Machining fixture layout optimisation under dynamic conditions based on evolutionary techniques

Optimisation of fixture layout is critical to reduce geometric and form error of the workpiece during the machining process. In this paper the optimal placement of fixture elements (locator and clamp locations) under dynamic conditions is investigated using evolutionary techniques. The application of the newly developed particle swarm optimisation (PSO) algorithm and widely used genetic algorithm (GA) is presented to minimise elastic deformation of the workpiece considering its dynamic response. To improve the performances of GA and PSO, an improved GA (IGA) obtained by basic GA (GA) with sharing and adaptive mutation and an improved PSO (IPSO) obtained by basic PSO (PSO) incorporated into adaptive mutation are developed. ANSYS parametric design language (APDL) of finite element analysis is employed to compute the objective function for a given fixture layout. Three layout optimisation cases derived from the high speed slot milling case are used to test the effectiveness of the GA, IGA, PSO and IPSO based approaches. The comparisons of computational results show that IPSO seems superior to GA, IGA and PSO approaches with respect to the trade-off between global optimisation capability and convergence speed for the presented type problems.     

A hybrid particle swarm based method for process planning optimisation

A process planning (PP) problem is defined as to determine a set of operation-methods (machine, tool, and set-up configuration) that can convert the given stock to the designed part. Essentially, the PP problem involves the simultaneous decision making of two tasks: operation-method selection and sequencing. This is a combinatorial optimisation problem and it is difficult to find the best solution in a reasonable amount of time. In this article, an optimisation approach based on particle swarm optimisation (PSO) is proposed to solve the PP problem. Due to the characteristic of discrete process planning solution space and the continuous nature of the original PSO, a novel solution representation scheme is introduced for the application of PSO in solving the PP problem. Moreover, two kinds of local search algorithms are incorporated and interweaved with PSO evolution to improve the best solution in each generation. The numerical experiments and analysis have demonstrated that the proposed algorithm is capable of gaining a good quality solution in an efficient way.     

Hybrid simplex search and particle swarm optimization for the global optimization of multimodal functions

This article proposes the hybrid Nelder–Mead (NM)–Particle Swarm Optimization (PSO) algorithm based on the NM simplex search method and PSO for the optimization of multimodal functions. The hybrid NM–PSO algorithm is very easy to implement, in practice, since it does not require gradient computation. This hybrid procedure performed the exploration with PSO and the exploitation with the NM simplex search method. In a suite of 17 multi-optima test functions taken from the literature, the computational results via various experimental studies showed that the hybrid NM–PSO approach is superior to the two original search techniques (i.e. NM and PSO) in terms of solution quality and convergence rate. In addition, the presented algorithm is also compared with eight other published methods, such as hybrid genetic algorithm (GA), continuous GA, simulated annealing (SA), and tabu search (TS) by means of a smaller set of test functions. On the whole, the new algorithm is demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for multimodal functions.     

Multi-objective resource assignment problem in a product-driven supply chain using a Taguchi-based DNA algorithm

This paper conceptualises the integration of tangible and intangible factors into the design consideration of a resource assignment problem for a product-driven supply chain. The problem is formulated mathematically as a multi-objective optimisation model to maximise the broad objectives of profit, ahead of time of delivery, quality, and volume flexibility. Product characteristics are associated with the design requirements of a supply chain. Different types of resources are considered, each differing in its characteristics, thereby providing various alternatives during the design process. The aim is to design integrated supply chains that maximise the weighted sum of the objectives, the weights being decided by the desired product characteristics. The problem is solved through the proposed Taguchi-based DNA algorithm that draws its traits from random search optimisation and the statistical design of experiments. In order to minimise the effect of the causes of variations, the fundamental Taguchi method is integrated with the DNA-metaheuristic. The suggested methodology exhibits the global exploration capability to exploit the optimal or near-optimal DNA strands with a faster convergence rate. In order to authenticate the performance of the proposed solution methodology, a set of ten problem instances are considered and the results obtained are compared with that of the basic DNA, particle swarm optimisation (PSO) and its variant (PSO — time varying acceleration coefficients). The results demonstrate the benefits of the proposed algorithm for solving this type of problem.     

求解包装生产中复杂问题的布谷鸟算法改进

目的 为了解决在求解复杂的高维函数优化问题时存在的求解精度不够高和易陷入局部最优等问题,提出一种基于莱维飞行发现概率的变步长布谷鸟搜索算法(LFCS).方法 在相同环境下,选取6个不同难度、不同类型的测试函数,将LFCS算法与IPSO,IDE,IABC,CS算法比较,分析算法的收敛速度和收敛精度.结果 相比其他4种算法,LFCS算法迭代次数更少,收敛速度更快,收敛精度更高.结论 无论是低维函数还是高维函数,LFCS算法在收敛速度和收敛精度方面都有所提高,尤其是针对复杂的高维函数优化问题,在取值范围较大的情况下,LFCS算法能够更快、更准地找到最优解.     

An improved hybrid self-inertia weight adaptive particle swarm optimization algorithm with local search

As an evolutionary computing technique, particle swarm optimization (PSO) has good global search ability, but the swarm can easily lose its diversity, leading to premature convergence. To solve this problem, an improved self-inertia weight adaptive particle swarm optimization algorithm with a gradient-based local search strategy (SIW-APSO-LS) is proposed. This new algorithm balances the exploration capabilities of the improved inertia weight adaptive particle swarm optimization and the exploitation of the gradient-based local search strategy. The self-inertia weight adaptive particle swarm optimization (SIW-APSO) is used to search the solution. The SIW-APSO is updated with an evolutionary process in such a way that each particle iteratively improves its velocities and positions. The gradient-based local search focuses on the exploitation ability because it performs an accurate search following SIW-APSO. Experimental results verified that the proposed algorithm performed well compared with other PSO variants on a suite of benchmark optimization functions.     

An ant colony optimisation algorithm for scheduling in agile manufacturing

Producing customised products in a short time at low cost is one of the goals of agile manufacturing. To achieve this goal an assembly-driven differentiation strategy has been proposed in the agile manufacturing literature. In this paper, we address a manufacturing system that applies the assembly-driven differentiation strategy. The system consists of machining and assembly stages, where there is a single machine at the machining stage and multiple identical assembly stations at the assembly stage. An ant colony optimisation (ACO) algorithm is developed for solving the scheduling problem of determining the sequence of parts to be produced in the system so as to minimise the maximum completion time (or makespan). The ACO algorithm uses a new dispatching rule as the heuristic desirability and variable neighbourhood search as the local search to make it more efficient and effective. To evaluate the performance of heuristic algorithms, a branch-and-bound procedure is proposed for deriving the optimal solution to the problem. Computational results show that the proposed ACO algorithm is superior to the existing algorithm, not only improving the performance but also decreasing the computation time.     

Robust single machine scheduling with uncertain release times for minimising the maximum waiting time

We study a single machine scheduling problem (SMSP) with uncertain job release times (JRTs) under the maximum waiting time (MWT) criterion. To deal with the uncertainty, a robust model is established to find an optimal schedule, which minimises the worst-case MWT (W-MWT) when JRTs vary over given time intervals. Although infinite possible scenarios for JRTs exist, we show that only n scenarios are needed for calculating the W-MWT, where n is the number of jobs. Based on this property, the robust (SMSP) with uncertain JRTs to minimise the W-MWT is formulated as a mixed integer linear programming problem. To solve large-size problem instances, an efficient two-stage heuristic (TSH) is proposed. In the first stage, n near-optimal schedules are obtained by solving n deterministic scenario-based SMSPs, and their W-MWTs are evaluated. To speed up the solution and evaluation process, a modified Gusfield’s heuristic is proposed by exploiting the inner connections of these SMSPs. To further improve the schedule obtained in the first stage, the second stage consists of a variable neighbourhood search method by combining both swap neighbourhood search and insert neighbourhood search. We also develop a method to calculate the lower bound of the proposed model so that we can evaluate the performance of the solutions given by the TSH. Experimental results confirm the robustness of schedules produced and advantages of the proposed TSH over other algorithms in terms of solution quality and run time.     

Drilling path optimization by the particle swarm optimization algorithm with global convergence characteristics

Drilling path optimization is one of the key problems in holes-machining. This paper presents a new approach to solve the drilling path optimization problem belonging to discrete space, based on the particle swarm optimization (PSO) algorithm. Since the standard PSO algorithm is not guaranteed to be global convergent or local convergent, based on the mathematical model, the algorithm is improved by adopting the method to generate the stop evolution particle once again to obtain the ability of convergence on the global optimization solution. Also, the operators are proposed by establishing the Order Exchange Unit (OEU) and the Order Exchange List (OEL) to satisfy the need of integer coding in drilling path optimization. The experimentations indicate that the improved algorithm has the characteristics of easy realization, fast convergence speed, and better global convergence capability. Hence the new PSO can play a role in solving the problem of drilling path optimization.     

A novel hybrid combination optimization algorithm based on search area segmentation and fast Fourier transform

A novel hybrid optimization algorithm combining search area segmentation technique and the fast Fourier transform (HSAS/FFT) is presented to solve the numerical optimization problems. Firstly, the spectrum of each dimension of the objective function can be acquired by the FFT. The search space is segmented by using the spectrum to ensure that each subspace is unimodal. Secondly, the population of subspaces is produced and the optimal individual can be obtained by gradient descent algorithm. Finally, the local optimal solution in the optimal subspace is generated by the binary search algorithm. Make the optimal individual the new search space and repeat the process until meeting the termination condition. The proposed HSAS/FFT was tested on the CEC2017 benchmark, which evaluates the performance of the proposed algorithm on solving global optimization problems. Results obtained show that HSAS/FFT has an excellent performance and better convergence speed in comparison with some of the state-of-the-art algorithms.     

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.     

基于改进PSO算法的结构损伤检测

结构的损伤检测常转化为求解约束优化问题,针对粒子群算法容易出现早熟问题,增大算法后期的粒子位置的改变量,从而增加粒子位置的差异,因而能够增强其在求解约束优化问题时抵抗局部极小的能力。两层刚架单损伤和多损伤识别的数值结果和收敛曲线表明了改进后的粒子群算法优于传统的带惯性因子的粒子群算法。三层框架结构的4种损伤工况的试验研究进一步说明了该算法应用于结构损伤检测领域的有效性。     

Armijo型线搜索下一种共轭梯度法的收敛性

对无约束非线性规划问题,本文分别在两种不同的Armijo型线搜索下证明了Liu-Storey共轭梯度法的所有搜索方向都是充分下降的,并进一步证明了该算法是全局强收敛的。对另一种放松了函数值下降条件可以获得更大步长的Armijo型线搜索,本文还证明了该算法是全局强收敛的。     

Automatic clustering for generalised cell formation using a hybrid particle swarm optimisation

This paper considers the cell formation (CF) problem in which parts have alternative process routings and the number of machine cells is not known a priori. Very few studies address these two practical issues at the same time. This paper proposes an automatic clustering approach based on a hybrid particle swarm optimisation (PSO) algorithm that can automatically evolve the number and cluster centres of machine cells for a generalised CF problem. In the proposed approach, a solution representation, comprising an integer number and a set of real numbers, is adopted to encode the number of cells and machine cluster centres, respectively. Besides, a discrete PSO algorithm is utilised to search for the number of machine cells, and a continuous PSO algorithm is employed to perform machine clustering. Effectiveness of the proposed approach has been demonstrated for test problems selected from the literature and those generated in this study. The experimental results indicate that the proposed approach is capable of solving the generalised machine CF problem without predetermination of the number of cells.     

应用蜜蜂繁殖进化型粒子群算法求解车辆路径问题

为了提高粒子群算法求解车辆路径问题时收敛速度和全局搜索能力,将蜜蜂繁殖进化机制与粒子群算法相结合,应用到CVRP问题的求解。该算法中,最优的个体作为蜂王与通过选择机制选择的雄蜂以随机概率进行交叉,增强了最优个体信息的应用能力;同时,随机产生一部分雄蜂种群,并将其与蜂王交叉增加了算法的多样性。实例分析表明该算法具有较好的全局搜索能力,验证了该算法的可行性。     

基于混合粒子群算法的物流配送路径优化问题研究

针对物流配送路径优化问题,提出了一种融合Powell局部寻优算法和模拟退火算法的混合粒子群算法,以克服单用粒子群算法求解问题早熟收敛的不足,增加算法的开发能力,提高算法的全局搜索能力,并进行了实验计算.计算结果表明,用混合粒子群算法求解物流配送路径优化问题,可以在一定程度上提高粒子群算法在局部搜索能力和搜索全局最优解概率,从而得到质量较高的解.     

一个充分下降的修正 PRP 型谱共轭梯度法

谱共轭梯度法是共轭梯度法的一种重要延拓,可以通过共轭参数和谱参数二维度调整,使得所设计算法的搜索方向满足某一预设条件,比如充分下降条件或共轭条件等。谱参数和共轭参数的设计是谱共轭梯度法的两大核心工作,决定方法的收敛性和数值效果。基于 PRP 方法,构造了一个修正的 PRP 型共轭参数,该共轭参数不仅保持了 PRP 公式的结构和性能,而且具有 FR 方法的收敛性质。利用充分下降条件取定一个谱参数,与修正的 PRP 型共轭参数结合,建立一个新的谱共轭梯度算法。该算法不依赖于任何线搜索就可以满足充分下降条件。常规假设条件下,采用强 Wolfe 线搜索准则产生步长,证明了新算法的全局敛性。通过 100 个算例对该算法进行数值测试并与其他五个算法进行比较,同时采用性能图对数值结果进行直观展示,结果表明该算法是有效的。     

Cross-docking truck scheduling with product unloading/loading constraints based on an improved particle swarm optimisation algorithm

Cross-docking is a very useful logistics technique that can substantially reduce distribution costs and improve customer satisfaction. A key problem in its success is truck scheduling, namely, decision on assignment and docking sequence of inbound/outbound trucks to receiving/shipping dock doors. This paper focuses on the problem with the requirement of unloading/loading products in a given order, which is very common in many industries, but is less concerned by existing researches. An integer programming model is established to minimise the makespan. An improved particle swarm optimisation (ωc-PSO) algorithm is proposed for solving it. In the algorithm, a cosine decreasing strategy of inertia weight is designed to dynamically balance global and local search. A repair strategy is put forward for continuous search in the feasible solution space and a crossover strategy is presented to prevent the algorithm from falling into local optimum. After algorithm parameters are tuned using Taguchi method, computational experiments are conducted on different problem scales to evaluate ωc-PSO against genetic algorithm, basic PSO and GLNPSO. The results show that ωc-PSO outperforms other three algorithms, especially when the number of dock doors, trucks and product types is great. Statistical tests show that the performance difference is statistically significant.     

An optimal and a heuristic algorithm for the single-item retrieval problem in puzzle-based storage systems with multiple escorts

Puzzle-based storage systems consist of densely stored unit loads on a square grid. The problem addressed in this paper is to retrieve a stored unit load from a puzzle-based storage using the minimum number of item moves. While previous research contributed optimal algorithms for only up to two empty locations (escorts), our approach solves configurations where multiple empty locations are arbitrarily positioned in the grid. The problem is formulated as a state space problem and solved to optimality using an exact search algorithm. To reduce the search space, we derive bounds on the number of eligible empty locations and develop several search-guiding estimate functions. Furthermore, we present a heuristic variant of the search algorithm to solve larger problem instances. We evaluate both solution algorithms on a large set of problem instances. Our computational results show that the algorithms clearly outperform existing approaches where they are applicate and solve more general configurations, which could not be solved to optimality before. The heuristic variant efficiently yields high-quality solutions for significantly larger instances of practically relevant size.     

A particle swarm optimization algorithm for hybrid flow-shop scheduling with multiprocessor tasks

The multistage hybrid flow-shop scheduling problem with multiprocessor tasks has been found in many practical situations. Due to the essential complexity of the problem, many researchers started to apply metaheuristics to solve the problem. In this paper, we address the problem by using particle swarm optimization (PSO), a novel metaheuristic inspired by the flocking behaviour of birds. The proposed PSO algorithm has several features, such as a new encoding scheme, an implementation of the best velocity equation and neighbourhood topology among several different variants, and an effective incorporation of local search. To verify the PSO algorithm, computational experiments are conducted to make a comparison with two existing genetic algorithms (GAs) and an ant colony system (ACS) algorithm based on the same benchmark problems. The results show that the proposed PSO algorithm outperforms all the existing algorithms for the considered problem.