An interval space reducing method for constrained problems with particle swarm optimization

In this paper, we propose a method for solving constrained optimization problems using interval analysis combined with particle swarm optimization. A set inverter via interval analysis algorithm is used to handle constraints in order to reduce constrained optimization to quasi unconstrained one. The algorithm is useful in the detection of empty search spaces, preventing useless executions of the optimization process. To improve computational efficiency, a space cleaning algorithm is used to remove solutions that are certainly not optimal. As a result, the search space becomes smaller at each step of the optimization procedure. After completing pre-processing, a modified particle swarm optimization algorithm is applied to the reduced search space to find the global optimum. The efficiency of the proposed approach is demonstrated through comprehensive experimentation involving 100 000 runs on a set of well-known benchmark constrained engineering design problems. The computational efficiency of the new method is quantified by comparing its results with other PSO variants found in the literature.     

A new algorithm inspired in the behavior of the social-spider for constrained optimization

During the past decade, solving constrained optimization problems with swarm algorithms has received considerable attention among researchers and practitioners. In this paper, a novel swarm algorithm called the Social Spider Optimization (SSO-C) is proposed for solving constrained optimization tasks. The SSO-C algorithm is based on the simulation of cooperative behavior of social-spiders. In the proposed algorithm, individuals emulate a group of spiders which interact to each other based on the biological laws of the cooperative colony. The algorithm considers two different search agents (spiders): males and females. Depending on gender, each individual is conducted by a set of different evolutionary operators which mimic different cooperative behaviors that are typically found in the colony. For constraint handling, the proposed algorithm incorporates the combination of two different paradigms in order to direct the search towards feasible regions of the search space. In particular, it has been added: (1) a penalty function which introduces a tendency term into the original objective function to penalize constraint violations in order to solve a constrained problem as an unconstrained one; (2) a feasibility criterion to bias the generation of new individuals toward feasible regions increasing also their probability of getting better solutions. In order to illustrate the proficiency and robustness of the proposed approach, it is compared to other well-known evolutionary methods. Simulation and comparisons based on several well-studied benchmarks functions and real-world engineering problems demonstrate the effectiveness, efficiency and stability of the proposed method.     

组织进化数值优化算法

基于经济学中“组织”的概念 ,该文提出一种新的进化算法———组织进化算法 ,来解决无约束和有约束的数值优化问题 .该算法与传统遗传算法、进化规划、进化策略的运行机制完全不同 ,其进化操作不直接作用于个体上 ,而作用在组织上 ,为此 ,该文定义了三种组织进化算子———分裂算子、吞并算子和合作算子来引导种群进化 .理论分析证明组织进化算法具有全局收敛性 .实验中 ,用 4个无约束和 6个有约束标准函数对算法进行了测试 ,与 3个新算法作了比较 ,并对组织进化算法的性能作了深入分析 .结果表明 ,该文算法无论在解的质量上还是在计算复杂度上都优于其它算法 .对于有约束问题 ,只用了简单的静态罚函数就得到了良好的效果 ,这表明该文算法的搜索机制非常有效 ,不易陷入局部最优 .最后 ,参数分析的结果表明该文算法具有性能稳定、成功率高、对参数不敏感等优越的性能     

自收缩性的演化算法及其在布局优化问题中的应用

布局优化问题是现代工程应用中广泛存在的一类组合优化问题,但在理论上它却属于NPC(NP-Complete)问题,如果需考虑性能约束,则问题将更难于求解。论文基于演化算法自适应,自组织,自学习的特性,针对布局优化问题自身的特点,提出了一种自收缩性的演化算法(SCEA)。该算法采用浮点编码方式,定义了二元实向量类型的适应值及适应值间的严格偏序关系。算法借鉴日常生活中的一个简单事实—振动容器则装物更多,引入了三类自适应性的收缩算子(其中第三类特别适用于带性能约束的布局优化问题)。此外,文中使用了对带约束的函数优化问题特别有效的多父体杂交算子,并且针对带性能约束的布局优化问题,提出了“零性能约束初始化”过程。文后,引用了两个带性能约束的布局优化问题的已知例子和一个作者构造的较大规模布局优化问题的例子,实验结果表明,前两个问题对比目前已知最好结果无论在求解时间或结果的精度上均有较大突破,后一个问题也获得了相当好的结果,从而充分验证了算法的有效性和可行性。     

A hybrid shuffled complex evolution approach with pattern search for unconstrained optimization

The difficulties associated with using classical mathematical programming methods on complex optimization problems have contributed to the development of alternative and efficient numerical approaches. Recently, to overcome the limitations of classical optimization methods, researchers have proposed a wide variety of meta-heuristics for searching near-optimum solutions to problems. Among the existing meta-heuristic algorithms, a relatively new optimization paradigm is the Shuffled Complex Evolution at the University of Arizona (SCE-UA) which is a global optimization strategy that combines concepts of the competition evolution theory, downhill simplex procedure of Nelder-Mead, controlled random search and complex shuffling. In an attempt to reduce processing time and improve the quality of solutions, particularly to avoid being trapped in local optima, in this paper is proposed a hybrid SCE-UA approach. The proposed hybrid algorithm is the combination of SCE-UA (without Nelder-Mead downhill simplex procedure) and a pattern search approach, called SCE-PS, for unconstrained optimization. Pattern search methods are derivative-free, meaning that they do not use explicit or approximate derivatives. Moreover, pattern search algorithms are direct search methods well suitable for the global optimization of highly nonlinear, multiparameter, and multimodal objective functions. The proposed SCE-PS method is tested with six benchmark optimization problems. Simulation results show that the proposed SCE-PS improves the searching performance when compared with the classical SCE-UA and a genetic algorithm with floating-point representation for all the tested problems. As evidenced by the performance indices based on the mean performance of objective function in 30 runs and mean of computational time, the SCE-PS algorithm has demonstrated to be effective and efficient at locating best-practice optimal solutions for unconstrained optimization.     

求解优化问题的混合PSO-Solver算法

融合了粒子群算法(PSO) 和Solver 加载宏,形成混合PSO-Solver算法进行优化问题的求解。PSO作为全局搜索算法首先给出问题的全局可行解,Solver则是基于梯度信息的局部搜索工具,对粒子群算法得出的解再进行改进,二者互相结合,既加快了全局搜索的速度,又有效地避免了陷入局部最优。算法用VBA语言进行编程,简单且易于实现。通过对无约束优化问题和约束优化问题的求解,以及和标准PSO、其他一些混合算法的比较表明,PSO-Solver算法能够有效地提高求解过程的收敛速度和解的精确性。     

Artificial bee colony algorithm for large-scale problems and engineering design optimization

Engineering design problems are generally large scale or nonlinear or constrained optimization problems. The Artificial Bee Colony (ABC) algorithm is a successful tool for optimizing unconstrained problems. In this work, the ABC algorithm is used to solve large scale optimization problems, and it is applied to engineering design problems by extending the basic ABC algorithm simply by adding a constraint handling technique into the selection step of the ABC algorithm in order to prefer the feasible regions of entire search space. Nine well-known large scale unconstrained test problems and five well-known constrained engineering problems are solved by using the ABC algorithm and the performance of ABC algorithm is compared against those of state-of-the-art algorithms.     

Memetic algorithm with Preferential Local Search using adaptive weights for multi-objective optimization problems

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.     

A parallel boundary search particle swarm optimization algorithm for constrained optimization problems

During the past decade, considerable research has been conducted on constrained optimization problems (COPs) which are frequently encountered in practical engineering applications. By introducing resource limitations as constraints, the optimal solutions in COPs are generally located on boundaries of feasible design space, which leads to search difficulties when applying conventional optimization algorithms, especially for complex constraint problems. Even though penalty function method has been frequently used for handling the constraints, the adjustment of control parameters is often complicated and involves a trial-and-error approach. To overcome these difficulties, a modified particle swarm optimization (PSO) algorithm named parallel boundary search particle swarm optimization (PBSPSO) algorithm is proposed in this paper. Modified constrained PSO algorithm is adopted to conduct global search in one branch while Subset Constrained Boundary Narrower (SCBN) function and sequential quadratic programming (SQP) are applied to perform local boundary search in another branch. A cooperative mechanism of the two branches has been built in which locations of the particles near boundaries of constraints are selected as initial positions of local boundary search and the solutions of local boundary search will lead the global search direction to boundaries of active constraints. The cooperation behavior of the two branches effectively reinforces the optimization capability of the PSO algorithm. The optimization performance of PBSPSO algorithm is illustrated through 13 CEC06 test functions and 5 common engineering problems. The results are compared with other state-of-the-art algorithms and it is shown that the proposed algorithm possesses a competitive global search capability and is effective for constrained optimization problems in engineering applications.     

采用不可微精确罚函数的约束优化演化算法

针对多数已有的采用罚函数的约束优化遗传算法存在优化效果差的问题 ,提出了一种新的求解约束优化问题的演化算法 .借助不可微精确罚函数把约束问题转化为单个无约束问题来处理 .采用混合杂交和间歇变异来提高算法的搜索能力 .数值实验结果表明了新算法的优化效果远远优于已有的几种采用罚函数的遗传算法     

An adaptive balance optimization algorithm and its engineering application

The policy of balance between exploration capability and exploitation capability directly affects the solution performance of the meta-heuristic algorithm in a limited time. In order to better balance the exploration and exploitation capabilities of the algorithm and meet the solution requirements of complex real-world problems, the adaptive balance optimization algorithm (ABOA) is proposed in this paper. The algorithm consists of a global search phase (GSP) and a local search phase (LSP) and is controlled by a fixed parameter. ABOA not only considers the balance of exploration and exploitation capabilities of the algorithm throughout the whole iterative process but also focuses on the balance of exploration and exploitation in both GSP and LSP. The search in both phases is focused around the respective search centers from outside to inside. ABOA balances the exploration and exploitation capabilities of the algorithm throughout the search process by two adaptive policies: changing the search area and changing the search center. Fifty-two unconstrained benchmark test functions were employed to evaluate the performance of ABOA. The results of ABOA were compared with nine excellent optimization algorithms available in the literature. The statistical results and Friedman test showed that ABOA was significantly competitive. Finally, the results of the examined engineering design problems showed that ABOA can solve the constrained optimization problem better compared to other methods.     

JayaX: Jaya algorithm with xor operator for binary optimization

Jaya is a population-based heuristic optimization algorithm proposed for solving constrained and unconstrained optimization problems. The peculiar distinct feature of Jaya from the other population-based algorithms is that it updates the positions of artificial agent in the population by considering the best and worst individuals. This is an important property for the algorithm to balance exploration and exploitation on the solution space. However, the basic Jaya cannot be applied to binary optimization problems because the solution space is discretely structured for this type of optimization problems and the decision variables of the binary optimization problems can be element of set [0,1]. In this study, we first focus on discretization of Jaya by using a logic operator, exclusive or – xor. The proposed idea is simple but effective because the solution update rule of Jaya is replaced with the xor operator, and when the obtained results are compared with the state-of-art algorithms, it is seen that the Jaya-based binary optimization algorithm, JayaX for short, produces better quality results for the binary optimization problems dealt with the study. The benchmark problems in this study are uncapacitated facility location problems and CEC2015 numeric functions, and the performance of the algorithms is compared on these problems. In order to improve the performance of the proposed algorithm, a local search module is also integrated with the JayaX. The obtained results show that the proposed algorithm is better than the compared algorithms in terms of solution quality and robustness.     

求解约束优化问题的改进果蝇优化算法及其工程应用

针对基本果蝇优化算法收敛速度慢、求解精度低、易于陷入局部极值以及算法候选解不能取负值等不足,提出一种用于解决约束优化问题的改进果蝇优化算法.该算法利用果蝇个体历史最佳记忆信息和种群全局历史最佳记忆信息构建多策略混合协同进化的搜索机制,以达到有效平衡算法的全局探索与局部开发的目的,同时也能够较好地避免算法的早熟收敛问题;...     

动态分级中心引力约束优化算法及工程应用

结合非固定多段罚函数处理约束条件,提出一种动态分级中心引力优化算法用于求解约束优化问题。该算法利用佳点集初始化个体以保证种群的多样性。在每次迭代过程中将种群分为两个子种群,分别用于全局搜索和局部搜索,根据搜索阶段动态调整子种群个体数目。对几个标准的测试问题和工程优化问题进行数值实验,结果表明该算法能处理不同的约束优化问题。     

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.     

A novel memetic algorithm based on invasive weed optimization and differential evolution for constrained optimization

This paper presents a novel memetic algorithm, named as IWO_DE, to tackle constrained numerical and engineering optimization problems. In the proposed method, invasive weed optimization (IWO), which possesses the characteristics of adaptation required in memetic algorithm, is firstly considered as a local refinement procedure to adaptively exploit local regions around solutions with high fitness. On the other hand, differential evolution (DE) is introduced as the global search model to explore more promising global area. To accommodate the hybrid method with the task of constrained optimization, an adaptive weighted sum fitness assignment and polynomial distribution are adopted for the reproduction and the local dispersal process of IWO, respectively. The efficiency and effectiveness of the proposed approach are tested on 13 well-known benchmark test functions. Besides, our proposed IWO_DE is applied to four well-known engineering optimization problems. Experimental results suggest that IWO_DE can successfully achieve optimal results and is very competitive compared with other state-of-art algorithms.     

求解带约束优化问题的混合式多策略萤火虫算法

目前多目标优化算法主要针对如何处理多个目标之间的冲突,对于如何处理约束考虑较少,鉴于此,提出一种求解带约束优化问题的混合式多策略萤火虫算法(HMSFA-PC).首先,提出一种改进的动态罚函数策略对约束优化问题进行预处理,将其转换为非约束优化问题;其次,对萤火虫算法本身进行改进,采用Lévy flights搜索机制有效地增大搜索范围;接着,引入随机扩张因子改进算法吸引模型,使种群突破束缚,有效避免早熟收敛,提出自适应维度重组机制,根据不同迭代时期选择差异性较大的个体进行信息交互、相互学习.为检验算法处理无约束优化问题的性能,将其在基准测试函数上与部分典型算法进行比较;为检验算法处理约束优化问题的性能,将其在实际约束测试问题中与一些顶尖约束求解算法进行比较.结果表明,HMSFA-PC在处理无约束优化问题时具有收敛速度快、收敛精度高等优势,并且在动态罚函数的协作下求解实际约束优化问题时仍具有良好的优化性能.     

A modified augmented Lagrangian with improved grey wolf optimization to constrained optimization problems

This paper presents a novel constrained optimization algorithm named MAL-IGWO, which integrates the benefit of the improved grey wolf optimization (IGWO) capability for discovering the global optimum with the modified augmented Lagrangian (MAL) multiplier method to handle constraints. In the proposed MAL-IGWO algorithm, the MAL method effectively converts a constrained problem into an unconstrained problem and the IGWO algorithm is applied to deal with the unconstrained problem. This algorithm is tested on 24 well-known benchmark problems and 3 engineering applications, and compared with other state-of-the-art algorithms. Experimental results demonstrate that the proposed algorithm shows better performance in comparison to other approaches.

     

求解约束优化问题的改进灰狼优化算法

针对基本灰狼优化(GWO)算法存在求解精度低、收敛速度慢、局部搜索能力差的问题,提出一种改进灰狼优化(IGWO)算法用于求解约束优化问题。该算法采用非固定多段映射罚函数法处理约束条件,将原约束优化问题转化为无约束优化问题,然后利用IGWO算法对转换后的无约束优化问题进行求解。在IGWO算法中,引入佳点集理论生成初始种群,为算法全局搜索奠定基础;为了提高局部搜索能力和加快收敛,对当前最优灰狼个体执行Powell局部搜索。采用几个标准约束优化测试问题进行仿真实验,结果表明该算法不仅克服了基本GWO的缺点,而且性能优于差分进化和粒子群优化算法。