Multi-objective optimization using teaching-learning-based optimization algorithm

Two major goals in multi-objective optimization are to obtain a set of nondominated solutions as closely as possible to the true Pareto front (PF) and maintain a well-distributed solution set along the Pareto front. In this paper, we propose a teaching-learning-based optimization (TLBO) algorithm for multi-objective optimization problems (MOPs). In our algorithm, we adopt the nondominated sorting concept and the mechanism of crowding distance computation. The teacher of the learners is selected from among current nondominated solutions with the highest crowding distance values and the centroid of the nondominated solutions from current archive is selected as the Mean of the learners. The performance of proposed algorithm is investigated on a set of some benchmark problems and real life application problems and the results show that the proposed algorithm is a challenging method for multi-objective algorithms.     

Biogeography-based optimization for constrained optimization problems

Biogeography-based optimization (BBO) has been recently proposed as a viable stochastic optimization algorithm and it has so far been successfully applied in a variety of fields, especially for unconstrained optimization problems. The present paper shows how BBO can be applied for constrained optimization problems, where the objective is to find a solution for a given objective function, subject to both inequality and equality constraints.     

Blended biogeography-based optimization for constrained optimization

Biogeography-based optimization (BBO) is a new evolutionary optimization method that is based on the science of biogeography. We propose two extensions to BBO. First, we propose a blended migration operator. Benchmark results show that blended BBO outperforms standard BBO. Second, we employ blended BBO to solve constrained optimization problems. Constraints are handled by modifying the BBO immigration and emigration procedures. The approach that we use does not require any additional tuning parameters beyond those that are required for unconstrained problems. The constrained blended BBO algorithm is compared with solutions based on a stud genetic algorithm (SGA) and standard particle swarm optimization 2007 (SPSO 07). The numerical results demonstrate that constrained blended BBO outperforms SGA and performs similarly to SPSO 07 for constrained single-objective optimization problems.     

Multiobjective optimization using population-based extremal optimization

In recent years, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied in some NP-hard combinatorial optimization problems. In this paper, we present a novel Pareto-based algorithm, which can be regarded as an extension of EO, to solve multiobjective optimization problems. The proposed method, called Multiobjective Population-based Extremal Optimization (MOPEO), is validated by using five benchmark functions and metrics taken from the standard literature on multiobjective evolutionary optimization. The experimental results demonstrate that MOPEO is competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOPEO can be considered as a viable alternative to solve multiobjective optimization problems.     

全局优化的蝴蝶优化算法

针对基本蝴蝶优化算法中存在的易陷入局部最优值、收敛速度慢等问题,提出一种全局优化的蝴蝶算法,引入limit阈值来限定蝴蝶优化算法陷入局部最优解的次数,从而改变算法易陷入早熟的问题,结合单纯形策略优化迭代后期位置较差的蝴蝶使种群能够较快地找到全局最优解;将正弦余弦算法作为局部算子融入BOA中,改善迭代后期种群多样性下降的缺陷,加快算法跳出局部最优。在仿真模拟实验中与多个算法进行对比,结果表明改进算法的寻优性能更好。     

Combining Bayesian optimization and Lipschitz optimization

Machine Learning - Bayesian optimization and Lipschitz optimization have developed alternative techniques for optimizing black-box functions. They each exploit a different form of prior about the...     

Variable mesh optimization for continuous optimization problems

Population-based meta-heuristics are algorithms that can obtain very good results for complex continuous optimization problems in a reduced amount of time. These search algorithms use a population of solutions to maintain an acceptable diversity level during the process, thus their correct distribution is crucial for the search. This paper introduces a new population meta-heuristic called “variable mesh optimization” (VMO), in which the set of nodes (potential solutions) are distributed as a mesh. This mesh is variable, because it evolves to maintain a controlled diversity (avoiding solutions too close to each other) and to guide it to the best solutions (by a mechanism of resampling from current nodes to its best neighbour). This proposal is compared with basic population-based meta-heuristics using a benchmark of multimodal continuous functions, showing that VMO is a competitive algorithm.     

Robust optimization using multi-objective particle swarm optimization

This article proposes an algorithm to search for solutions which are robust against small perturbations in design variables. The proposed algorithm formulates robust optimization as a bi-objective optimization problem, and fi nds solutions by multi-objective particle swarm optimization (MOPSO). Experimental results have shown that MOPSO has a better performance at fi nding multiple robust solutions than a previous method using a multi-objective genetic algorithm.     

Benchmarking optimization solvers for structural topology optimization

The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point solvers in IPOPT and FMINCON, and the sequential quadratic programming method in SNOPT, are benchmarked on the library using performance profiles. Whenever possible the methods are applied to both the nested and the Simultaneous Analysis and Design (SAND) formulations of the problem. The performance profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving SAND formulations consumes more computational time than solving the corresponding nested formulations.     

Accelerated biogeography-based optimization with neighborhood search for optimization

Biogeography-based optimization (BBO) inherently lacks exploration capability that leads to slow convergence. To address this limitation, authors present a memetic algorithm (MA) named as aBBOmDE, which is a new variant of BBO. In aBBOmDE, the performance of BBO is accelerated with the help of a modified mutation and clear duplicate operators. Then modified DE (mDE) is embedded as a neighborhood search operator to improve the fitness from a predefined threshold. mDE is used with mutation operator DE/best/1/bin to explore the search near the best solution. The length of local search is a choice that balances between the search capability and the computational cost. In aBBOmDE, migration mechanism is kept same as that of BBO in order to maintain its exploitation ability. Modified operators are utilized to enhance the exploration ability while a neighborhood search operator further enhances the search capability of the algorithm. This combination significantly improves the convergence characteristics of the original algorithm. Extensive experiments have been carried out on forty benchmark functions to show the effectiveness of the proposed algorithm. The results have been compared with original BBO, DE, CMAES, other MA and DE/BBO, a hybrid version of DE and BBO. aBBOmDE is also applied to compute patch dimensions of rectangular microstrip patch antennas (MSAs) with various substrate thicknesses so as to be used a CAD formula for antenna design.     

基于参考点的高维多目标粒子群算法

高维多目标优化问题一般指目标个数为4个 或以上时的多目标优化问题.由于种群中非支配解数量随着目标数量的增加而急剧增多,导致进化算法的进化压力严重降低,求解效率低.针对该问题,提出一种基于粒子群的高维多目标问题求解方法,在目标空间中引入一系列的参考点,根据参考点筛选出能兼顾多样性和收敛性的非支配解作为粒子的全局最优,以增大选择压力.同时,提出了基于参考点的外部档案维护策略,以保持最后所得解集的多样性.在标准测试函数DTLZ2上的仿真结果表明,所提方法在求解高维多目标问题时能够得到收敛性和分布性都较好的解集.     

一种改进的约束优化粒子群算法*

提出一种新的约束优化粒子群算法。该算法采用非固定多段映射罚函数法处理约束条件。在进化过程中,利用混沌序列初始化种群,选取最优粒子进行局部一维搜索,增强了在最优点附近的局部搜索能力,以加快算法的收敛速度;引入维变异方法保持种群的多样性。数值实验结果表明了该算法的有效性。     

Multi-objective ordinal optimization for simulation optimization problems

Ordinal optimization (OO) has been successfully applied to accelerate the simulation optimization process with single objective by quickly narrowing down the search space. In this paper, we extend the OO techniques to address multi-objective simulation optimization problems by using the concept of Pareto optimality. We call this technique the multi-objective OO (MOO). To define the good enough set and the selected set, we introduce two performance indices based on the non-dominance relationship among the designs. Then we derive several lower bounds for the alignment probability under various scenarios by using a Bayesian approach. Numerical experiments show that the lower bounds of the alignment probability are valid when they are used to estimate the size of the selected set as well as the expected alignment level. Though the lower bounds are conservative, they have great practical value in terms of narrowing down the search space.     

Non-parametric particle swarm optimization for global optimization

In recent years, particle swarm optimization (PSO) has extensively applied in various optimization problems because of its simple structure. Although the PSO may find local optima or exhibit slow convergence speed when solving complex multimodal problems. Also, the algorithm requires setting several parameters, and tuning the parameters is a challenging for some optimization problems. To address these issues, an improved PSO scheme is proposed in this study. The algorithm, called non-parametric particle swarm optimization (NP-PSO) enhances the global exploration and the local exploitation in PSO without tuning any algorithmic parameter. NP-PSO combines local and global topologies with two quadratic interpolation operations to increase the search ability. Nineteen (19) unimodal and multimodal nonlinear benchmark functions are selected to compare the performance of NP-PSO with several well-known PSO algorithms. The experimental results showed that the proposed method considerably enhances the efficiency of PSO algorithm in terms of solution accuracy, convergence speed, global optimality, and algorithm reliability.     

Example-based learning particle swarm optimization for continuous optimization

Particle swarm optimization (PSO) is a heuristic optimization technique based on swarm intelligence that is inspired by the behavior of bird flocking. The canonical PSO has the disadvantage of premature convergence. Several improved PSO versions do well in keeping the diversity of the particles during the searching process, but at the expense of rapid convergence. This paper proposes an example-based learning PSO (ELPSO) to overcome these shortcomings by keeping a balance between swarm diversity and convergence speed. Inspired by a social phenomenon that multiple good examples can guide a crowd towards making progress, ELPSO uses an example set of multiple global best particles to update the positions of the particles. In this study, the particles of the example set were selected from the best particles and updated by the better particles in the first-in-first-out order in each iteration. The particles in the example set are different, and are usually of high quality in terms of the target optimization function. ELPSO has better diversity and convergence speed than single-gbest and non-gbest PSO algorithms, which is proved by mathematical and numerical results. Finally, computational experiments on benchmark problems show that ELPSO outperforms all of the tested PSO algorithms in terms of both solution quality and convergence time.     

Two-layer particle swarm optimization for unconstrained optimization problems

In this article, a two-layer particle swarm optimization (TLPSO) is proposed to increase the diversity of the particles so that the drawback of trapping in a local optimum is avoided. In order to design the TLPSO, a structure with two layers (top layer and bottom layer) is proposed so that M swarms of particles and one swarm of particles are generated in the bottom layer and the top layer, respectively. Each global best position in each swarm of the bottom layer is set to be the position of the particle in the swarm of the top layer. Therefore, the global best position in the swarm of the top layer influences indirectly the particles of each swarm in the bottom layer so that the diversity of the particles increases to avoid trapping into a local optimum. Besides, a mutation operation is added into the particles of each swarm in the bottom layer so that the particles leap the local optimum to find the global optimum. Finally, some optimization problems of different types of high dimensional functions are used to illustrate the efficiency of the proposed method.     

一种用于多目标优化的混合粒子群优化算法

将粒子群算法与局部优化方法相结合,提出了一种混合粒子群多目标优化算法（HMOPSO）。该算法针对粒子群局部优化性能较差的缺点,引入多目标线搜索与粒子群算法相结合的策略,以增强粒子群算法的局部搜索能力。HMOPSO首先运行PSO算法,得到近似的Pareto最优解;然后启动多目标线搜索,发挥传统数值优化算法的优势,对其进行进一步的优化。数值实验表明,HMOPSO具有良好的全局优化性能和较强的局部搜索能力,同时HMOPSO所得的非劣解集在分散性、错误率和逼近程度等量化指标上优于MOPSO。     

国外新型智能优化算法——北极熊算法

北极熊算法(Polar Bear Optimization, PBO)是2017年由David等人提出的一种受自然界启发的优化算法,算法的灵感来自于北极熊赖以在北极严酷的环境下生存下来的捕猎方式。由于PBO是近年才提出来的新颖智能优化算法,中文文献中关于PBO算法的描述和应用微乎其微。还原了PBO的开发背景,介绍了算法的相关运算算子和算法的详细执行步骤,展现了PBO算法在现实世界中的应用领域和实际效果。     

一种新的多目标粒子群优化算法

论文提出了一种基于拥挤度和动态惯性权重聚合的多目标粒子群优化算法,该算法采用Pareto支配关系来更新粒子的个体最优值,用外部存档策略保存搜索过程中发现的非支配解;采用适应值拥挤度裁剪归档中的非支配解,并从归档中的稀松区域随机选取精英作为粒子的全局最优位置,以保持解的多样性;采用动态惯性权重聚合的方法以使算法尽可能地逼近各目标的最优解。仿真结果表明,该算法性能较好,能很好地求解多目标优化问题。     

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.