An efficient hybrid technique for numerical optimization and applications

Real World Optimization Problems is one of the major concerns to show the potential and effectiveness of an optimization algorithm. In this context, a hybrid algorithm of two popular heuristics namely Differential Evolution (DE) and Particle Swarm Optimization (PSO) engaged on a ‘tri-population’ environment. Initially, the whole population (in increasing order of fitness) is divided into three groups – Inferior Group, Mid Group and Superior Group. DE is employed in the inferior and superior groups, whereas PSO is used in the mid-group. The proposed method is abbreviated as DPD as it uses DE–PSO–DE on a population. Two strategies namely Elitism (to retain the best obtained values so far) and Non-redundant search (to improve the solution quality) have been additionally employed in DPD cycle. Moreover, the robustness of the mutation strategies of DE have been well studied and suitable mutation strategies for both DEs (for DPD) are investigated over a set of existing 8 popular mutation strategies which results 64 variants of DPD. The top DPD is further tested through the test functions of CEC2006, CEC2010 and 5 Engineering Design Problems. Also it is used to solve CEC2011 Real World Optimization problems. An excellent efficiency of the recommended DPD is confirmed over the state-of-the-art algorithms.     

多策略调和的布谷鸟搜索算法

布谷鸟搜索（CS）算法是一种新型的群智能算法,结构简单且寻优能力较强,但存在勘探与开采不平衡以及易陷入局部极值的问题。提出一种多策略调和的布谷鸟搜索（MSRCS）算法,基于概率规则选择由自适应步长和改进解更新方法组成的调和策略对布谷鸟个体进行更新,其中自适应步长引导布谷鸟在更好的方向上寻优,3种改进的解更新方法分别从自身邻域、当前最优个体和随机位置3个角度对勘探和开采进行调和,从而提升全局搜索和局部搜索在迭代过程中的适应性。在CEC2013测试集的28个基准函数上的实验结果表明,MSRCS算法至少有12个测试函数优于原始CS及其7种改进算法且排名第一,在求解单峰、多峰和组合函数问题时寻优能力更强,同时相比于3种经典群智能优化算法具有更快的收敛速度和更高的解精度。     

An efficient modified grey wolf optimizer with Lévy flight for optimization tasks

The grey wolf optimizer (GWO) is a new efficient population-based optimizer. The GWO algorithm can reveal an efficient performance compared to other well-established optimizers. However, because of the insufficient diversity of wolves in some cases, a problem of concern is that the GWO can still be prone to stagnation at local optima. In this article, an improved modified GWO algorithm is proposed for solving either global or real-world optimization problems. In order to boost the efficacy of GWO, Lévy flight (LF) and greedy selection strategies are integrated with the modified hunting phases. LF is a class of scale-free walks with randomly-oriented steps according to the Lévy distribution. In order to investigate the effectiveness of the modified Lévy-embedded GWO (LGWO), it was compared with several state-of-the-art optimizers on 29 unconstrained test beds. Furthermore, 30 artificial and 14 real-world problems from CEC2014 and CEC2011 were employed to evaluate the LGWO algorithm. Also, statistical tests were employed to investigate the significance of the results. Experimental results and statistical tests demonstrate that the performance of LGWO is significantly better than GWO and other analyzed optimizers.     

Improved backtracking search algorithm for pseudo dynamic active earth pressure on retaining wall supporting c-Ф backfill

Optimization algorithms are effective and powerful tools for solving the non-linear optimization problems. Backtracking Search Optimization Algorithm (BSA) is a newly proposed Evolutionary Algorithm (EA) and has been applied to optimize different complex optimization problems in science and engineering. In the present study, a new adaptive control parameter based Improved Backtracking Search Optimization Algorithm (IBSA) is suggested. Due to the validation of the suggested method, it has been applied to CEC2005 benchmark functions and the simulation results are compared with different existing algorithms. Also, it has been used to determine active earth pressure on retaining wall supporting c-Ф backfill using the pseudo dynamic method. Simulation result shows that the proposed method is suitable to solve such type of problems and the results obtained are found satisfactory.     

A multi-point sampling method based on kriging for global optimization

In general, sampling strategy plays a very important role in metamodel based design optimization, especially when computationally expensive simulations are involved in the optimization process. The research on new optimization methods with less sampling points and higher convergence speed receives great attention in recent years. In this paper, a multi-point sampling method based on kriging (MPSK) is proposed for improving the efficiency of global optimization. The sampling strategy of this method is based on a probabilistic distribution function converted from the expected improvement (EI) function. It can intelligently draw appropriate new samples in an area with certain probability according to corresponding EI values. Besides, three strategies are also proposed to speed up the sequential sampling process and the corresponding convergence criterions are put forward to stop the searching process reasonably. In order to validate the efficiency of this method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the higher global optimization efficiency of this method makes it particularly suitable for design optimization problems involving computationally expensive simulations.     

A Novel Multiobjective Fireworks Algorithm and Its Applications to Imbalanced Distance Minimization Problems

Recently, multimodal multiobjective optimization problems (MMOPs) have received increasing attention. Their goal is to find a Pareto front and as many equivalent Pareto optimal solutions as possible. Although some evolutionary algorithms for them have been proposed, they mainly focus on the convergence rate in the decision space while ignoring solutions diversity. In this paper, we propose a new multiobjective fireworks algorithm for them, which is able to balance exploitation and exploration in the decision space. We first extend a latest single-objective fireworks algorithm to handle MMOPs. Then we make improvements by incorporating an adaptive strategy and special archive guidance into it, where special archives are established for each firework, and two strategies (i.e., explosion and random strategies) are adaptively selected to update the positions of sparks generated by fireworks with the guidance of special archives. Finally, we compare the proposed algorithm with eight state-of-the-art multimodal multiobjective algorithms on all 22 MMOPs from CEC2019 and several imbalanced distance minimization problems. Experimental results show that the proposed algorithm is superior to compared algorithms in solving them. Also, its runtime is less than its peers’.      

基于多目标飞蛾算法的电力系统无功优化研究

鉴于电力需求的日益增长与传统无功优化方法的桎梏,如何更加合理有效地解决电力系统的无功优化问题逐渐成为了研究的热点。提出一种多目标飞蛾扑火算法来解决电力系统多目标无功优化的问题,算法引入固定大小的外部储存机制、自适应的网格和筛选机制来有效存储和提升无功优化问题的帕累托最优解集,算法采用CEC2009标准多目标测试函数来进行仿真实验,并与两种经典算法进行性能的对比分析。此外,在电力系统IEEE 30节点上将该算法与MOPSO,NGSGA-II算法的求解结果进行比较分析的结果表明,多目标飞蛾算法具有良好的性能,并在解决电力系统多目标无功优化问题上具有良好的潜力。     

LADPSO: using fuzzy logic to conduct PSO algorithm

Optimization plays a critical role in human modern life. Nowadays, optimization is used in many aspects of human modern life including engineering, medicine, agriculture and economy. Due to the growing number of optimization problems and their growing complexity, we need to improve and develop theoretical and practical optimization methods. Stochastic population based optimization algorithms like genetic algorithms and particle swarm optimization are good candidates for solving complex problems efficiently. Particle swarm optimization (PSO) is an optimization algorithm that has received much attention in recent years. PSO is a simple and computationally inexpensive algorithm inspired by the social behavior of bird flocks and fish schools. However, PSO suffers from premature convergence, especially in high dimensional multi-modal functions. In this paper, a new method for improving PSO has been introduced. The Proposed method which has been named Light Adaptive Particle Swarm Optimization is a novel method that uses a fuzzy control system to conduct the standard algorithm. The suggested method uses two adjunct operators along with the fuzzy system in order to improve the base algorithm on global optimization problems. Our approach is validated using a number of common complex uni-modal/multi-modal benchmark functions and results have been compared with the results of Standard PSO (SPSO2011) and some other methods. The simulation results demonstrate that results of the proposed approach is promising for improving the standard PSO algorithm on global optimization problems and also improving performance of the algorithm.     

An improved electromagnetism-like mechanism algorithm for constrained optimization

Many problems in scientific research and engineering applications can be decomposed into the constrained optimization problems. Most of them are the nonlinear programming problems which are very hard to be solved by the traditional methods. In this paper, an electromagnetism-like mechanism (EM) algorithm, which is a meta-heuristic algorithm, has been improved for these problems. Firstly, some modifications are made for improving the performance of EM algorithm. The process of calculating the total force is simplified and an improved total force formula is adopted to accelerate the searching for optimal solution. In order to improve the accuracy of EM algorithm, a parameter called as move probability is introduced into the move formula where an elitist strategy is also adopted. And then, to handle the constraints, the feasibility and dominance rules are introduced and the corresponding charge formula is used for biasing feasible solutions over infeasible ones. Finally, 13 classical functions, three engineering design problems and 22 benchmark functions in CEC’06 are tested to illustrate the performance of proposed algorithm. Numerical results show that, compared with other versions of EM algorithm and other state-of-art algorithms, the improved EM algorithm has the advantage of higher accuracy and efficiency for constrained optimization problems.     

A covariance matrix adaptation evolution strategy variant and its engineering application

This paper proposes a novel covariance matrix adaptation evolution strategy (CMA-ES) variant, named AEALSCE, for single-objective numerical optimization problems in the continuous domain. To avoid premature convergence and strengthen the exploration capacity of the basic CMA-ES, AEALSCE is obtained by integrating the CMA-ES with two strategies that can adjust the evolutionary directions and enrich the population diversity. The first strategy is named the anisotropic eigenvalue adaptation (AEA) technique, which adapts the search scope towards the optimal evolutionary directions. It scales the eigenvalues of the covariance matrix anisotropically based on local fitness landscape detection. The other strategy is named the local search (LS) strategy, which is executed under the eigen coordinate system and can be subdivided into two parts. In the first part, the new candidates of superior solutions are sampled around the best solution to perform local exploration. In the other part, the new candidates of inferior solutions are generated using a modified mean point along the fitness descent direction. The proposed AEALSCE algorithm is compared with other top competitors, including the CEC 2014 champion, L-SHADE, and the promising NBIPOP-aCMA-ES, by benchmarking the CEC 2014 testbed. Moreover, AEALSCE is applied in solving three constrained engineering design problems and parameter estimation of photovoltaic (PV) models. According to the statistical results of the experiments, our proposed AEALSCE is competitive with other algorithms in convergence efficiency and accuracy. AEALSCE benefits from a good balance of exploration and exploitation, and it exhibits a potential to address real-world optimization problems.     

求解约束优化问题的复合人工蜂群算法

针对约束优化问题,提出一种复合人工蜂群算法.该算法引入多维随机变异操作和最优引导变异操作平衡算法的探索能力和开发能力.将ε约束和可行性规则相结合平衡目标函数与约束,加快算法的收敛.通过对CEC 2006中20个测试函数和CEC 2010中18个测试函数及3个实际工程优化问题的实验结果分析表明,该算法对约束优化问题可行有...     

A portfolio optimization model using Genetic Network Programming with control nodes

Many evolutionary computation methods applied to the financial field have been reported. A new evolutionary method named “Genetic Network Programming” (GNP) has been developed and applied to the stock market recently. The efficient trading rules created by GNP has been confirmed in our previous research. In this paper a multi-brands portfolio optimization model based on Genetic Network Programming with control nodes is presented. This method makes use of the information from technical indices and candlestick chart. The proposed optimization model, consisting of technical analysis rules, are trained to generate trading advice. The experimental results on the Japanese stock market show that the proposed optimization system using GNP with control nodes method outperforms other traditional models in terms of both accuracy and efficiency. We also compared the experimental results of the proposed model with the conventional GNP based methods, GA and Buy&Hold method to confirm its effectiveness, and it is clarified that the proposed trading model can obtain much higher profits than these methods.     

A memory based differential evolution algorithm for unconstrained optimization

In optimization, the performance of differential evolution (DE) and their hybrid versions exist in the literature is highly affected by the inappropriate choice of its operators like mutation and crossover. In general practice, during simulation DE does not employ any strategy of memorizing the so-far-best results obtained in the initial part of the previous generation. In this paper, a new “Memory based DE (MBDE)” presented where two “swarm operators” have been introduced. These operators based on the pBEST and gBEST mechanism of particle swarm optimization. The proposed MBDE is employed to solve 12 basic, 25 CEC 2005, and 30 CEC 2014 unconstrained benchmark functions. In order to further test its efficacy, five different test system of model order reduction (MOR) problem for single-input and single-output system are solved by MBDE. The results of MBDE are compared with state-of-the-art algorithms that also solved those problems. Numerical, statistical, and graphical analysis reveals the competency of the proposed MBDE.     

A hybrid approach to constrained global optimization

In this paper, we propose a novel hybrid global optimization method to solve constrained optimization problems. An exact penalty function is first applied to approximate the original constrained optimization problem by a sequence of optimization problems with bound constraints. To solve each of these box constrained optimization problems, two hybrid methods are introduced, where two different strategies are used to combine limited memory BFGS (L-BFGS) with Greedy Diffusion Search (GDS). The convergence issue of the two hybrid methods is addressed. To evaluate the effectiveness of the proposed algorithm, 18 box constrained and 4 general constrained problems from the literature are tested. Numerical results obtained show that our proposed hybrid algorithm is more effective in obtaining more accurate solutions than those compared to.     

Cooperative differential evolution with fast variable interdependence learning and cross-cluster mutation

Cooperative optimization algorithms have been applied with success to solve many optimization problems. However, many of them often lose their effectiveness and advantages when solving large scale and complex problems, e.g., those with interacted variables. A key issue involved in cooperative optimization is the task of problem decomposition. In this paper, a fast search operator is proposed to capture the interdependencies among variables. Problem decomposition is performed based on the obtained interdependencies. Another key issue involved is the optimization of the subproblems. A cross-cluster mutation strategy is proposed to further enhance exploitation and exploration. More specifically, each operator is identified as exploitation-biased or exploration-biased. The population is divided into several clusters. For the individuals within each cluster, the exploitation-biased operators are applied. For the individuals among different clusters, the exploration-biased operators are applied. The proposed operators are incorporated into the original differential evolution algorithm. The experiments were carried out on CEC2008, CEC2010, and CEC2013 benchmarks. For comparison, six algorithms that yield top ranked results in CEC competition are selected. The comparison results demonstrated that the proposed algorithm is robust and comprehensive for large scale optimization problems.     

Solving the quadratic assignment problem with clues from nature

This paper describes a new evolutionary approach to solving quadratic assignment problems. The proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies (ES). These methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems, particularly in continuous optimization. The combinatorial variant of ES presented here performs very well on the given test problems as compared with the standard 2-Opt heuristic and results with simulated annealing and tabu search. Extensions for practical applications in factory layout are described.     

分布式空间数据分片与跨边界拓扑连接优化方法

研究分布式空间数据库(distributed spatial database,简称DSDB)中数据按区域分片时的跨边界片段拓扑连接查询问题,并提出相应的优化方法.首先研究了分布式环境下的空间数据的分片与分布,提出了空间数据分片的扩展原则:空间聚集性、空间对象的不分割性、逻辑无缝保持性.然后,将区域分割分片环境下的片段连接分为跨边界和非跨边界两类;同时,将拓扑关系分为两类,重点研究跨边界的两类片段拓扑连接.提出了跨边界空间片段拓扑连接优化的两个定理,并给出了证明.以此为基础,给出了跨边界空间拓扑连接优化规则,包括连接去除规则和连接优化转化规则.最后设计了详细的实验,对自然连接策略、半连接策略以及所提出的连接策略进行效率比较,结果表明,所提出的方法对跨边界连接优化有明显优势.因此,所提出的理论和方法可以用于分布式跨边界拓扑关系查询的优化.     

On an evolutionary approach for constrained optimization problem solving

Over the last few decades, many different evolutionary algorithms have been introduced for solving constrained optimization problems. However, due to the variability of problem characteristics, no single algorithm performs consistently over a range of problems. In this paper, instead of introducing another such algorithm, we propose an evolutionary framework that utilizes existing knowledge to make logical changes for better performance. The algorithmic aspects considered here are: the way of using search operators, dealing with feasibility, setting parameters, and refining solutions. The combined impact of such modifications is significant as has been shown by solving two sets of test problems: (i) a set of 24 test problems that were used for the CEC2006 constrained optimization competition and (ii) a second set of 36 test instances introduced for the CEC2010 constrained optimization competition. The results demonstrate that the proposed algorithm shows better performance in comparison to the state-of-the-art algorithms.     

Memory based Hybrid Dragonfly Algorithm for numerical optimization problems

Dragonfly algorithm (DA) is a recently proposed optimization algorithm based on the static and dynamic swarming behaviour of dragonflies. Due to its simplicity and efficiency, DA has received interest of researchers from different fields. However, it lacks internal memory which may lead to its premature convergence to local optima. To overcome this drawback, we propose a novel Memory based Hybrid Dragonfly Algorithm (MHDA) for solving numerical optimization problems. The pbestand gbest concept of Particle Swarm optimization (PSO) is added to conventional DA to guide the search process for potential candidate solutions and PSO is then initialized with pbest of DA to further exploit the search space. The proposed method combines the exploration capability of DA and exploitation capability of PSO to achieve global optimal solutions. The efficiency of the MHDA is validated by testing on basic unconstrained benchmark functions and CEC 2014 test functions. A comparative performance analysis between MHDA and other powerful optimization algorithms have been carried out and significance of the results is proved by statistical methods. The results show that MHDA gives better performance than conventional DA and PSO. Moreover, it gives competitive results in terms of convergence, accuracy and search-ability when compared with the state-of-the-art algorithms. The efficacy of MHDA in solving real world problems is also explained with three engineering design problems.     

Multi-strategy ensemble grey wolf optimizer and its application to feature selection

To overcome the limitation of single search strategy of grey wolf optimizer (GWO) in solving various function optimization problems, we propose a multi-strategy ensemble GWO (MEGWO) in this paper. The proposed MEGWO incorporates three different search strategies to update the solutions. Firstly, the enhanced global-best lead strategy can improve the local search ability of GWO by fully exploiting the search space around the current best solution. Secondly, the adaptable cooperative strategy embeds one-dimensional update operation into the framework of GWO to provide a higher population diversity and promote the global search ability. Thirdly, the disperse foraging strategy forces a part of search agents to explore a promising area based on a self-adjusting parameter, which contributes to the balance between the exploitation and exploration. We conducted numerical experiments based on various functions form CEC2014. The obtained results are compared with other three modified GWO and seven state-of-the-art algorithms. Furthermore, feature selection is employed to investigate the effectiveness of MEGWO on real-world applications. The experimental results show that the proposed algorithm which integrate multiple improved search strategies, outperforms other variants of GWO and other algorithms in terms of accuracy and convergence speed. It is validated that MEGWO is an efficient and reliable algorithm not only for optimization of functions with different characteristics but also for real-world optimization problems.