An upgraded artificial bee colony (ABC) algorithm for constrained optimization problems

Artificial bee colony (ABC) algorithm developed by Karaboga is a nature inspired metaheuristic based on honey bee foraging behavior. It was successfully applied to continuous unconstrained optimization problems and later it was extended to constrained design problems as well. This paper introduces an upgraded artificial bee colony (UABC) algorithm for constrained optimization problems. Our UABC algorithm enhances fine-tuning characteristics of the modification rate parameter and employs modified scout bee phase of the ABC algorithm. This upgraded algorithm has been implemented and tested on standard engineering benchmark problems and the performance was compared to the performance of the latest Akay and Karaboga’s ABC algorithm. Our numerical results show that the proposed UABC algorithm produces better or equal best and average solutions in less evaluations in all cases.     

An efficient artificial bee colony algorithm with application to nonlinear predictive control

In this paper a constrained nonlinear predictive control algorithm, that uses the artificial bee colony (ABC) algorithm to solve the optimization problem, is proposed. The main objective is to derive a simple and efficient control algorithm that can solve the nonlinear constrained optimization problem with minimal computational time. Indeed, a modified version, enhancing the exploring and the exploitation capabilities, of the ABC algorithm is proposed and used to design a nonlinear constrained predictive controller. This version allows addressing the premature and the slow convergence drawbacks of the standard ABC algorithm, using a modified search equation, a well-known organized distribution mechanism for the initial population and a new equation for the limit parameter. A convergence statistical analysis of the proposed algorithm, using some well-known benchmark functions is presented and compared with several other variants of the ABC algorithm. To demonstrate the efficiency of the proposed algorithm in solving engineering problems, the constrained nonlinear predictive control of the model of a Multi-Input Multi-Output industrial boiler is considered. The control performances of the proposed ABC algorithm-based controller are also compared to those obtained using some variants of the ABC algorithms.     

A hybrid optimization method and its role in computer-aided design

The variable metric methods have been analyzed and exploited in the past to achieve a superlinear rate of convergence in unconstrained optimization. Recently, the update formulas used in these methods have been extended for constrained optimization. The update formulas construct approximate second order derivatives using first order information. These are referred to as constrained variable metric (CVM) methods. Higher order of convergence is often accompanied by a smaller domain of convergence. To overcome this limitation of CVM methods, a hybrid optimization algorithm is presented in this paper. It uses a cost function bounding concept initially and a CVM method in later stages of the search process. In addition, the algorithm uses an active set strategy and is globally convergent. An improved active set strategy is suggested. Besides developing a superlinear optimization algorithm, an efficient programming structure for computer-aided design of engineering systems is suggested and implemented. A number of mathematical programming problems, and small and large scale engineering design problems are solved to test numerical aspects of the algorithm. The algorithm has performed extremely well on the test problems.     

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 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.

     

Discrete optimum design of truss structures using artificial bee colony algorithm

Over the past few years, swarm intelligence based optimization techniques such as ant colony optimization and particle swarm optimization have received considerable attention from engineering researchers and practitioners. These algorithms have been used in the solution of various engineering problems. Recently, a relatively new swarm based optimization algorithm called the Artificial Bee Colony (ABC) algorithm has begun to attract interest from researchers to solve optimization problems. The aim of this study is to present an optimization algorithm based on the ABC algorithm for the discrete optimum design of truss structures. The ABC algorithm is a meta-heuristic optimization technique that mimics the process of food foraging of honeybees. Originally the ABC algorithm was developed for continuous function optimization problems. This paper describes the modifications made to the ABC algorithm in order to solve discrete optimization problems and to improve the algorithm’s performance. In order to demonstrate the effectiveness of the modified algorithm, four structural problems with up to 582 truss members and 29 design variables were solved and the results were compared with those obtained using other well-known meta-heuristic search techniques. The results demonstrate that the ABC algorithm is very effective and robust for the discrete optimization designs of truss structural problems.     

Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization

The performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process. The fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve. Modern metaheuristic algorithms are generally more suitable for global optimization. This paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution. After a detailed formulation and explanation of its implementation, the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks. For the validation against constrained problems, this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature. The performance of the proposed algorithm is further compared with various, state-of-the-art algorithms in the area. The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods. The unique search features used in the proposed algorithm are analyzed, and their implications for future research are also discussed in detail.     

正交文化算法及其在布局优化问题中的应用

布局优化问题是工程应用中普遍存在的一种组合优化问题,属于NP完备问题。针对布局优化问题,将差异演化算法和郭涛算法融入文化算法的框架,利用正交设计方法初始化种群,提出了一种正交文化算法。通过对一个带约束的和一个较大规模的不带约束的布局优化问题进行性能比较,验证了该算法的可行性和有效性。     

基于最优高斯随机游走和个体筛选策略的差分进化算法

针对差分进化算法开发能力较差的问题, 提出一种具有快速收敛的新型差分进化算法. 首先, 利用最优高斯随机游走策略提高算法的开发能力; 然后, 采用基于个体优化性能的简化交叉变异策略实现种群的进化操作以加强其局部搜索能力; 最后, 通过个体筛选策略进一步提高算法的探索能力以避免陷入局部最优. 12 个标准测试函 数和两种带约束的工程优化问题的实验结果表明, 所提出的算法在收敛速度、算法可靠性及收敛精度方面均优于EPSDE、SaDE、JADE、BSA、CoBiDE、GSA和ABC等算法, 在加强算法探索能力的同时能够有效地提高算法的开发能力.

     

求解工程约束优化问题的PSO-ABC混合算法*

针对包含约束条件的工程优化问题,提出了基于人工蜂群的粒子群优化PSO-ABC算法。将PSO中较优的粒子作为ABC算法的蜜源,并使用禁忌表存储其局部极值,克服粒子群优化算法易陷入局部最优的缺陷。采用可行性规则进行约束处理,将粒子种群分为可行子群和不可行子群,并在ABC算法产生蜜源的过程中保留部分较优的可行解和不可行解的信息,弥补了可行性规则处理最优点位于约束边界附近的问题时存在的不足。四个典型工程优化设计的实验结果表明,该算法能够寻得更优的约束最优化解,且稳健性更强。     

Investigating Multi-View Differential Evolution for solving constrained engineering design problems

Several constrained and unconstrained optimization problems have been adequately solved over the years thanks to advances in the metaheuristics area. In the last decades, different metaheuristics have been proposed employing new ideas, and hybrid algorithms that improve the original metaheuristics have been developed. One of the most successfully employed metaheuristics is the Differential Evolution. In this paper it is proposed a Multi-View Differential Evolution algorithm (MVDE) in which several mutation strategies are applied to the current population to generate different views at each iteration. The views are then merged according to the winner-takes-all paradigm, resulting in automatic exploration/exploitation balance. MVDE was tested to solve a set of well-known constrained engineering design problems and the obtained results were compared to those from many state-of-the-art metaheuristics. Results show that MVDE was very competitive in the considered problems, largely outperforming several of the compared algorithms.     

An exact penalty function algorithm for solving general constrained parameter optimization problems

An exact penalty function type of algorithm is proposed to solve a general class of constrained parameter optimization problems. The proposed algorithm has the property that any solution obtained by it will always satisfy the problem constraints, and that it will obtain a solution to the constrained problem, within a given specified tolerance, by solving a single unconstrained problem, i.e. it is not necessary to solve a sequence of unconstrained optimization problems. The algorithm applies a modification of Rosenbrock's (Rosenbrock, 1960) polynomial boundary penalty function, and a negative exponential penalty function with moving parameters, to modify the objective function in the neighborhood of the constrained region; a robust unconstrained algorithm (Davison and Wong, 1975) is then used to solve the resulting unconstrained optimization problem. Some standard test functions are included to show the performance of the algorithhm. Application of the algorithm is then made to solve some computer-aided design problems occurring in the area of control system synthesis.     

Evaluating differential evolution with penalty function to solve constrained engineering problems

Over the years, several metaheuristics have been developed to solve hard constrained and unconstrained optimization problems. In general, a metaheuristic is proposed and following researches are made to improve the original algorithm. In this paper, we evaluate a not so new metaheuristic called differential evolution (DE) to solve constrained engineering design problems and compare the results with some recent metaheuristics. Results show that the classical DE with a very simple penalty function to handle constraints is still very competitive in the tested problems.     

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。     

BSTBGA: A hybrid genetic algorithm for constrained multi-objective optimization problems

Most of the existing multi-objective genetic algorithms were developed for unconstrained problems, even though most real-world problems are constrained. Based on the boundary simulation method and trie-tree data structure, this paper proposes a hybrid genetic algorithm to solve constrained multi-objective optimization problems (CMOPs). To validate our approach, a series of constrained multi-objective optimization problems are examined, and we compare the test results with those of the well-known NSGA-II algorithm, which is representative of the state of the art in this area. The numerical experiments indicate that the proposed method can clearly simulate the Pareto front for the problems under consideration.     

A new PSO-based algorithm for multi-objective optimization with continuous and discrete design variables

This paper presents a new multi-objective optimization algorithm called FC-MOPSO for optimal design of engineering problems with a small number of function evaluations. The proposed algorithm expands the main idea of the single-objective particle swarm optimization (PSO) algorithm to deal with constrained and unconstrained multi-objective problems (MOPs). FC-MOPSO employs an effective procedure in selection of the leader for each particle to ensure both diversity and fast convergence. Fifteen benchmark problems with continuous design variables are used to validate the performance of the proposed algorithm. Finally, a modified version of FC-MOPSO is introduced for handling discrete optimization problems. Its performance is demonstrated by optimizing five space truss structures. It is shown that the FC-MOPSO can effectively find acceptable approximations of Pareto fronts for structural MOPs within very limited number of function evaluations.     

Cognitive behavior optimization algorithm for solving optimization problems

Nature-based algorithms have become popular in recent fifteen years and have been widely applied in various fields of science and engineering, such as robot control, cluster analysis, controller design, dynamic optimization and image processing. In this paper, a new swarm intelligence algorithm named cognitive behavior optimization algorithm (COA) is introduced, which is used to solve the real-valued numerical optimization problems. COA has a detailed cognitive behavior model. In the model of COA, the common phenomenon of foraging food source for population is summarized as the process of exploration–communication–adjustment. Matching with the process, three main behaviors and two groups in COA are introduced. Firstly, cognitive population uses Gaussian and Levy flight random walk methods to explore the search space in the rough search behavior. Secondly, the improved crossover and mutation operator are used in the information exchange and share behavior between the two groups: cognitive population and memory population. Finally, the intelligent adjustment behavior is used to enhance the exploitation of the population for cognitive population. To verify the performance of our approach, both the classic and modern complex benchmark functions considered as the unconstrained functions are employed. Meanwhile, some well-known engineering design optimization problems are used as the constrained functions in the literature. The experimental results, considering both convergence and accuracy simultaneously, demonstrate the effectiveness of COA for global numerical and engineering optimization problems.     

A hybrid cooperative search algorithm for constrained optimization

Many engineering design problems can be formulated as constrained optimization problems which often consist of many mixed equality and inequality constraints. In this article, a hybrid coevolutionary method is developed to solve constrained optimization problems formulated as min–max problems. The new method is fast and capable of global search because of combining particle swarm optimization and gradient search to balance exploration and exploitation. It starts by transforming the problem into unconstrained one using an augmented Lagrangian function, then using two groups to optimize different components of the solution vector in a cooperative procedure. In each group, the final stage of the search procedure is accelerated by via a simple local search method on the best point reached by the preceding exploration based search. We validated the effectiveness and robustness of the proposed algorithm using several engineering problems taken from the specialised literature.     

Interval-based global optimization in engineering using model reformulation and constraint propagation

This paper deals with the preliminary design problem when the product is modeled as an analytic model. The analytic models based method aims to use mathematical equations to address both multi-physic and economic characteristics of a product. The proposed approach is to convert the preliminary design problem into a global constrained optimization problem. The objective is to develop powerful optimization methods enough to handle complex analytical models. We propose to adapt an approach to solve this problem based on interval analysis, constraint propagation and model reformulation. In order to understand the optimization algorithm used for engineering design problems, some basic definitions and properties of interval analysis are introduced. Then, the basic optimization algorithms for both unconstrained and constrained problems are introduced and illustrated. The next section introduces the reformulation technique as main accelerating device. An application of the reformulation device and its global optimization algorithm on the optimal design of electrical actuators is presented.     

An improved dynamic membrane evolutionary algorithm for constrained engineering design problems

Constrained global optimization is a highly important and challenging task in the field of optimization, and is embedded in many science and engineering optimizations. In this paper, an improved dynamic membrane evolutionary algorithm based on particle swarm optimization and differential evolution (IDMEA-PSO/DE) is proposed to solve constrained engineering design problems. The method combines the dynamic membrane structure of P systems and the PSO/DE search strategy. The performance of IDMEA-PSO/DE is tested on several well-known engineering design problems. The results of the simulation experiments show that the proposed algorithm is effective and outperforms other state-of-the-art-algorithms.