Multimodal estimation of distribution algorithms

Taking the advantage of estimation of distribution algorithms (EDAs) in preserving high diversity, this paper proposes a multimodal EDA. Integrated with clustering strategies for crowding and speciation, two versions of this algorithm are developed, which operate at the niche level. Then these two algorithms are equipped with three distinctive techniques: 1) a dynamic cluster sizing strategy; 2) an alternative utilization of Gaussian and Cauchy distributions to generate offspring; and 3) an adaptive local search. The dynamic cluster sizing affords a potential balance between exploration and exploitation and reduces the sensitivity to the cluster size in the niching methods. Taking advantages of Gaussian and Cauchy distributions, we generate the offspring at the niche level through alternatively using these two distributions. Such utilization can also potentially offer a balance between exploration and exploitation. Further, solution accuracy is enhanced through a new local search scheme probabilistically conducted around seeds of niches with probabilities determined self-adaptively according to fitness values of these seeds. Extensive experiments conducted on 20 benchmark multimodal problems confirm that both algorithms can achieve competitive performance compared with several state-of-the-art multimodal algorithms, which is supported by nonparametric tests. Especially, the proposed algorithms are very promising for complex problems with many local optima

Invasion and adaptive evolution for individual-based spatially structured populations

The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution are closely related. Here we model the interplay between space and evolution starting with an individual-based approach and show the important role of parameter scalings on clustering and invasion. We consider a stochastic discrete model with birth, death, competition, mutation and spatial diffusion, where all the parameters may depend both on the position and on the trait of individuals. The spatial motion is driven by a reflected diffusion in a bounded domain. The interaction is modelled as a trait competition between individuals within a given spatial interaction range. First, we give an algorithmic construction of the process. Next, we obtain large population approximations, as weak solutions of nonlinear reaction-diffusion equations with Neumann's boundary conditions. As the spatial interaction range is fixed, the nonlinearity is nonlocal. Then, we make the interaction range decrease to zero and prove the convergence to spatially localized nonlinear reaction-diffusion equations, with Neumann's boundary conditions. Finally, simulations based on the microscopic individual-based model are given, illustrating the strong effects of the spatial interaction range on the emergence of spatial and phenotypic diversity (clustering and polymorphism) and on the interplay between invasion and evolution. The simulations focus on the qualitative differences between local and nonlocal interactions

Differential evolution with an evolution path: a DEEP evolutionary algorithm

Utilizing cumulative correlation information already existing in an evolutionary process, this paper proposes a predictive approach to the reproduction mechanism of new individuals for differential evolution (DE) algorithms. DE uses a distributed model (DM) to generate new individuals, which is relatively explorative, whilst evolution strategy (ES) uses a centralized model (CM) to generate offspring, which through adaptation retains a convergence momentum. This paper adopts a key feature in the CM of a covariance matrix adaptation ES, the cumulatively learned evolution path (EP), to formulate a new evolutionary algorithm (EA) framework, termed DEEP, standing for DE with an EP. Without mechanistically combining two CM and DM based algorithms together, the DEEP framework offers advantages of both a DM and a CM and hence substantially enhances performance. Under this architecture, a self-adaptation mechanism can be built inherently in a DEEP algorithm, easing the task of predetermining algorithm control parameters. Two DEEP variants are developed and illustrated in the paper. Experiments on the CEC'13 test suites and two practical problems demonstrate that the DEEP algorithms offer promising results, compared with the original DEs and other relevant state-of-the-art EAs

A MOS-based Dynamic Memetic Differential Evolution Algorithm for Continuous Optimization: A Scalability Test

Continuous optimization is one of the areas with more activity in the field of heuristic optimization. Many algorithms have been proposed and compared on several benchmarks of functions, with different performance depending on the problems. For this reason, the combination of different search strategies seems desirable to obtain the best performance of each of these approaches. This contribution explores the use of a hybrid memetic algorithm based on the multiple offspring framework. The proposed algorithm combines the explorative/exploitative strength of two heuristic search methods that separately obtain very competitive results. This algorithm has been tested with the benchmark problems and conditions defined for the special issue of the Soft Computing Journal on Scalability of Evolutionary Algorithms and other Metaheuristics for Large Scale Continuous Optimization Problems. The proposed algorithm obtained the best results compared with both its composing algorithms and a set of reference algorithms that were proposed for the special issue

Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL) optimization framework

Simplicity and flexibility of meta-heuristic optimization algorithms have attracted lots of attention in the field of optimization. Different optimization methods, however, hold algorithm-specific strengths and limitations, and selecting the best-performing algorithm for a specific problem is a tedious task. We introduce a new hybrid optimization framework, entitled Shuffled Complex-Self Adaptive Hybrid EvoLution (SC-SAHEL), which combines the strengths of different evolutionary algorithms (EAs) in a parallel computing scheme. SC-SAHEL explores performance of different EAs, such as the capability to escape local attractions, speed, convergence, etc., during population evolution as each individual EA suits differently to various response surfaces. The SC-SAHEL algorithm is benchmarked over 29 conceptual test functions, and a real-world hydropower reservoir model case study. Results show that the hybrid SC-SAHEL algorithm is rigorous and effective in finding global optimum for a majority of test cases, and that it is computationally efficient in comparison to algorithms with individual EA

Adaptive multimodal continuous ant colony optimization

Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization algorithms in preserving high diversity, this paper intends to extend ant colony optimization algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ant colony optimization algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima