A comparison of swarm intelligence algorithms for structural engineering optimization

This paper compares the performance of three swarm intelligence algorithms for the optimization of hard engineering problems. The algorithms tested were bacterial foraging optimization (BFO), particle swarm optimization (PSO), and artificial bee colony (ABC). Besides the regular BFO, two other variants reported in the literature were also included in the study: adaptive BFO and swarming BFO. Both PSO and ABC were tested using the regular algorithm and variants that include explosion (mass extinction). Three optimization problems of structural engineering were used: minimization of the cost of a welded beam, minimization of the construction cost of a pressure vessel, and minimization of the total weight of a 10‐bar plane truss. All problems are strongly constrained. The algorithms were evaluated using two criteria: quality of solutions and the number of function evaluations. The results show that PSO presented the best balance between these two criteria. For the optimization problems approached in this paper, we can also conclude that the explosion procedure resulted in no significant improvements. Copyright © 2012 John Wiley & Sons, Ltd.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

Evolutionary computation of unconstrained and constrained problems using a novel momentum-type particle swarm optimization

This study proposes a novel momentum-type particle swarm optimization (PSO) method, which will find good solutions of unconstrained and constrained problems using a delta momentum rule to update the particle velocity. The algorithm modifies Shi and Eberhart's PSO to enhance the computational efficiency and solution accuracy. This study also presents a continuous non-stationary penalty function, to force design variables to satisfy all constrained functions. Several well-known and widely used benchmark problems were employed to compare the performance of the proposed PSO with Kennedy and Eberhart's PSO and Shi and Eberhart's modified PSO. Additionally, an engineering optimization task for designing a pressure vessel was applied to test the three PSO algorithms. The optimal solutions are presented and compared with the data from other works using different evolutionary algorithms. To show that the proposed momentum-type PSO algorithm is robust, its convergence rate, solution accuracy, mean absolute error, standard deviation, and CPU time were compared with those of both the other PSO algorithms. The experimental results reveal that the proposed momentum-type PSO algorithm can efficiently solve unconstrained and constrained engineering optimization problems.     

Particle swarm optimization: an alternative in marine propeller optimization?

This article deals with improving and evaluating the performance of two evolutionary algorithm approaches for automated engineering design optimization. Here a marine propeller design with constraints on cavitation nuisance is the intended application. For this purpose, the particle swarm optimization (PSO) algorithm is adapted for multi-objective optimization and constraint handling for use in propeller design. Three PSO algorithms are developed and tested for the optimization of four commercial propeller designs for different ship types. The results are evaluated by interrogating the generation medians and the Pareto front development. The same propellers are also optimized utilizing the well established NSGA-II genetic algorithm to provide benchmark results. The authors' PSO algorithms deliver comparable results to NSGA-II, but converge earlier and enhance the solution in terms of constraints violation.     

Enhancing particle swarm optimization algorithm using two new strategies for optimizing design of truss structures

This work develops an augmented particle swarm optimization (AugPSO) algorithm using two new strategies,: boundary-shifting and particle-position-resetting. The purpose of the algorithm is to optimize the design of truss structures. Inspired by a heuristic, the boundary-shifting approach forces particles to move to the boundary between feasible and infeasible regions in order to increase the convergence rate in searching. The purpose of the particle-position-resetting approach, motivated by mutation scheme in genetic algorithms (GAs), is to increase the diversity of particles and to prevent the solution of particles from falling into local minima. The performance of the AugPSO algorithm was tested on four benchmark truss design problems involving 10, 25, 72 and 120 bars. The convergence rates and final solutions achieved were compared among the simple PSO, the PSO with passive congregation (PSOPC) and the AugPSO algorithms. The numerical results indicate that the new AugPSO algorithm outperforms the simple PSO and PSOPC algorithms. The AugPSO achieved a new and superior optimal solution to the 120-bar truss design problem. Numerical analyses showed that the AugPSO algorithm is more robust than the PSO and PSOPC algorithms.     

Biogeography-based particle swarm optimization with fuzzy elitism and its applications to constrained engineering problems

In evolutionary algorithms, elites are crucial to maintain good features in solutions. However, too many elites can make the evolutionary process stagnate and cannot enhance the performance. This article employs particle swarm optimization (PSO) and biogeography-based optimization (BBO) to propose a hybrid algorithm termed biogeography-based particle swarm optimization (BPSO) which could make a large number of elites effective in searching optima. In this algorithm, the whole population is split into several subgroups; BBO is employed to search within each subgroup and PSO for the global search. Since not all the population is used in PSO, this structure overcomes the premature convergence in the original PSO. Time complexity analysis shows that the novel algorithm does not increase the time consumption. Fourteen numerical benchmarks and four engineering problems with constraints are used to test the BPSO. To better deal with constraints, a fuzzy strategy for the number of elites is investigated. The simulation results validate the feasibility and effectiveness of the proposed algorithm.     

Multi-objective optimization of engineering systems using game theory and particle swarm optimization

This study proposes particle swarm optimization (PSO) based algorithms to solve multi-objective engineering optimization problems involving continuous, discrete and/or mixed design variables. The original PSO algorithm is modified to include dynamic maximum velocity function and bounce method to enhance the computational efficiency and solution accuracy. The algorithm uses a closest discrete approach (CDA) to solve optimization problems with discrete design variables. A modified game theory (MGT) approach, coupled with the modified PSO, is used to solve multi-objective optimization problems. A dynamic penalty function is used to handle constraints in the optimization problem. The methodologies proposed are illustrated by several engineering applications and the results obtained are compared with those reported in the literature.     

A constraint consensus memetic algorithm for solving constrained optimization problems

Constraint handling is an important aspect of evolutionary constrained optimization. Currently, the mechanism used for constraint handling with evolutionary algorithms mainly assists the selection process, but not the actual search process. In this article, first a genetic algorithm is combined with a class of search methods, known as constraint consensus methods, that assist infeasible individuals to move towards the feasible region. This approach is also integrated with a memetic algorithm. The proposed algorithm is tested and analysed by solving two sets of standard benchmark problems, and the results are compared with other state-of-the-art algorithms. The comparisons show that the proposed algorithm outperforms other similar algorithms. The algorithm has also been applied to solve a practical economic load dispatch problem, where it also shows superior performance over other algorithms.     

Swarm algorithms for single- and multi-objective optimization problems incorporating sensitivity analysis

Swarm algorithms such as particle swarm optimization (PSO) are non-gradient probabilistic optimization algorithms that have been successfully applied for global searches in complex problems such as multi-peak problems. However, application of these algorithms to structural and mechanical optimization problems still remains a complex matter since local optimization capability is still inferior to general numerical optimization methods. This article discusses new swarm metaphors that incorporate design sensitivities concerning objective and constraint functions and are applicable to structural and mechanical design optimization problems. Single- and multi-objective optimization techniques using swarm algorithms are combined with a gradient-based method. In the proposed techniques, swarm optimization algorithms and a sequential linear programming (SLP) method are conducted simultaneously. Finally, truss structure design optimization problems are solved by the proposed hybrid method to verify the optimization efficiency.     

Hybridization of ABC and PSO algorithms for improved solutions of RCPSP

A resource-constrained project scheduling problem (RCPSP) is one of the most famous intractable NP-hard problems in the operational research area in terms of its practical value and research significance. To effectively solve the RCPSP, we propose a hybrid approach by integrating artificial bee colony (ABC) and particle swarm optimization (PSO) algorithms. Moreover, a novel structure of ABC-PSO is devised based on embedded ABC-PSO (EABC-PSO) and sequential ABC-PSO (SABC-PSO) strategies. The EABC-PSO strategy mainly applies the PSO algorithm to update the process of the ABC algorithm while the SABC-PSO strategy demonstrates an approach in which computational results obtained from the ABC algorithm are further improved based on the PSO algorithm. In both strategies, bees in the ABC process are entitled to learning capacity from the best local and global solutions in terms of the PSO concept. Subsequently, the updates of solutions are premeditated with crossover and insert operators together with double justification methods. Computational results obtained from the tests on benchmark sets show that the proposed ABC-PSO algorithm is efficient in solving RCPSP problems, demonstrating clear advantages over the pure ABC algorithm, the PSO algorithm, and a number of listed heuristics.     

An improvement of Kriging based sequential approximate optimization method via extended use of design of experiments

When Kriging is used as a meta-model for an inequality constrained function, approximate optimal solutions are sometimes infeasible in the case where they are active at the constraint boundary. This article explores the development of a Kriging-based meta-model that enhances the constraint feasibility of an approximate optimal solution. The trust region management scheme is used to ensure the convergence of the approximate optimal solution. The present study proposes a method of enhancing the constraint feasibility in which the currently infeasible design is replaced by the most feasible-usable design during the sequential approximate optimization process. An additional convergence condition is also included to reinforce the design accuracy and feasibility. Latin hypercube design and (2n+1) design are used as tools for design of experiments. The proposed approach is verified through a constrained mathematical function problem and a number of engineering optimization problems to support the proposed strategies.     

A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.     

Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems

An efficient optimization algorithm called teaching–learning-based optimization (TLBO) is proposed in this article to solve continuous unconstrained and constrained optimization problems. The proposed method is based on the effect of the influence of a teacher on the output of learners in a class. The basic philosophy of the method is explained in detail. The algorithm is tested on 25 different unconstrained benchmark functions and 35 constrained benchmark functions with different characteristics. For the constrained benchmark functions, TLBO is tested with different constraint handling techniques such as superiority of feasible solutions, self-adaptive penalty, ?-constraint, stochastic ranking and ensemble of constraints. The performance of the TLBO algorithm is compared with that of other optimization algorithms and the results show the better performance of the proposed algorithm.     

An efficient particle swarm approach for mixed-integer programming in reliability-redundancy optimization applications

The reliability-redundancy optimization problems can involve the selection of components with multiple choices and redundancy levels that produce maximum benefits, and are subject to the cost, weight, and volume constraints. Many classical mathematical methods have failed in handling nonconvexities and nonsmoothness in reliability-redundancy optimization problems. As an alternative to the classical optimization approaches, the meta-heuristics have been given much attention by many researchers due to their ability to find an almost global optimal solutions. One of these meta-heuristics is the particle swarm optimization (PSO). PSO is a population-based heuristic optimization technique inspired by social behavior of bird flocking and fish schooling. This paper presents an efficient PSO algorithm based on Gaussian distribution and chaotic sequence (PSO-GC) to solve the reliability-redundancy optimization problems. In this context, two examples in reliability-redundancy design problems are evaluated. Simulation results demonstrate that the proposed PSO-GC is a promising optimization technique. PSO-GC performs well for the two examples of mixed-integer programming in reliability-redundancy applications considered in this paper. The solutions obtained by the PSO-GC are better than the previously best-known solutions available in the recent literature.     

混流装配线调度问题的离散粒子群优化解

混流装配线调度问题是JIT生产中的一个重要问题。借鉴二进制遗传算法中的交叉操作过程，对传统的连续型粒子群算法进行改进，使其适用于离散问题的优化处理。然后以丰田公司的汽车组装调度函数作为目标函数，利用改进的离散粒子群算法进行求解。对比分析表明：新算法所得结果优于常用的目标追随法、遗传算法、模拟退火等方法。     

Guided particle swarm optimization method to solve general nonlinear optimization problems

The development of hybrid algorithms is becoming an important topic in the global optimization research area. This article proposes a new technique in hybridizing the particle swarm optimization (PSO) algorithm and the Nelder–Mead (NM) simplex search algorithm to solve general nonlinear unconstrained optimization problems. Unlike traditional hybrid methods, the proposed method hybridizes the NM algorithm inside the PSO to improve the velocities and positions of the particles iteratively. The new hybridization considers the PSO algorithm and NM algorithm as one heuristic, not in a sequential or hierarchical manner. The NM algorithm is applied to improve the initial random solution of the PSO algorithm and iteratively in every step to improve the overall performance of the method. The performance of the proposed method was tested over 20 optimization test functions with varying dimensions. Comprehensive comparisons with other methods in the literature indicate that the proposed solution method is promising and competitive.     

A surrogate-assisted particle swarm optimization algorithm based on efficient global optimization for expensive black-box problems

Evolutionary algorithms cannot effectively handle computationally expensive problems because of the unaffordable computational cost brought by a large number of fitness evaluations. Therefore, surrogates are widely used to assist evolutionary algorithms in solving these problems. This article proposes an improved surrogate-assisted particle swarm optimization (ISAPSO) algorithm, in which a hybrid particle swarm optimization (PSO) is combined with global and local surrogates. The global surrogate is not only used to predict fitness values for reducing computational burden but also regarded as a global searcher to speed up the global search process of PSO by using an efficient global optimization algorithm, while the local one is constructed for a local search in the neighbourhood of the current optimal solution by finding the predicted optimal solution of the local surrogate. Empirical studies on 10 widely used benchmark problems and a real-world structural design optimization problem of a driving axle show that the ISAPSO algorithm is effective and highly competitive.     

Solving constrained optimization problems with a hybrid particle swarm optimization algorithm

This article presents a particle swarm optimization algorithm for solving general constrained optimization problems. The proposed approach introduces different methods to update the particle's information, as well as the use of a double population and a special shake mechanism designed to avoid premature convergence. It also incorporates a simple constraint-handling technique. Twenty-four constrained optimization problems commonly adopted in the evolutionary optimization literature, as well as some structural optimization problems are adopted to validate the proposed approach. The results obtained by the proposed approach are compared with respect to those generated by algorithms representative of the state of the art in the area.     

求解约束优化问题的改进布谷鸟搜索算法

为了提高约束优化问题的求解精度和收敛速度,提出求解约束优化问题的改进布谷鸟搜索算法。首先分析了基本布谷鸟搜索算法全局搜索和局部搜索过程中的不足,对其中全局搜索和局部搜索迭代公式进行重新定义,然后以一定概率在最优解附近进行搜索。对12个标准约束优化问题和4个工程约束优化问题进行测试并与多种算法进行对比,实验结果和统计分析表明所提算法在求解约束优化问题上具有较强的优越性。     

Modified Differential Evolution Algorithm for Solving Dynamic Optimization with Existence of Infeasible Environments

Dynamic constrained optimization is a challenging research topic in which the objective function and/or constraints change over time. In such problems, it is commonly assumed that all problem instances are feasible. In reality some instances can be infeasible due to various practical issues, such as a sudden change in resource requirements or a big change in the availability of resources. Decision-makers have to determine whether a particular instance is feasible or not, as infeasible instances cannot be solved as there are no solutions to implement. In this case, locating the nearest feasible solution would be valuable information for the decision-makers. In this paper, a differential evolution algorithm is proposed for solving dynamic constrained problems that learns from past environments and transfers important knowledge from them to use in solving the current instance and includes a mechanism for suggesting a good feasible solution when an instance is infeasible. To judge the performance of the proposed algorithm, 13 well-known dynamic test problems were solved. The results indicate that the proposed algorithm outperforms existing recent algorithms with a margin of 79.40% over all the environments and it can also find a good, but infeasible solution, when an instance is infeasible.