A Cluster-Based Differential Evolution With Self-Adaptive Strategy for Multimodal Optimization

Differential evolution (DE) is an effective and efficient evolutionary algorithm in continuous space. The setting of control parameters is highly relevant with the convergence efficiency, and varies with different optimization problems even at different stages of evolution. Self-adapting control parameters for finding global optima is a long-term target in evolutionary field. This paper proposes a two-layered DE (TLDE) with self-adaptive control parameters combined with niching method based mutation strategy. The TLDE consists of two DE layers: a bottom DE layer for the basic evolution procedure, and a top DE layer for control parameter adaptation. Both layers follow the procedure of DE. Moreover, to mitigate the common phenomenon of premature convergence in DE, a clearing niching method is brought out in finding efficient mutation individuals to maintain diversity during the evolution and stabilize the evolution system. The performance is validated by a comprehensive set of twenty benchmark functions in parameter optimization and competitive results are presented.

In this paper, fitness euclidean-distance ratio (FER) is incorprated into differential evolution to solve multimodal optimization problems. The prime target of multi-modal optimization is to finding multiple global and local optima of a problem in one single run. Though variants of differential evolution (DE) are highly effective in locating single global optimum, few DE algorithms perform well when solving multi-optima problems. This work uses the FER technique to enhance the DE’s ability of locating and maintaining multiple peaks. The proposed algorithm is tested on a number of benchmark test function and the experimental results show that the proposed simple algorithm performs better comparing with a number of state-of-the-art multimodal optimization approaches.Keywordsmultimodal optimizationniching algorithmdifferential evolutionfitness euclidean-distance ratio

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.

Multimodal optimization is one of the most challenging issues in the field of optimization, which requires to detect and locate multiple global and local optima. Differential evolution (DE) is a well-known and powerful optimization algorithm with fast convergence capability. In this paper, we proposed a method to accurately solve high dimensional multimodal problems based on DE. Parallel sub-populations that are created using roaming algorithm, are randomly assigned with several chaotically improved strategies. Furthermore, a novel Hill-Valley method is proposed for detecting whether two points are in same species or not. Finally, our proposed approach is compared with well-known state-of-the-art niching algorithms and results show that our approach outperforms all of them.

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 clustering-based differential evolution with random-based sampling and Gaussian sampling

Many of optimization problems possess dynamic characteristics. Introducing strategies to maintain population diversity plays a key role in Dynamic Optimization Problems (DOPs), thus making the balance of exploration ability and the exploitation ability of the proposed algorithm. In this study, a crowding based differential evolution, combined with self-adaptive control parameters (CaDE)was proposed. Our proposed method adopts crowding with the least individual within a predefined neighborhood radius, and the control parameters are self-adaptive during the evolution process. For comparative analysis, several schemes incorporated with differential evolution are tested on a widely used moving peaks benchmark (MPB). Performance of the proposed algorithm is validated on the selected benchmark function in each circumstance.

We compared two floating-point-encoded evolutionary algorithms (EA) – differential evolution (DE) and the generalized generation gap (G3) – using a set of problems with different characteristics. G3 is reported to offer superior performance with unimodal functions, which are, however, often solved more efficiently using derivative-based optimization for example and it is interesting to know, how these algorithms perform in multimodal global optimization problems. Our results suggest that G3 converges fast but is prone to converge prematurely rather than finding the global optimum in high-dimensional multimodal problems. DE, in contrast, appears to handle multimodal problems better but cannot match convergence speed of G3 in unimodal problems.

This article proposes a two-stage hybrid multimodal optimizer based on invasive weed optimization (IWO) and differential evolution (DE) algorithms for locating and preserving multiple optima of a real-parameter functional landscape in a single run. Both IWO and DE have been modified from their original forms to meet the demands of the multimodal problems used in this work. A p-best crossover operation is introduced in the subregional DEs to improve their exploitative behaviour. The performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark suite comprising 21 basic multimodal problems and seven composite multimodal problems. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for the majority of test problems without incurring any serious computational burden.

Differential evolution (DE) is undoubtedly one of the most powerful stochastic searching optimization algorithms. However, solving a specific problem using DE crucially depends on appropriately choosing of trial vector generation strategies and their associated control parameters. At the same time, multimodal optimization refers to locating not only one optimum but a set of optimal solutions. Niching is a useful technique to solve multi-modal optimization problems. Discovering multiple niches is the key capability of niching algorithms. In this paper, we propose a Strategy Adaptive Memetci Crowding DE (SAMCDE), which incorporate Crowding DE (CDE) with strategies and control parameter self-adaptation technique as well as fine search technique to handle multi-modal optimization problems. The algorithm is tested on 10 benchmark multi-modal functions and compared with the original CDE as well as several popular multimodal optimization algorithms in literature. As shown by the experimental results, the proposed algorithm is able to generate superior performance on the tested functions.

Differential evolution algorithms are extremely effective in solving the single global optimization problems, but no DE variants perform competitively in solving multimodal optimization. In this paper, a differential evolution algorithm with dynamic niche radius strategy (DNRDE) is proposed, for multimodal optimization. In DNRDE, a new two-stage annealing schedule is designed to making the algorithm navigate from global exploration to local exploitation dynamically. Besides, in order to generate some high-quality individuals, the mutation is performed within each Euclidean neighborhood of the seed, and generating trial individuals by the perturbing procedure. Subsequently, we update the population according to the dynamic niche radius. Experiments have been performed on eight benchmark test functions. The results indicate that the proposed algorithm is better than the state-of-the-art multimodal algorithms.

The Differential Evolution (DE) is a stochastic population-based search method for global optimization over continuous spaces. This paper presents an efficient strategy for self-adapting control parameters in Differential Evolution to solve real-parameter optimization problems. The proposed strategy introduces an adaptive mechanism at the individual level based on Cauchy distribution (CD) where the step length and crossover rate are self-adapted during the evolution process. This strategy is to utilize attractive features of CD, which has thick tails that enable it to generate considerable changes more frequently and to escape a local optima for multi-modal optimization problems. Detailed performance comparisons of a DE using the proposed strategy on wide range of fifteen standard benchmark test problems are carried out. The obtained results showed that the performance of the DE had been improved with the proposed self-adaptive strategy.

Parameters setting is an important problem of evolution algorithms, include differential evolution algorithm. It has an effect on the performance of evolution algorithms. Although there is only three control parameters in differential evolution (DE) algorithm, the parameters setting is also a difficult problem. Self-adaptation is highly beneficial for adjusting the control parameters, especially when done without any user interaction. This paper presents differential evolution algorithm, called (AdaptDE), which use self-adaptive mechanisms applied to the control parameters. It can get the optimal control parameters for different optimization problem without user interaction. Experimental results indicate that AdaptDE algorithm is efficient and feasible. It is superior to jDE algorithm and FADE algorithm on the quality of solution.

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

A fireworks algorithm (FWA) is a recent swarm intelligence algorithm that is inspired by observing fireworks explosions. An adaptive fireworks algorithm (AFWA) proposes additional adaptive amplitudes to improve the performance of the enhanced fireworks algorithm (EFWA). The purpose of this paper is to add opposition-based learning (OBL) to AFWA with the goal of further boosting performance and achieving global optimization. Twelve benchmark functions are tested in use of an opposition-based adaptive fireworks algorithm (OAFWA). The final results conclude that OAFWA significantly outperformed EFWA and AFWA in terms of solution accuracy. Additionally, OAFWA was compared with a bat algorithm (BA), differential evolution (DE), self-adapting control parameters in differential evolution (jDE), a firefly algorithm (FA), and a standard particle swarm optimization 2011 (SPSO2011) algorithm. The research results indicate that OAFWA ranks the highest of the six algorithms for both solution accuracy and runtime cost.