A hybrid differential evolution augmented Lagrangian method for constrained numerical and engineering optimization

We present a new hybrid method for solving constrained numerical and engineering optimization problems in this paper. The proposed hybrid method takes advantage of the differential evolution (DE) ability to find global optimum in problems with complex design spaces while directly enforcing feasibility of constraints using a modified augmented Lagrangian multiplier method. The basic steps of the proposed method are comprised of an outer iteration, in which the Lagrangian multipliers and various penalty parameters are updated using a first-order update scheme, and an inner iteration, in which a nonlinear optimization of the modified augmented Lagrangian function with simple bound constraints is implemented by a modified differential evolution algorithm. Experimental results based on several well-known constrained numerical and engineering optimization problems demonstrate that the proposed method shows better performance in comparison to the state-of-the-art algorithms.     

A new chaotic multi-verse optimization algorithm for solving engineering optimization problems

Multi-verse optimization algorithm (MVO) is one of the recent meta-heuristic optimization algorithms. The main inspiration of this algorithm came from multi-verse theory in physics. However, MVO like most optimization algorithms suffers from low convergence rate and entrapment in local optima. In this paper, a new chaotic multi-verse optimization algorithm (CMVO) is proposed to overcome these problems. The proposed CMVO is applied on 13 benchmark functions and 7 well-known design problems in the engineering and mechanical field; namely, three-bar trust, speed reduce design, pressure vessel problem, spring design, welded beam, rolling element-bearing and multiple disc clutch brake. In the current study, a modified feasible-based mechanism is employed to handle constraints. In this mechanism, four rules were used to handle the specific constraint problem through maintaining a balance between feasible and infeasible solutions. Moreover, 10 well-known chaotic maps are used to improve the performance of MVO. The experimental results showed that CMVO outperforms other meta-heuristic optimization algorithms on most of the optimization problems. Also, the results reveal that sine chaotic map is the most appropriate map to significantly boost MVO’s performance.     

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.     

Cohort intelligence algorithm for discrete and mixed variable engineering problems

Abstract

In this study, the performance of an emerging socio inspired metaheuristic optimization technique referred to as Cohort Intelligence (CI) algorithm is evaluated on discrete and mixed variable nonlinear constrained optimization problems. The investigated problems are mainly adopted from discrete structural optimization and mixed variable mechanical engineering design domains. For handling the discrete solution variables, a round off integer sampling approach is proposed. Furthermore, in order to deal with the nonlinear constraints, a penalty function method is incorporated. The obtained results are promising and computationally more efficient when compared to the other existing optimization techniques including a Multi Random Start Local Search algorithm. The associated advantages and disadvantages of CI algorithm are also discussed evaluating the effect of its two parameters namely the number of candidates, and sampling space reduction factor.     

约束进化算法及其应用研究综述

约束优化问题广泛存在于科学研究和工程实践中,其对应的约束优化进化算法也成为了进化领域的重要研究方向。约束优化进化算法的本质问题是如何有效地利用不可行解和可行解的信息,平衡目标函数和约束条件,使得算法更加高效。首先对约束优化问题进行定义;然后详细分析了目前主流的约束进化算法,同时,基于不同的约束处理机制,将这些机制分为约束和目标分离法、惩罚函数法、多目标优化法、混合法和其他算法,并对这些方法进行了详细的分析和总结;接着指出约束进化算法亟待解决的问题,并明确指出未来需要进一步研究的方向;最后对约束进化算法在工程优化、电子和通信工程、机械设计、环境资源配置、科研领域和管理分配等方面的应用进行了介绍。     

A ranking selection-based particle swarm optimizer for engineering design optimization problems

Particle swarm optimization (PSO) algorithms have been proposed to solve optimization problems in engineering design, which are usually constrained (possibly highly constrained) and may require the use of mixed variables such as continuous, integer, and discrete variables. In this paper, a new algorithm called the ranking selection-based PSO (RSPSO) is developed. In RSPSO, the objective function and constraints are handled separately. For discrete variables, they are partitioned into ordinary discrete and categorical ones, and the latter is managed and searched directly without the concept of velocity in the standard PSO. In addition, a new ranking selection scheme is incorporated into PSO to elaborately control the search behavior of a swarm in different search phases and on categorical variables. RSPSO is relatively simple and easy to implement. Experiments on five engineering problems and a benchmark function with equality constraints were conducted. The results indicate that RSPSO is an effective and widely applicable optimizer for optimization problems in engineering design in comparison with the state-of-the-art algorithms in the area.     

A novel physical based meta-heuristic optimization method known as Lightning Attachment Procedure Optimization

In this article, A novel nature-inspired optimization algorithm known as Lightning Attachment Procedure Optimization (LAPO) is proposed. The proposed approach mimics the lightning attachment procedure including the downward leader movement, the upward leader propagation, the unpredictable trajectory of lightning downward leader, and the branch fading feature of lightning. Final optimum result would be the lightning striking point. The proposed method is free from any parameter tuning and it is rarely stuck in the local optimum points. To evaluate the proposed algorithm, 29 mathematical benchmark functions are employed and the results are compared to those of 9 high quality well-known optimization methods The results of the proposed method are compared from different points of views, including quality of the results, convergence behavior, robustness, and CPU time consumption. Superiority and high quality performance of the proposed method are demonstrated through comparing the results. Moreover, the proposed method is also tested by five classical engineering design problems including tension/compression spring, welded beam, pressure vessel designs, Gear train design, and Cantilever beam design and a high constraint optimization problem known as Optimal Power Flow (OPF) which is a high constraint electrical engineering problem. The excellence performance of the proposed method in solving the problems with large number of constraints and also discrete optimization problems are also concluded from the results of the six engineering problem.     

一种新的约束优化遗传算法及其工程应用

提出一种新的用于求解约束优化问题的遗传算法,该算法利用佳点集方法初始化个体以维持种群的多样性.在进化过程中,通过可行解与不可行解算术交叉对问题的决策空间进行搜索;对可行种群与不可行种群分别采用高斯变异和柯西变异,从而协调算法的勘探和开采能力.几个标准测试问题的实验结果表明该算法的有效性;应用新算法求解两个工程优化设计问题,结果表明该算法的可行性.     

An efficient multiobjective differential evolution algorithm for engineering design

Solving engineering design and resources optimization via multiobjective evolutionary algorithms (MOEAs) has attracted much attention in the last few years. In this paper, an efficient multiobjective differential evolution algorithm is presented for engineering design. Our proposed approach adopts the orthogonal design method with quantization technique to generate the initial archive and evolutionary population. An archive (or secondary population) is employed to keep the nondominated solutions found and it is updated by a new relaxed form of Pareto dominance, called Pareto-adaptive ϵ-dominance (paϵ-dominance), at each generation. In addition, in order to guarantee to be the best performance produced, we propose a new hybrid selection mechanism to allow the archive solutions to take part in the generating process. To handle the constraints, a new constraint-handling method is employed, which does not need any parameters to be tuned for constraint handling. The proposed approach is tested on seven benchmark constrained problems to illustrate the capabilities of the algorithm in handling mathematically complex problems. Furthermore, four well-studied engineering design optimization problems are solved to illustrate the efficiency and applicability of the algorithm for multiobjective design optimization. Compared with Nondominated Sorting Genetic Algorithm II, one of the best MOEAs available at present, the results demonstrate that our approach is found to be statistically competitive. Moreover, the proposed approach is very efficient and is capable of yielding a wide spread of solutions with good coverage and convergence to true Pareto-optimal fronts.     

自适应惩罚策略及其在交通信号优化中的应用

针对约束优化问题的求解,设计了一种处理约束条件的自适应惩罚策略,用于将具有不等式约束和等式约束的优化问题转变为仅包含决策变量上、下限约束的优化问题。该策略通过引入约束可行测度、可行度的概念来描述决策变量服从于不等式约束和等式约束的程度,并以此构造处理约束条件的自适应惩罚函数,惩罚值随着约束可行度的变化而动态自适应地改变。为了检验该惩罚策略的有效性,针对单路口交通信号优化问题进行了应用研究,并用三种不同算法进行了大量的仿真计算,结果表明所设计的自适应策略在具有高度约束条件的城市交通信号优化问题中具有良好的效果。     

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。     

直接搜索模拟退火算法的自适应改进

针对直接搜索模拟退火算法求解高维优化问题存在稳定性差、收敛成功率低现象,提出一种自适应的直接搜索模拟退火算法。该算法通过构造基于迭代温度动态调整搜索范围的新点产生方式和自适应寻优模块,增强了算法跳出局部极值和加快邻域搜索的能力,利用柯西分布状态发生函数的大范围遍历特点,弥补了直接搜索模拟退火算法求解高维多峰值问题易陷入局部解和计算效率低的不足。结合可行规则法处理约束问题,典型高维函数和工程优化设计实例的测试结果表明,该算法能够有效求解高维优化问题,整体性能较直接搜索模拟退火算法有显著提高。     

求解约束优化问题的中心引力优化算法及其工程应用

为了平衡算法的全局探测能力和局部搜索能力,提出一种基于交叉与变异的中心引力优化算法用于求解约束优化问题。该算法首先利用佳点集方法构造初始种群以保证粒子的多样性。以一定概率随机选择粒子与当前最优粒子进行算术交叉操作,引导粒子向全局最优解靠拢。对当前最优粒子进行多样性变异以避免算法陷入局部最优。标准测试函数和工程优化应用问题的实验结果表明,新算法能有效求解不同的约束优化问题。     

Hybrid evolutionary algorithm and application to structural optimization

This paper introduces a new evolutionary algorithm with a globally stochastic but locally heuristic search strategy. It is implemented by incorporating a modified micro-genetic algorithm with two local optimization operators. Performance tests using two benchmarking functions demonstrate that the new algorithm has excellent convergence performance when applied to multimodal optimization problems. The number of objective function evaluations required to obtain global optima is only 3.5–3.7% of that of using the conventional micro-genetic algorithm. The new algorithm is used to optimize the design of an 18-bar truss, with the aim of minimizing its weight while meeting the stress, section area, and geometry constraints. The corresponding optimal design is obtained with considerably fewer computational operations than required for the existing algorithms.     

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...     

基于遗传算法的大规模矩形件优化排样

大规模矩形件优化排样是一个典型的组合优化问题，属于NP-hard问题．实际工程中对一个排样方案一般有满足“一刀切”的工艺要求，“一刀切”要求增加了对排样的约束．提出的优化算法，将矩形匹配分割算法作为遗传算法染色体的解码器实现一个排样方案，用遗传算法进行排样方案的全局搜索．算例比较表明，该算法可以求得满足“一刀切”约束的最优解．     

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.     

基于遗传算法的城市混合型路网设计问题研究

针对目前城市路网设计中存在的一些缺陷,提出一种基于遗传算法的城市混合型路网设计的多目标优化模型,它可一次性求得多个可供规划决策者进行选择的路网设计方案,并利用一个算例进行仿真试验,结果表明,该模型和算法是可行的、有效的,可以为城市路网规划提供借鉴。     

基于微粒群算法的生料浆调配多目标满意优化

氧化铝生料浆优化调配是一个多目标、多约束且非线性的0-1组合优化问题。首先给出了该问题的数学描述,然后根据调配过程判断生料浆质量是否达标的不同满意标准,基于满意度原理,将带约束的多目标优化问题转换为求多目标和多约束综合满意度最大的满意优化问题,最后提出一种改进的离散微粒群算法对该问题进行求解。实例仿真和工业应用证明了模型与算法的有效性     

A hybrid CBO–PSO algorithm for optimal design of truss structures with dynamic constraints

The vibration domain of structures can be reduced by imposing some constraints on their natural frequencies. For this purpose optimal design of structures under frequency constraints is required which involves highly non-linear and non-convex problems. In this paper an efficient hybrid algorithm is developed for solving such optimization problems. This algorithm utilizes the recently developed colliding bodies optimization (CBO) algorithm as the main engine and uses the positive properties of the particle swarm optimization (PSO) algorithm to increase the efficiency of the CBO. The distinct feature of the present hybrid algorithm is that it requires no parameter tuning. The CBO is known for being parameter independent, and avoiding the use of the traditional penalty method to handle the constraints upholds this property. Two mathematical constrained functions taken from the literature are studied to verify the performance of the algorithm. The algorithm is then applied to optimize truss structures with frequency limitations. The numerical results demonstrate the efficiency of the presented algorithm for this class of problems.