Abstract:A new mutation concept is proposed to generalize local selection based Differential Evolution algorithm to work in general multimodal 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 globa… Show more
“…the two classic DE/rand/1/bin and DE/rand/2/bin algorithms and three methods that have been designed to handle multimodal problems, namely the FERPSO [22], the Crowding DE [17], and the DELS [19]. Throughout this section, all the reported results are averaged over 100 independent simulations.…”
Section: Resultsmentioning
confidence: 99%
“…Although SDE is computationally more efficient than the Crowding DE, it incorporates a user-specified and problem dependent parameter called species radius, which should be properly chosen. Furthermore, DE using local selection (DELS) [19] employs a new mutation strategy that divides the mutation operation into the local and the global mutation stages. With a pre-specified probability, it selects a different mutation strategy to perform either a global or a local mutation.…”
Abstract-Handling multimodal functions is a very important and challenging task in evolutionary computation community, since most of the real-world applications exhibit highly multimodal landscapes. Motivated by the dynamics and the proximity characteristics of Differential Evolution's mutation strategies tending to distribute the individuals of the population to the vicinity of the problem's minima, we introduce two new Differential Evolution mutation strategies. The new mutation strategies incorporate spatial information about the neighborhood of each potential solution and exhibit a niching formation, without incorporating any additional parameter. Experimental results on eight well known multimodal functions and comparisons with some state-of-the-art algorithms indicate that the proposed mutation strategies are competitive and very promising, since they are able to reliably locate and maintain many global optima throughout the evolution process.
“…the two classic DE/rand/1/bin and DE/rand/2/bin algorithms and three methods that have been designed to handle multimodal problems, namely the FERPSO [22], the Crowding DE [17], and the DELS [19]. Throughout this section, all the reported results are averaged over 100 independent simulations.…”
Section: Resultsmentioning
confidence: 99%
“…Although SDE is computationally more efficient than the Crowding DE, it incorporates a user-specified and problem dependent parameter called species radius, which should be properly chosen. Furthermore, DE using local selection (DELS) [19] employs a new mutation strategy that divides the mutation operation into the local and the global mutation stages. With a pre-specified probability, it selects a different mutation strategy to perform either a global or a local mutation.…”
Abstract-Handling multimodal functions is a very important and challenging task in evolutionary computation community, since most of the real-world applications exhibit highly multimodal landscapes. Motivated by the dynamics and the proximity characteristics of Differential Evolution's mutation strategies tending to distribute the individuals of the population to the vicinity of the problem's minima, we introduce two new Differential Evolution mutation strategies. The new mutation strategies incorporate spatial information about the neighborhood of each potential solution and exhibit a niching formation, without incorporating any additional parameter. Experimental results on eight well known multimodal functions and comparisons with some state-of-the-art algorithms indicate that the proposed mutation strategies are competitive and very promising, since they are able to reliably locate and maintain many global optima throughout the evolution process.
“…Moreover, DE with local selection [21] designs a mutation strategy with two main components: a local and a global mutation rule. Throughout the evolutionary process, the two rules are probabilistically selected by a fixed and pre-specified probability.…”
Section: Related Workmentioning
confidence: 99%
“…If the new individual is qualified for insertion then it is kept in the archive. If the solution is already in the archive (Algorithm 1, lines [20][21][22] then this solution is re-initialized within the bounds of the problem at hand, in an attempt to search for unexplored regions. The algorithmic scheme of the proposed algorithm (dADE/nrand/1) and the dynamic archive are briefly illustrated in Algorithm 1 and 2 respectively.…”
Abstract-Highly multimodal landscapes with multiple local/global optima represent common characteristics in real-world applications. Many niching algorithms have been proposed in the literature which aim to search such landscapes in an attempt to locate as many global optima as possible. However, to locate and maintain a large number of global solutions, these algorithms are substantially influenced by their parameter values, such as a large population size. Here, we propose a new niching Differential Evolution algorithm that attempts to overcome the population size influence and produce good performance almost independently of its population size. To this end, we incorporate two mechanisms into the algorithm: a control parameter adaptation technique and an external dynamic archive along with a reinitialization mechanism. The first mechanism is designed to efficiently adapt the control parameters of the algorithm, whilst the second one is responsible for enabling the algorithm to investigate unexplored regions of the search space and simultaneously keep the best solutions found by the algorithm. The proposed approach is compared with two Differential Evolution variants on a recently proposed benchmark suite. Empirical results indicate that the proposed niching algorithm is competitive and very promising. It exhibits a robust and stable behavior, whilst the incorporation of the dynamic archive seems to tackle the population size influence effectively. Moreover, it alleviates the problem of having to finetune the population size parameter in a niching algorithm.
“…Additionally, DE using local selection (DELS) [21] employs a new mutation strategy that divides the mutation operation into the local and the global mutation stages. It selects a different mutation strategy, with a pre-specified probability, to perform either a global or a local mutation.…”
Abstract-A new family of Differential Evolution mutation strategies (DE/nrand) that are able to handle multimodal functions, have been recently proposed. The DE/nrand family incorporates information regarding the real nearest neighborhood of each potential solution, which aids them to accurately locate and maintain many global optimizers simultaneously, without the need of additional parameters. However, these strategies have increased computational cost. To alleviate this problem, instead of computing the real nearest neighbor, we incorporate an indexbased neighborhood into the mutation strategies. The new mutation strategies are evaluated on eight well-known and widely used multimodal problems and their performance is compared against five state-of-the-art algorithms. Simulation results suggest that the proposed strategies are promising and exhibit competitive behavior, since with a substantial lower computational cost they are able to locate and maintain many global optima throughout the evolution process.
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