(cDE), Superior-Superior based DE (ssDE), Superior-Inferior DE (siDE), Centroid Superior-Superior DE (cssDE) and Centroid Superior-Inferior DE (csiDE). These algorithms were evaluated by comparison of the values of their mean objective function (MOV), and their speed, at solving the global optimization problems in a simple benchmarking function suite with 4 functions of different categories. The study concludes that the DE algorithm shows enhancement performance with modified mutation and crossover components. However, with a trend for inconsistency for varying values of its control parameters and benchmarking problems.

In this paper we present an empirical , comparative performance, analysis of fourteen variants of Differential Evolution (DE) and Multiple Trial Vectors Differential Evolution algorithms to solve unconstrained global optimization problems. The aim is (1) to compare Multiple Trial Vectors DE, which allows each parent vector in the population to generate more than one trial vector, against the classical DE and (2) to identify the competitive variants which perform reasonably well on problems with different features. The DE and Multiple Trial Vectors DE variants are benchmarked on 6 test functions grouped by features --- unimodal separable, unimodal nonseparable, multimodal separable and multimodal non-separable. The analysis identifies the competitive variants and shows that Multiple Trial Vectors DE compares well with the classical DE.

Environmental/economic power dispatch problem using multi-objective differential evolution algorithm

Differential evolution is a simple yet efficient heuristic originally designed for global optimization over continuous spaces that has been used in many research areas. The question how to improve its performance is still popular and during the years, many successful methods dealing with optimal setting or hybridization of the control parameters were proposed. In this paper, we propose a novel approach based on modeling of the differential evolution dynamics by complex networks. In each generation, the individuals are mapped to the nodes and the relationships between them are modeled by the edges of the graph. Thanks to this simple visualization, the interconnection between the differential evolution convergence speed and the weighted clustering coefficients has been revealed. As a consequence, we have focused on the parents selection in the mutation step where the individuals are not selected randomly as usual but on the basis of their weighted clustering coefficients. Our enhancement has been incorporated in the classical differential evolution, self-adaptive differential evolution (jDE) and differential evolution with composite trial vector generation strategies and control parameters. Finally, a set of well-known benchmark functions (including 21 functions) has been used to test and evaluate the performance of the proposed enhancement of the differential evolution. The experimental results and statistical analysis indicate that the enhanced algorithms perform better or at least comparable to their original versions and the analysis of the differential evolution dynamics with the aim of the complex network might be an effective tool to improve the differential evolution convergence in the future.

A new mutation concept is proposed to generalize local selection based Differential Evolution algorithm to work in general multi-modal problems. Three variations of the proposed method are compared with classic Differential Evolution algorithm using a set of five well known test functions and their variants. The general idea of the new mutation operation is to divide the mutation into two parts: the local and global mutation. The global mutation works as a migration operator allowing the algorithm perform global search efficiently, while the local mutation improves the efficiency of local search.The results show that the concept of global mutation is able to generalize the good performance of local selection based Differential Evolution from convex uni-modal functions to general non-convex and multi-modal problems. Among the tested functions, the new method was able to outperform the classic Differential Evolution in all butone. A limited analysis of the effects of control parameters to the performance of the algorithm is also done.

A Differential Evolution Clustering algorithm with weighted validity function is presented in this paper, five validity functions are selected to form the fitness function with weights, and in selection of Differential Evolution, individuals not being selected are put into secondary population. During evolution, individuals in secondary population replace those in main population if their fitness values are less than those in main population. We have carried out experiments on 3 datasets from UCI machine learning repository and compared validity results to those from K-Means and classical Differential Evolution, experimental results show that our approach can improve clustering performance.

Social learning differential evolution

This study presents the multi-objective cropping pattern modeling of a farm in the Vaalharts irrigation scheme (VIS) in South Africa. The cropping pattern model presents three objectives and three constraints. The objectives are to maximize the total net benefit (NB) in monetary terms (South African Rand, ZAR) generated by planting four different crops, maximize total agricultural output (tons) and minimize the irrigation water use (m3). The total farm size is 77.1 ha while the total available water for irrigation is 9,140 m3 per ha/annum. Multi-objective differential evolution algorithm (MDEA) which is a stochastic multi-objective evolutionary algorithm recently developed was used to solve the multi-objective model in this study. The model produced non-dominated solutions that converge to Pareto optimal front. The averages of total net benefit, total agricultural output, total irrigation water and total area planted are ZAR 882 890.63, 3 439 518.75 tons, 702 522.50 m3 and 661 444.06 m2 respectively with corresponding average planting areas of 416 680, 53 030, 87 620 and 212 410 m2 for maize, groundnut, Lucerne and Pecan nuts respectively. It is concluded that MDEA is a good optimizer for multi-objective cropping pattern model for generating maximum agricultural output for the farmers in the area with the constraints of land and water availabilities. Key words: Cropping pattern, irrigation, agricultural output, differential evolution, non-dominated solutions.

Differential Evolution (DE) is an algorithm to solve possibly nonlinear and non-differentiable global optimization problems. Classical Differential Evolution (CDE) employs a synchronous generation-based evolution strategy. We propose a modification of the CDE algorithm by incorporating mutation, crossover and selection operations into an asynchronous strategy. A novel Asynchronous Differential Evolution (ADE) is well suited for parallel optimization. Moreover even in the sequential mode its rate of convergence is competitive to CDE. The performance of the Asynchronous Differential Evolution is reported on a set of benchmark functions.

This paper presents a cooperative differential evolution (DE) with multiple populations for multiobjective optimization. The proposed algorithm has M single-objective optimization subpopulations and an archive population for an M -objective optimization problem. An adaptive DE is applied to each subpopulation to optimize the corresponding objective of the multiobjective optimization problem (MOP). The archive population is also optimized by an adaptive DE. The archive population is used not only to maintain all nondominated solutions found so far but also to guide each subpopulation to search along the whole Pareto front. These (M+1) populations cooperate to optimize all objectives of the MOP by using adaptive DEs. Simulation results on benchmark problems with two, three, and many objectives show that the proposed algorithm is better than some state-of-the-art multiobjective DE algorithms and other popular multiobjective evolutionary algorithms. The online search behavior and parameter sensitivity of the proposed algorithm are also investigated.

Simultaneous optimization of two or more objectives is an instance of multi-objective optimization (MOO). However, for most of the Multi-Objective Problems (MOPs), no single solution can optimize all the objective functions simultaneously. Evolutionary algorithms are a type of optimization algorithm used for constructing a well-distributed optimal front more quickly than a much more efficient approach. One of the most commonly used algorithms in this regard is differential evolution (DE). To solve the problem of non-dominated sorting for Multi-Objective DE (MODE), an approach is proposed that reduces the time complexity. DE is commonly recognized as one of the best methods for solving the MOPs. Several versions of DEs have been proposed for MOPs. This article proposes a novel mutation technique, named Environmental Parameter-based Multi-Objective Differential Evolution (EP-MODE) that acquires two additional environmental parameters to preserve diversity and accelerate the convergence. The proposed approach also reduces the time complexity of non-dominated sorting for Multi-Objective DE (MODE). The proposed mutation's performance has been evaluated on DTLZ series and ZDT series benchmark test functions on the Pareto-optimal front and compared with existing multi-objective algorithms (MODE and MODE-RMO). The solution comparatively verifies that the proposed EP-MODE outperforms most of the MODEs for lower dimension functions and higher functions. HIGHLIGHTS New environmental parameters-based mutation has been introduced in a differential evolution algorithm to solve multi-objective optimization problems (EP-mode) The addition of two additional environmental parameters to EP-mode has been found to be appropriate for maintaining diversity while also accelerating the convergence rate EP-MODE evaluated on bi-objective (DTLZ series) and tri-objective (ZDT series) benchmark test functions on the Pareto-optimal front and found EP-MODE's efficiency is higher than that of the MODE algorithm and the MODE algorithm with a ranking-based mutation operator GRAPHICAL ABSTRACT

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

MODENAR: Multi-objective differential evolution algorithm for mining numeric association rules

The Algebraic Differential Evolution (ADE) is a recently proposed combinatorial evolutionary scheme which mimics the behaviour of the classical Differential Evolution (DE) in discrete search spaces which can be represented as finitely generated groups. ADE has been successfully applied to both permutation and binary optimization problems. However, in the previous works, the relationship between ADE and the classical continuous DE has been only intuitively sketched without any theoretical or experimental proof. Here, we fill this gap by providing both theoretical and experimental justifications proving that ADE is a full-fledged generalization of DE which works across different search spaces. First, we formally prove that there exists a concrete implementation of ADE's algebraic operations converging to the classical vector operations of DE, then we propose a real-vector implementation of ADE and we experimentally prove that its behaviour is statistically equivalent to DE. As conclusion, we also pave the way for further applications of the original DE idea to mixed discrete/continuous search spaces.

New quantum inspired meta-heuristic techniques for multi-level colour image thresholding