Differential Evolution algorithm with Separated Groups for multi-dimensional optimization problems

The classical Differential Evolution (DE) algorithm, one of population-based Evolutionary Computation methods, proved to be a successful approach for relatively simple problems, but does not perform well for difficult multi-dimensional non-convex functions. A number of significant modifications of DE have been proposed in recent years, including very few approaches referring to the idea of distributed Evolutionary Algorithms. The present paper presents a new algorithm to improve optimization performance, namely DE with Separated Groups (DE-SG), which distributes population into small groups, defines rules of exchange of information and individuals between the groups and uses two different strategies to keep balance between exploration and exploitation capabilities. The performance of DE-SG is compared to that of eight algorithms belonging to the class of Evolutionary Strategies (Covariance Matrix Adaptation ES), Particle Swarm Optimization (Comprehensive Learning PSO and Efficient Population Utilization Strategy PSO), Differential Evolution (Distributed DE with explorative-exploitative population families, Self-adaptive DE, DE with global and local neighbours and Grouping Differential Evolution) and multi-algorithms (AMALGAM). The comparison is carried out for a set of 10-, 30- and 50-dimensional rotated test problems of varying difficulty, including 10- and 30-dimensional composition functions from CEC2005. Although slow for simple functions, the proposed DE-SG algorithm achieves a great success rate for more difficult 30- and 50-dimensional problems.     

改进种群多样性的双变异差分进化算法

差分进化算法(DE)是一种基于种群的启发式随机搜索技术,对于解决连续性优化问题具有较强的鲁棒性.然而传统差分进化算法存在种群多样性和收敛速度之间的矛盾,一种改进种群多样性的双变异差分进化算法(DADE),通过引入BFS-best机制(基于排序的可行解选取递减策略)改进变异算子"DE/current-to-best",将其与DE/rand/1构成双变异策略来改善DE算法中种群多样性减少的问题.同时,每个个体的控制参数基于排序自适应更新.最后,利用多个CEC2013标准测试函数对改进算法进行测试,实验结果表明,改进后的算法能有效改善种群多样性,较好地提高了算法的全局收敛能力和收敛速度.     

A niche hybrid genetic algorithm for global optimization of continuous multimodal functions

A niche hybrid genetic algorithm (NHGA) is proposed in this paper to solve continuous multimodal optimization problems more efficiently, accurately and reliably. It provides a new architecture of hybrid algorithms, which organically merges the niche techniques and Nelder–Mead's simplex method into GAs. In the new architecture, the simplex search is first performed in the potential niches, which likely contain a global optimum, to locate the promising zones within search space, quickly and reliably. Then another simplex search is used to quickly discover the global optimum in the located promising zones. The proposed method not only makes the exploration capabilities of GAs stronger through niche techniques, but also has more powerful exploitation capabilities by using simplex search. So it effectively alleviates premature convergence and improves weak exploitation capacities of GAs. A set of benchmark functions is used to demonstrate the validity of NHGA and the role of every component of NHGA. Numerical experiments show that the NHGA may, efficiently and reliably, obtain a more accurate global optimum for the complex and high-dimension multimodal optimization problems. It also demonstrates that the new hybrid architecture is potential and can be used to generate more potential hybrid algorithms.     

Balancing global and local search in parallel efficient global optimization algorithms

Most parallel efficient global optimization (EGO) algorithms focus only on the parallel architectures for producing multiple updating points, but give few attention to the balance between the global search (i.e., sampling in different areas of the search space) and local search (i.e., sampling more intensely in one promising area of the search space) of the updating points. In this study, a novel approach is proposed to apply this idea to further accelerate the search of parallel EGO algorithms. In each cycle of the proposed algorithm, all local maxima of expected improvement (EI) function are identified by a multi-modal optimization algorithm. Then the local EI maxima with value greater than a threshold are selected and candidates are sampled around these selected EI maxima. The results of numerical experiments show that, although the proposed parallel EGO algorithm needs more evaluations to find the optimum compared to the standard EGO algorithm, it is able to reduce the optimization cycles. Moreover, the proposed parallel EGO algorithm gains better results in terms of both number of cycles and evaluations compared to a state-of-the-art parallel EGO algorithm over six test problems.     

A particle swarm optimization-based hybrid algorithm for minimum concave cost network flow problems

Traditionally, minimum cost transshipment problems have been simplified as linear cost problems, which are not practical in real applications. Some advanced local search algorithms have been developed to solve concave cost bipartite network problems. These have been found to be more effective than the traditional linear approximation methods and local search methods. Recently, a genetic algorithm and an ant colony system algorithm were employed to develop two global search algorithms for solving concave cost transshipment problems. These two global search algorithms were found to be more effective than the advanced local search algorithms for solving concave cost transshipment problems. Although the particle swarm optimization algorithm has been used to obtain good results in many applications, to the best of our knowledge, it has not yet been applied in minimum concave cost network flow problems. Thus, in this study, we employ an arc-based particle swarm optimization algorithm, coupled with some genetic algorithm and threshold accepting method techniques, as well as concave cost network heuristics, to develop a hybrid global search algorithm for efficiently solving minimum cost network flow problems with concave arc costs. The proposed algorithm is evaluated by solving several randomly generated network flow problems. The results indicate that the proposed algorithm is more effective than several other recently designed methods, such as local search algorithms, genetic algorithms and ant colony system algorithms, for solving minimum cost network flow problems with concave arc costs.     

Adaptive variable space differential evolution algorithm based on population distribution

A novel memetic computing optimization algorithms, i.e. an adaptive variable space differential evolution algorithm (AVSDE), is proposed to improve the global optimization performance. AVSDE guides most individuals search in adaptive variable space (AVS) and employs adaptive mutation and adaptive control parameter. In AVSDE, AVS is determined by population global distribution information, and DE’s operators depend on the local information of the distance and direction. The performance of AVSDE is improved by integrating the global information with the local information. In addition, different mutation strategies are selected according to the evolution stage and random probability to balance AVSDE’s exploration and exploitation abilities, and adaptive control parameter is used to further enhance the performance of AVSDE. 19 scalable benchmark functions are employed to demonstrate the performance of AVSDE. Comparing with two well-tuned conventional DE and several state $-$ of-the $-$ art parameter adaptive DE variants, the whole performance of AVSDE is the best. Finally, two experiments are conducted to analyze the effect of the key parameters on AVSDE’s performance, and the optimal parameters are obtained.     

Scale factor local search in differential evolution

This paper proposes the scale factor local search differential evolution (SFLSDE). The SFLSDE is a differential evolution (DE) based memetic algorithm which employs, within a self-adaptive scheme, two local search algorithms. These local search algorithms aim at detecting a value of the scale factor corresponding to an offspring with a high performance, while the generation is executed. The local search algorithms thus assist in the global search and generate offspring with high performance which are subsequently supposed to promote the generation of enhanced solutions within the evolutionary framework. Despite its simplicity, the proposed algorithm seems to have very good performance on various test problems. Numerical results are shown in order to justify the use of a double local search instead of a single search. In addition, the SFLSDE has been compared with a standard DE and three other modern DE based metaheuristic for a large and varied set of test problems. Numerical results are given for relatively low and high dimensional cases. A statistical analysis of the optimization results has been included in order to compare the results in terms of final solution detected and convergence speed. The efficiency of the proposed algorithm seems to be very high especially for large scale problems and complex fitness landscapes.     

A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions

Genetic algorithms are stochastic search approaches based on randomized operators, such as selection, crossover and mutation, inspired by the natural reproduction and evolution of the living creatures. However, few published works deal with their application to the global optimization of functions depending on continuous variables.A new algorithm called Continuous Genetic Algorithm (CGA) is proposed for the global optimization of multiminima functions. In order to cover a wide domain of possible solutions, our algorithm first takes care over the choice of the initial population. Then it locates the most promising area of the solution space, and continues the search through an intensification inside this area. The selection, the crossover and the mutation are performed by using the decimal code. The efficiency of CGA is tested in detail through a set of benchmark multimodal functions, of which global and local minima are known. CGA is compared to Tabu Search and Simulated Annealing, as alternative algorithms.     

A hybrid method for multidimensional scaling using city-block distances

The problem of multidimensional scaling with city-block distances in the embedding space is reduced to a two level optimization problem consisting of a combinatorial problem at the upper level and a quadratic programming problem at the lower level. A hybrid method is proposed combining randomized search for the upper level problem with a standard quadratic programming algorithm for the lower level problem. Several algorithms for the combinatorial problem have been tested and an evolutionary global search algorithm has been proved most suitable. An experimental code of the proposed hybrid multidimensional scaling algorithm is developed and tested using several test problems of two- and three-dimensional scaling.     

An innovative flower pollination algorithm for continuous optimization problem

The flower pollination algorithm (FPA) is a relatively new swarm optimization algorithm that inspired by the pollination phenomenon of natural phanerogam. Since its proposed, it has received widespread attention and been applied in various engineering fields. However, the FPA still has certain drawbacks, such as inadequate optimization precision and poor convergence. In this paper, an innovative flower pollination algorithm based on cloud mutation is proposed (CMFPA), which adds information of all dimensions in the global optimization stage and uses the designed cloud mutation method to redistribute the population center. To verify the performance of the CMFPA in solving continuous optimization problems, we test twenty-four well-known functions, composition functions of CEC2013 and all benchmark functions of CEC2017. The results demonstrate that the CMFPA has better performance compared with other state-of-the-art algorithms. In addition, the CMFPA is implemented for five constrained optimization problems in practical engineering, and the performance is compared with state-of-the-art algorithms to further prove the effectiveness and efficiency of the CMFPA.     

A local linear embedding module for evolutionary computation optimization

A Local Linear Embedding (LLE) module enhances the performance of two Evolutionary Computation (EC) algorithms employed as search tools in global optimization problems. The LLE employs the stochastic sampling of the data space inherent in Evolutionary Computation in order to reconstruct an approximate mapping from the data space back into the parameter space. This allows to map the target data vector directly into the parameter space in order to obtain a rough estimate of the global optimum, which is then added to the EC generation. This process is iterated and considerably improves the EC convergence. Thirteen standard test functions and two real-world optimization problems serve to benchmark the performance of the method. In most of our tests, optimization aided by the LLE mapping outperforms standard implementations of a genetic algorithm and a particle swarm optimization. The number and ranges of functions we tested suggest that the proposed algorithm can be considered as a valid alternative to traditional EC tools in more general applications. The performance improvement in the early stage of the convergence also suggests that this hybrid implementation could be successful as an initial global search to select candidates for subsequent local optimization.     

蚁群遗传混合算法

将蚁群遗传混合算法分别求解离散空间的和连续空间优化问题.求解旅行商问题的混合算法是以遗传算法为整个算法的框架,利用了蚁群算法中的信息素特性的进行交叉操作;根据旅行商问题的特点,给出了4种变异策略;针对遗传算法存在的过早收敛问题,加入2-0pt方法对问题求解进行了局部优化.与模拟退火算法、标准遗传算法和标准蚁群算法进行比较,4种混合算法效果都比较好,策略D的混合算法效果最好.求解连续空间优化问题是以蚁群算法为整个算法的框架,加入遗传算法的交叉操作和变异操作,用测试函数验证了混合蚁群算法的正确性.     

A DERIVATIVE-FREE ALGORITHM FOR UNCONSTRAINED OPTIMIZATION

In this paper a hybrid algorithm which combines the pattern search method and the genetic algorithm for unconstrained optimization is presented. The algorithm is a deterministic pattern search algorithm,but in the search step of pattern search algorithm,the trial points are produced by a way like the genetic algorithm. At each iterate, by reduplication,crossover and mutation, a finite set of points can be used. In theory,the algorithm is globally convergent. The most stir is the numerical results showing that it can find the global minimizer for some problems ,which other pattern search algorithms don＇t bear.     

A hybrid method combining continuous tabu search and Nelder–Mead simplex algorithms for the global optimization of multiminima functions

Tabu search (TS) is a metaheuristic, which proved efficient to solve various combinatorial optimization problems. However, few works deal with its application to the global minimization of functions depending on continuous variables. To perform this task, we propose an hybrid method combining tabu search and simplex search (SS). TS allows to cover widely the solution space, to stimulate the search towards solutions far from the current solution, and to avoid the risk of trapping into a local minimum. SS is used to accelerate the convergence towards a minimum. The Nelder–Mead simplex algorithm is a classical very powerful local descent algorithm, making no use of the objective function derivatives. A “simplex” is a geometrical figure consisting, in n-dimensions, of (n+1) points. If any point of a simplex is taken as the origin, the n other points define vector directions that span the n-dimension vector space. Through a sequence of elementary geometric transformations (reflection, contraction and extension), the initial simplex moves, expands or contracts. To select the appropriate transformation, the method only uses the values of the function to be optimized at the vertices of the simplex considered. After each transformation, the current worst vertex is replaced by a better one. Our algorithm called continuous tabu simplex search (CTSS) implemented in two different forms (CTSS_single, CTSS_multiple) is made up of two steps: first, an adaptation of TS to continuous optimization problems, allowing to localize a “promising area”; then, intensification within this promising area, involving SS. The efficiency of CTSS is extensively tested by using analytical test functions of which global and local minima are known. A comparison is proposed with several variants of tabu search, genetic algorithms and simulated annealing. CTSS is applied to the design of a eddy current sensor aimed at non-destructive control.     

A new hybrid method for solving global optimization problem

In this paper we present a new hybrid method, called the SASP method. The purpose of this method is the hybridization of the simulated annealing (SA) with the descent method, where we estimate the gradient using simultaneous perturbation. Firstly, the new hybrid method finds a local minimum using the descent method, then SA is executed in order to escape from the currently discovered local minimum to a better one, from which the descent method restarts a new local search, and so on until convergence.The new hybrid method can be widely applied to a class of global optimization problems for continuous functions with constraints. Experiments on 30 benchmark functions, including high dimensional functions, show that the new method is able to find near optimal solutions efficiently. In addition, its performance as a viable optimization method is demonstrated by comparing it with other existing algorithms. Numerical results improve the robustness and efficiency of the method presented.     

Deterministic parallel global parameter estimation for a model of the budding yeast cell cycle

Two parallel deterministic direct search algorithms are combined to find improved parameters for a system of differential equations designed to simulate the cell cycle of budding yeast. Comparing the model simulation results to experimental data is difficult because most of the experimental data is qualitative rather than quantitative. An algorithm to convert simulation results to mutant phenotypes is presented. Vectors of the 143 parameters defining the differential equation model are rated by a discontinuous objective function. Parallel results on a 2200 processor supercomputer are presented for a global optimization algorithm, DIRECT, a local optimization algorithm, MADS, and a hybrid of the two.     

A Staged Continuous Tabu Search Algorithm for the Global Optimization and its Applications to the Design of Fiber Bragg Gratings

A novel staged continuous Tabu search (SCTS) algorithm is proposed for solving global optimization problems of multi-minima functions with multi-variables. The proposed method comprises three stages that are based on the continuous Tabu search (CTS) algorithm with different neighbor-search strategies, with each devoting to one task. The method searches for the global optimum thoroughly and efficiently over the space of solutions compared to a single process of CTS. The effectiveness of the proposed SCTS algorithm is evaluated using a set of benchmark multimodal functions whose global and local minima are known. The numerical test results obtained indicate that the proposed method is more efficient than an improved genetic algorithm published previously. The method is also applied to the optimization of fiber grating design for optical communication systems. Compared with two other well-known algorithms, namely, genetic algorithm (GA) and simulated annealing (SA), the proposed method performs better in the optimization of the fiber grating design.     

A hybrid immune multiobjective optimization algorithm

In this paper, we develop a hybrid immune multiobjective optimization algorithm (HIMO) based on clonal selection principle. In HIMO, a hybrid mutation operator is proposed with the combination of Gaussian and polynomial mutations (GP-HM operator). The GP-HM operator adopts an adaptive switching parameter to control the mutation process, which uses relative large steps in high probability for boundary individuals and less-crowded individuals. With the generation running, the probability to perform relative large steps is reduced gradually. By this means, the exploratory capabilities are enhanced by keeping a desirable balance between global search and local search, so as to accelerate the convergence speed to the true Pareto-optimal front in the global space with many local Pareto-optimal fronts. When comparing HIMO with various state-of-the-art multiobjective optimization algorithms developed recently, simulation results show that HIMO performs better evidently.     

Massively parallel differential evolution—pattern search optimization with graphics hardware acceleration: an investigation on bound constrained optimization problems

This paper presents a novel parallel Differential Evolution (DE) algorithm with local search for solving function optimization problems, utilizing graphics hardware acceleration. As a population-based meta-heuristic, DE was originally designed for continuous function optimization. Graphics Processing Units (GPU) computing is an emerging desktop parallel computing technology that is becoming popular with its wide availability in many personal computers. In this paper, the classical DE was adapted in the data-parallel CPU-GPU heterogeneous computing platform featuring Single Instruction-Multiple Thread (SIMT) execution. The global optimal search of the DE was enhanced by the classical local Pattern Search (PS) method. The hybrid DE–PS method was implemented in the GPU environment and compared to a similar implementation in the common computing environment with a Central Processing Unit (CPU). Computational results indicate that the GPU-accelerated SIMT-DE-PS method is orders of magnitude faster than the corresponding CPU implementation. The main contribution of this paper is the parallelization analysis and performance analysis of the hybrid DE–PS with GPU acceleration. The research results demonstrate a promising direction for high speed optimization with desktop parallel computing on a personal computer.     

Global optimization based on novel heuristics,low-discrepancy sequences and genetic algorithms

In this paper a new heuristic hybrid technique for bound-constrained global optimization is proposed. We developed iterative algorithm called GLP_τS that uses genetic algorithms, LP_τ low-discrepancy sequences of points and heuristic rules to find regions of attraction when searching a global minimum of an objective function. Subsequently Nelder–Mead Simplex local search technique is used to refine the solution. The combination of the three techniques (Genetic algorithms, LP_τO Low-discrepancy search and Simplex search) provides a powerful hybrid heuristic optimization method which is tested on a number of benchmark multimodal functions with 10–150 dimensions, and the method properties – applicability, convergence, consistency and stability are discussed in detail.