Multi-population Differential Evolution Algorithm Research Articles

Multi-Population Differential Evolution Algorithm with Uniform Local Search

Differential evolution (DE) is a very effective stochastic optimization algorithm based on population for solving various real-world problems. The quality of solutions to these problems is mainly determined by the combination of mutation strategies and their parameters in DE. However, in the process of solving these problems, the population diversity and local search ability will gradually deteriorate. Therefore, we propose a multi-population differential evolution (MUDE) algorithm with a uniform local search to balance exploitation and exploration. With MUDE, the population is divided into multiple subpopulations with different population sizes, which perform different mutation strategies according to the evolution ratio, i.e., DE/rand/1, DE/current-to-rand/1, and DE/current-to-pbest/1. To improve the diversity of the population, the information is migrated between subpopulations by the soft-island model. Furthermore, the local search ability is improved by way of the uniform local search. As a result, the proposed MUDE maintains exploitation and exploration capabilities throughout the process. MUDE is extensively evaluated on 25 functions of the CEC 2005 benchmark. The comparison results show that the MUDE algorithm is very competitive with other DE variants and optimization algorithms in generating efficient solutions.

A modified Boltzmann Annealing Differential Evolution algorithm for inversion of directional resistivity logging-while-drilling measurements

Being introduced in the last decade for proactive geosteering, directional resistivity logging-while-drilling (DRLWD) measurements have been used to predict and invert formation boundary, which provides more confidence to geosteering engineers in steering a well towards reservoirs’ sweet spots. However, the strong non-uniqueness of the inversion problems in the data processing in the DRLWD measurements requires a robust algorithm having a global optimization capability. We propose a modified Boltzmann Annealing Differential Evolution (BADE) algorithm to optimize the inversion problem in the DRLWD measurements. The algorithm combines a multi-population Differential Evolution (DE) algorithm with an annealing strategy. Controlled by the annealing temperature, a bad solution may be accepted probabilistically to avoid the local minima. Moreover, different differential strategies are employed at different stages of annealing to improve the convergence as well as to save computation time. The proposed algorithm is suitable for parallel implementation and it can be accelerated drastically. Synthetic and field examples are presented to showcase the effectiveness and accuracy of the BADE algorithm. Compared to the standard DE algorithm, the modified algorithm converges faster and finds global optimization easier. Combined with a multi-layer model, the BADE algorithm can be used to predict multiple formation boundaries and to evaluate the anisotropic formation resistivities, which will be of great help for proactive geosteering and well placement.

A multi-population differential evolution algorithm based on cellular learning automata and evolutionary context information for optimization in dynamic environments

This paper presents a multi-population differential evolution algorithm to address dynamic optimization problems. In the proposed approach, a cellular learning automaton adjusts the behavior of each subpopulation by adaptively controlling its updating schemes. As the environment changes over time, an evolving population may go through a quite number of state transitions. Each state demands specific characteristics from an optimizer; hence, an adapted evolutionary scheme for one state may be unsuitable for the upcoming ones. Additionally, a learning approach may have limited time to adapt to a newly encountered state due to the frequentness of the environmental changes. Hence, it is infeasible for a dynamic optimizer to unlearn its existing beliefs to accommodate the practices required to embrace newly encountered states. In order to address this issue, we introduce a context dependent learning approach, which can adapt the behavior of each subpopulation according to the contexts of its different states. The performance of the proposed approach is compared with several state-of-the-art dynamic optimizers over the GDBG benchmark set. Comparison results indicate that the proposed method can achieve statistically superior performances on a wide range of tested instances.

A self-adaptive multi-population differential evolution algorithm

Differential evolution (DE) is an efficient population-based search algorithm for solving numerical optimization problems. However, the performance of DE is very sensitive to the choice of mutation strategies and their associated control parameters. In this paper, we propose a self-adaptive multi-population differential evolution algorithm, called SAMDE. The population is randomly divided into three equally sized sub-populations, each with different mutation strategies. At the end of each generation, all sub-populations are updated independently and recombined. Each sub-population uses an adaptive mechanism for selecting how current generation control parameters are generated. An improved mutation strategy, “rand assemble/1”, is proposed, its base vector is composed proportionally of three randomly selected individuals. The performance of SAMDE is evaluated on the suite of CEC 2005 benchmark functions. A comparative study is carried out with other state-of-the-art optimization techniques. The results show that SAMDE has a competitive performance compared to several other efficient DE variants.

Application of Multi-Species Differential Evolution Algorithm in Sustainable Microgrid Model

The safety and stability of microgrid (MG) operations are closely related to the capacity of distributed energy resources. A conventional MG model usually adopts investment cost as an objective function. Recently, the issue of environmental protection has been gradually emphasized. Therefore, the objective function of the proposed sustainable microgrid (SMG) model in this study considers the investment cost and environmental protective cost and the decision variable is the capacity of the distributed power. Moreover, weather and electric power load data from the National Centers for Environmental Information database (2010) were analyzed in Matlab program for the case study of Alabaster city, United States of America (USA). For the sake of a stable and economical SMG operation, this study also attempts to use a multi-objective capacity optimal model for effectively solving SMG under a multi-population differential evolution (MPDE) algorithm with dominant population (DP), which can improve the convergence speed in an SMG model. At the same time, considering that different scheduling strategies will also affect the optimization results, two strategies are proposed for the priority order of distributed generation sources. The optimization results under the two scheduling strategies show that the validation of the MPDE algorithm in SMG capacity optimization problems can economize investment costs and enable an environmentally friendly power supply.

Multipopulation differential evolution algorithm based on the opposition-based learning for heat exchanger network synthesis

ABSTRACTMultipopulation differential evolution combined with opposition-based learning is developed to improve the convergence efficiency and optimization accuracy for heat exchanger network synthesis. The algorithm is based on a stagewise superstructure simultaneous optimization model without considering stream splitting. The candidate population and its opposite population are searched in parallel. Mutation operations are implemented on both populations to provide a full information exchange among populations at each generation. A regrouping schedule is introduced to avoid premature convergence. The algorithm is applied to five heat exchanger network cases of different sizes. More economic networks are found using this method with less computational time.

An adaptive multi-population differential evolution algorithm for continuous multi-objective optimization

For evolutionary algorithms, the search data during evolution has attracted considerable attention and many kinds of data mining methods have been proposed to derive useful information behind these data so as to guide the evolution search. However, these methods mainly centered on the single objective optimization problems. In this paper, an adaptive differential evolution algorithm based on analysis of search data is developed for the multi-objective optimization problems. In this algorithm, the useful information is firstly derived from the search data during the evolution process by clustering and statistical methods, and then the derived information is used to guide the generation of new population and the local search. In addition, the proposed differential evolution algorithm adopts multiple subpopulations, each of which evolves according to the assigned crossover operator borrowed from genetic algorithms to generate perturbed vectors. During the evolution process, the size of each subpopulation is adaptively adjusted based on the information derived from its search results. The local search consists of two phases that focus on exploration and exploitation, respectively. Computational results on benchmark multi-objective problems show that the improvements of the strategies are positive and that the proposed differential evolution algorithm is competitive or superior to some previous multi-objective evolutionary algorithms in the literature.

Adaptive Forking Multipopulation Differential Evolution Algorithm for Multimodal Optimization

Adaptive Forking Multipopulation Differential Evolution Algorithm for Multimodal Optimization