Particle swarm optimization: A study of particle displacement for solving continuous and combinatorial optimization problems

This article addresses the particle swarm optimization (PSO) method. It is a recent proposed algorithm by Kennedy and Eberhart [1995. Particle swarm optimization. In: Proceedings of the IEEE International Conference on Neural Networks (Perth, Australia), vol. IV, IEEE Service Center, Piscataway, NJ, pp. 1942–1948]. This optimization method is motivated by social behaviour of organisms such as bird flocking and fish schooling. PSO algorithm is not only a tool for optimization, but also a tool for representing socio-cognition of human and artificial agents, based on principles of social behaviour. Some scientists suggest that knowledge is optimized by social interaction and thinking is not only private but also interpersonal. PSO as an optimization tool, provides a population-based search procedure in which individuals called particles change their position (state) with time. In a PSO system, particles fly in a multidimensional search space. During flight, each particle adjusts its position according to its own experience, and according to the experience of neighbours, making use of the best position encountered by itself and its neighbours. In this paper, we propose firstly, an extension of the PSO system that integrates a new displacement of the particles (the balance between the intensification process and the diversification process) and we highlight a relation between the coefficients of update of each dimension velocity between the classical PSO algorithm and the extension. Secondly, we propose an adaptation of this extension of PSO algorithm to solve combinatorial optimization problem with precedence constraints in general and resource-constrained project scheduling problem in particular. The numerical experiments are done on the main continuous functions and on the resource-constrained project scheduling problem (RCPSP) instances provided by the psplib. The results obtained are encouraging and push us into accepting than both PSO algorithm and extensions proposed based on the new particles displacement are a promising direction for research.     

基于改进粒子群的分布式通信干扰资源分配

为了解决分布式通信干扰场景下面临的资源分配效率低、干扰效益无保障等问题,结合通信干扰资源分配数学模型,设计了一种改进的粒子群算法。首先设计了分布式通信干扰场景并构建了通信干扰资源分配模型,以最大化干扰效益作为目标函数;其次采用自适应惯性因子和学习因子,并引入遗传变异策略和精英保留策略,提出一种改进的粒子群算法,最后对不同场景规模的通信干扰资源分配进行仿真实验。结果表明,相比小生境遗传算法、粒子群算法、遗传算法,改进的粒子群算法在不同场景规模下,均能获得更优的干扰效益,性能方面具备整体干扰效益更高、算法收敛速度更快、算法收敛误差更小等优势。所设计的改进粒子群算法可应用在分布式通信干扰场景中,为指挥决策提供参考。     

Hybrid particle swarm optimization with mutation for optimizing industrial product lines: An application to a mixed solution space considering both discrete and continuous design variables

This article presents an artificial intelligence-based solution to the problem of product line optimization. More specifically, we apply a new hybrid particle swarm optimization (PSO) approach to design an optimal industrial product line. PSO is a biologically-inspired optimization framework derived from natural intelligence that exploits simple analogues of collective behavior found in nature, such as bird flocking and fish schooling. All existing product line optimization algorithms in the literature have been so far applied to consumer markets and product attributes that range across some discrete values. Our hybrid PSO algorithm searches for an optimal product line in a large design space which consists of both discrete and continuous design variables. The incorporation of a mutation operator to the standard PSO algorithm significantly improves its performance and enables our mechanism to outperform the state of the art Genetic Algorithm in a simulated study with artificial datasets pertaining to industrial cranes. The proposed approach deals with the problem of handling variables that can take any value from a continuous range and utilizes design variables associated with both product attributes and value-added services. The application of the proposed artificial intelligence framework yields important implications for strategic customer relationship and production management in business-to-business markets.     

基于改进粒子群算法的无人机航迹规划

针对当前基本粒子群算法无人机航迹规划在后期收敛速度比较慢、效率不高、易陷入局部最优等问题,提出一种改进粒子群算法。首先,在迭代前期和后期分段设置惯性权值的调整,实现粒子惯性和寻优行为的平衡;其次,设置一个定值与相邻2次适应度函数最优值比较策略,防止陷入局部最优;最后,引入遗传算法的交叉、变异机制,得出更优的结果。并通过仿真验证了改进粒子群算法在三维空间航迹规划的有效性和可行性。结果表明,与其他航迹规划算法相比,新算法具有路径长度更短、耗时更少、路径更平滑等优点,加快了收敛速度,提高了航迹规划效率和稳定性。因此,改进算法的航迹规划可得到满足约束关系的最优航迹,对实现自主飞行有重要的参考价值。     

基于CPSO的基础设施模糊投资组合优化模型

针对基础设施效益模糊、难以度量的特点,结合模糊集理论,建立了模糊投资组合优化模型,改进粒子群算法,加入混沌思想,使用混沌粒子群算法(CPSO)求解基础设施的模糊投资组合优化模型。以4个城市投资公司的数据为样本,验证该方法的科学性与有效性。研究结果表明:模糊投资组合优化模型可较好地表征基础设施的模糊效益,提高基础设施投资决策的科学性;混沌寻优思想改进的粒子群算法可求得模糊投资组合优化模型的全局最优解,增强算法的鲁棒性。     

Search for good policies in a single-warehouse, multi-retailer system by particle swarm optimisation

An optimal control of sufficiently realistic single-warehouse, multi-retailer systems (SWMR-systems) requires the simulation optimisation approach. After a brief discussion of modelling and simulation aspects for such systems, we present a simulator providing a sufficiently large set of options to customize it to realistic problem situations. The paper then focuses on the applicability of optimisation algorithms and introduces the methods particle swarm optimisation and threshold accepting. We show that both approaches yield good optimisation results for several examples of a 5-retailer system investigated according to their reordering strategy and transportation resources.     

A serial mixed produce-to-order and produce-in-advance inventory model with multiple retailers

We formulate a general mixed produce-to-order and produce-in-advance inventory model having multiple stocking echelons and multiple retailers. We show that the problem to find an optimal inventory policy for such a model with a uniform or a normal demand distribution can be reduced to a general constrained optimization problem.     

A Pareto approach to multi-objective flexible job-shop scheduling problem using particle swarm optimization and local search

The job-shop scheduling problem is one of the most arduous combinatorial optimization problems. Flexible job-shop problem is an extension of the job-shop problem that allows an operation to be processed by any machine from a given set along different routes. This paper present a new approach based on a hybridization of the particle swarm and local search algorithm to solve the multi-objective flexible job-shop scheduling problem. The particle swarm optimization is a highly efficient and a new evolutionary computation technique inspired by birds’ flight and communication behaviors. The multi-objective particle swarm algorithm is applied to the flexible job-shop scheduling problem based on priority. Also the presented approach will be evaluated for their efficiency against the results reported for similar algorithms (weighted summation of objectives and Pareto approaches). The results indicate that the proposed algorithm satisfactorily captures the multi-objective flexible job-shop problem and competes well with similar approaches.     

A heuristic for balancing the inventory level of different locations through lateral shipments

Solving transshipment problems to optimality is difficult, unless several simplifying hypotheses are assumed (such as unit-sized customer demands and replenishments, negligible replenishment lead time, etc.). For this reason, some heuristics have been recently proposed in order to provide rules, which incorporate relevant factors of the problem, to find conditions under which it makes sense to transship a certain number of units from one retailer to another. Most of these studies concern emergency transshipment, which means that shipments between locations can occur only when a shortage happens, and shipments are assumed to be fast enough to satisfy the location in shortage. When this assumption is not feasible, as in many real cases, transshipments between locations have to be performed before a shortage happens. The paper addresses this case, which can be named ‘preventive’ transshipment, where the inventory level of different locations at the same echelon is balanced through lateral shipments, before a shortage happens. A heuristic for deciding on transshipment policy (when to transship and how much), trying to minimise overall expected costs, is presented. A simulation study considering different scenarios is performed and results confirm the effectiveness of the heuristic.     

Supplier selection-order allocation: A two-stage multiple criteria dynamic programming approach

This paper proposes a two-stage multiple criteria dynamic programming approach for two of the most critical tasks in supply chain management, namely, supplier selection and order allocation. In the first stage, to address multiple decision criteria in supplier ranking, the analytic hierarchy process (AHP) is employed. In the second stage, supplier ranks are fed into an order allocation model that aims at maximizing a utility function for the firm as well as minimizing the total supply chain costs, subject to constraints on demand, capacity, and inventory levels. A dynamic programming approach is crafted to solve the proposed bi-objective model.     

A state space augmentation algorithm for the replenishment cycle inventory policy

In this work we propose an efficient dynamic programming approach for computing replenishment cycle policy parameters under non-stationary stochastic demand and service level constraints. The replenishment cycle policy is a popular inventory control policy typically employed for dampening planning instability. The approach proposed in this work achieves a significant computational efficiency and it can solve any relevant size instance in trivial time. Our method exploits the well known concept of state space relaxation. A filtering procedure and an augmenting procedure for the state space graph are proposed. Starting from a relaxed state space graph our method tries to remove provably suboptimal arcs and states (filtering) and then it tries to efficiently build up (augmenting) a reduced state space graph representing the original problem. Our experimental results show that the filtering procedure and the augmenting procedure often generate a small filtered state space graph, which can be easily processed using dynamic programming in order to produce a solution for the original problem.     

A consumer-oriented model for analysing the suitability of food classification systems

The main function of food classification systems is to regulate the market and inform it (consumers above all) about the different types of products and their characteristics. However, the reality is that many of these systems give rise to confusion and prevent consumers from obtaining a clear idea of them, making the purchasing process more difficult. The objective of this study was to propose a method that can be used as a basis or reference framework for analysing the suitability of any food classification system, based on maximising consumer comprehension and learning, before introducing it into the market. The model proposed establishes the procedure and the necessary indicators for identifying the advantages and drawbacks of each of the different systems, making it possible to compare their suitability. The model was tested empirically by comparing the current classification of orange juices and Iberian ham with two different proposals, in an experiment conducted with an online consumer panel, and using MANCOVA to analyse the differences between the six indicators related to consumer learning results. It was concluded that the model is suitable for assessing the suitability of the classification systems, as it shows technical viability, ease of introduction in practically any situation and the ability to facilitate and guide the process of drawing up consumer-oriented food classification systems.     

A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty

Manufacturers need to satisfy consumer demands in order to compete in the real world. This requires the efficient operation of a supply chain planning. In this research we consider a supply chain including multiple suppliers, multiple manufacturers and multiple customers, addressing a multi-site, multi-period, multi-product aggregate production planning (APP) problem under uncertainty. First a new robust multi-objective mixed integer nonlinear programming model is proposed to deal with APP considering two conflicting objectives simultaneously, as well as the uncertain nature of the supply chain. Cost parameters of the supply chain and demand fluctuations are subject to uncertainty. Then the problem transformed into a multi-objective linear one. The first objective function aims to minimize total losses of supply chain including production cost, hiring, firing and training cost, raw material and end product inventory holding cost, transportation and shortage cost. The second objective function considers customer satisfaction through minimizing sum of the maximum amount of shortages among the customers’ zones in all periods. Working levels, workers productivity, overtime, subcontracting, storage capacity and lead time are also considered. Finally, the proposed model is solved as a single-objective mixed integer programming model applying the LP-metrics method. The practicability of the proposed model is demonstrated through its application in solving an APP problem in an industrial case study. The results indicate that the proposed model can provide a promising approach to fulfill an efficient production planning in a supply chain.