An artificial bee colony algorithm approach for the team orienteering problem with time windows

This study addresses a highly constrained NP-hard problem called the team orienteering problem with time windows (TOPTW), which belongs to a well-known class of vehicle routing problems. This study proposes a relatively new technique called artificial bee colony (ABC) approach to solve the TOPTW. Moreover, considering that the number of studies for discrete optimization with an ABC algorithm is comparatively low, this study presents a new use of the ABC algorithm for a difficult discrete optimization problem. Additionally, this study introduces a new food source acceptance criterion and a new scout bee search behavior, both of which significantly contribute to the solution quality. The results show that the proposed method is effective, efficient, and comparable to other approaches.     

Iterated local search for the team orienteering problem with time windows

A personalised electronic tourist guide assists tourists in planning and enjoying their trip. The planning problem that needs to be solved, in real-time, can be modelled as a team orienteering problem with time windows (TOPTW). In the TOPTW, a set of locations is given, each with a score, a service time and a time window. The goal is to maximise the sum of the collected scores by a fixed number of routes. The routes allow to visit locations at the right time and they are limited in length. The main contribution of this paper is a simple, fast and effective iterated local search meta-heuristic to solve the TOPTW. An insert step is combined with a shake step to escape from local optima. The specific shake step implementation and the fast evaluation of possible improvements, produces a heuristic that performs very well on a large and diverse set of instances. The average gap between the obtained results and the best-known solutions is only 1.8% and the average computation time is decreased with a factor of several hundreds. For 31 instances, new best solutions are computed.     

混合粒子群算法求解带软时间窗的VRPSPD问题

针对带软时间窗的同时集配货车辆路径问题（VRPSPD）,建立了以车辆派遣成本、行驶成本和时间窗惩罚成本之和最小为目标的车辆路径优化模型;设计混合粒子群算法进行求解,该算法结合以变邻域下降搜索为主体的适应性扰动机制,采用适应性选择邻域策略,并在每个邻域搜索中应用可变的循环次数,以此提高对解空间的探测能力和搜索效率。数值实验结果表明了该算法的可行性和有效性。     

A modified particle swarm optimization with multiple subpopulations for multimodal function optimization problems

In this paper, a modified particle swarm optimization (PSO) algorithm is developed for solving multimodal function optimization problems. The difference between the proposed method and the general PSO is to split up the original single population into several subpopulations according to the order of particles. The best particle within each subpopulation is recorded and then applied into the velocity updating formula to replace the original global best particle in the whole population. To update all particles in each subpopulation, the modified velocity formula is utilized. Based on the idea of multiple subpopulations, for the multimodal function optimization the several optima including the global and local solutions may probably be found by these best particles separately. To show the efficiency of the proposed method, two kinds of function optimizations are provided, including a single modal function optimization and a complex multimodal function optimization. Simulation results will demonstrate the convergence behavior of particles by the number of iterations, and the global and local system solutions are solved by these best particles of subpopulations.     

A hybrid particle swarm optimization for job shop scheduling problem

A hybrid particle swarm optimization (PSO) for the job shop problem (JSP) is proposed in this paper. In previous research, PSO particles search solutions in a continuous solution space. Since the solution space of the JSP is discrete, we modified the particle position representation, particle movement, and particle velocity to better suit PSO for the JSP. We modified the particle position based on preference list-based representation, particle movement based on swap operator, and particle velocity based on the tabu list concept in our algorithm. Giffler and Thompson’s heuristic is used to decode a particle position into a schedule. Furthermore, we applied tabu search to improve the solution quality. The computational results show that the modified PSO performs better than the original design, and that the hybrid PSO is better than other traditional metaheuristics.     

A hybrid particle swarm optimization approach for the sequential ordering problem

The sequential ordering problem is a version of the asymmetric travelling salesman problem where precedence constraints on vertices are imposed. A tour is feasible if these constraints are fulfilled, and the objective is to find a feasible solution with minimum cost.     

Solving shortest path problem using particle swarm optimization

This paper presents the investigations on the application of particle swarm optimization (PSO) to solve shortest path (SP) routing problems. A modified priority-based encoding incorporating a heuristic operator for reducing the possibility of loop-formation in the path construction process is proposed for particle representation in PSO. Simulation experiments have been carried out on different network topologies for networks consisting of 15–70 nodes. It is noted that the proposed PSO-based approach can find the optimal path with good success rates and also can find closer sub-optimal paths with high certainty for all the tested networks. It is observed that the performance of the proposed algorithm surpasses those of recently reported genetic algorithm based approaches for this problem.     

Heuristics for the time dependent team orienteering problem: Application to tourist route planning

The Time Dependent Team Orienteering Problem with Time Windows (TDTOPTW) can be used to model several real life problems. Among them, the route planning problem for tourists interested in visiting multiple points of interest (POIs) using public transportation. The main objective of this problem is to select POIs that match tourist preferences, taking into account a multitude of parameters and constraints while respecting the time available for sightseeing in a daily basis and integrating public transportation to travel between POIs (Tourist Trip Design Problem, TTDP). TDTOPTW is NP-hard while almost the whole body of the related literature addresses the non-time dependent version of the problem. The only TDTOPTW heuristic proposed so far is based on the assumption of periodic transit service schedules. Herein, we propose efficient cluster-based heuristics for the TDTOPTW which yield high quality solutions, take into account time dependency in calculating travel times between POIs and make no assumption on periodic service schedules. The validation scenario for our prototyped algorithms involved the transit network and real POI datasets compiled from the metropolitan area of Athens (Greece). Our TTDP algorithms handle arbitrary (i.e. determined at query time) rather than fixed start/end locations for derived tourist itineraries.     

A particle swarm optimization approach with refinement procedure for nurse rostering problem

This study attempts to develop a model satisfying the rules of a typical hospital environment based both on published research data and on requirements of a local hospital under study. A mathematical formulation for the studied nurse rostering problem (NRP) is presented first. Due to the combinatorial nature of the NRP model, a particle swarm optimization (PSO) approach is proposed to solve this highly complicated NRP. The structure of the problem constraints is analyzed and used as base for generating workstretch patterns. These patterns serve as the base for generating fast initial solutions, and will later be improved upon by the proposed PSO algorithm. This study also proposes a simple yet effective procedure for attempting possible refinements on the solutions obtained by the PSO before reporting the final solutions. When fair shift assignment is considered as the decision objective, computational results show that the proposed PSO algorithm with refinement procedure is able to produce optimal solutions in all real test problems in a very efficient manner.     

An improved particle swarm optimization algorithm for flowshop scheduling problem

The flowshop scheduling problem has been widely studied and many techniques have been applied to it, but few algorithms based on particle swarm optimization (PSO) have been proposed to solve it. In this paper, an improved PSO algorithm (IPSO) based on the “alldifferent” constraint is proposed to solve the flow shop scheduling problem with the objective of minimizing makespan. It combines the particle swarm optimization algorithm with genetic operators together effectively. When a particle is going to stagnate, the mutation operator is used to search its neighborhood. The proposed algorithm is tested on different scale benchmarks and compared with the recently proposed efficient algorithms. The results show that the proposed IPSO algorithm is more effective and better than the other compared algorithms. It can be used to solve large scale flow shop scheduling problem effectively.     

A new particle swarm optimization for the open shop scheduling problem

This paper presents a new particle swarm optimization (PSO) for the open shop scheduling problem. Compared with the original PSO, we modified the particle position representation using priorities, and the particle movement using an insert operator. We also implemented a modified parameterized active schedule generation algorithm (mP-ASG) to decode a particle position into a schedule. In mP-ASG, we can reduce or increase the search area between non-delay schedules and active schedules by controlling the maximum delay time allowed. Furthermore, we hybridized our PSO with beam search. The computational results show that our PSO found many new best solutions of the unsolved problems.     

解决零空闲流水线调度问题的离散粒子群算法

研究了以最大完工时间为目标的零空闲流水线调度问题.提出一种复杂度为O(nm)的最大完工时间算法和一种快速插入邻域搜索算法;提出了解决该问题的离散粒子群调度算法,并结合简化邻域搜索算法给出了提高调度算法性能的措施.仿真实验表明了所得算法的有效性.     

星型结构的多目标粒子群算法求解多模态多目标问题

首先,根据多目标粒子群算法中的粒子结构信息,利用非支配解集构造粒子个体邻域之间的拓扑结构,提出星型结构的多目标粒子群算法用于求解多模态多目标问题。其次,针对多目标粒子群中全局最优个体选择困难,提出一种非支配解集分布均匀程度的评价方法,评价结果用于确定当前粒子对应的全局最优个体。最后,结合2种方法提出带均匀计算方法的星型拓扑结构多目标粒子群优化算法STMOPSONCMIU。通过测试函数分析算法的收敛性,表明改进的算法比原来的算法收敛速度快。实验结果表明,该算法可以较好地兼顾问题的目标空间和决策空间的分布,有效解决多模态多目标问题。     

求解背包问题的混合粒子群优化算法

提出一种新的遗传思想：父代的基因决定子代继承某一基因的概率,而不是由单纯的交叉产生子代。根据此思想,提出两种利用遗传概率产生子代的方法,并将它们分别与粒子群优化算法相结合得到两种求解背包问题的混合粒子群优化算法。通过数值实验说明了同样的算法采用遗传策略要比交叉策略寻优性更强,分析了变异概率对算法的影响。     

A particle swarm optimization for the vehicle routing problem with simultaneous pickup and delivery

This paper proposes a formulation of the vehicle routing problem with simultaneous pickup and delivery (VRPSPD) and a particle swarm optimization (PSO) algorithm for solving it. The formulation is a generalization of three existing VRPSPD formulations. The main PSO algorithm is developed based on GLNPSO, a PSO algorithm with multiple social structures. A random key-based solution representation and decoding method is proposed for implementing PSO for VRPSPD. The solution representation for VRPSPD with n customers and m   vehicles is a (n+2m)$(n+2m)$-dimensional particle. The decoding method starts by transforming the particle to a priority list of customers to enter the route and a priority matrix of vehicles to serve each customer. The vehicle routes are constructed based on the customer priority list and vehicle priority matrix. The proposed algorithm is tested using three benchmark data sets available from the literature. The computational result shows that the proposed method is competitive with other published results for solving VRPSPD. Some new best known solutions of the benchmark problem are also found by the proposed method.     

区域分割粒子群算法及多维背包问题求解

为克服离散粒子群算法早熟的缺陷,通过引入区域分割算法后,移除了解空间中一些无希望的点集,缩小了解的搜索空间,提高了找到最优解的概率,并通过贪心策略对产生的粒子进行了修复和改进,克服了离散粒子群算法收敛慢的缺点。对典型多维背包问题的仿真实验表明,区域分割粒子群算法寻优能力更强,收敛更快。     

Self-adaptive check and repair operator-based particle swarm optimization for the multidimensional knapsack problem

The multidimensional knapsack problem (MKP) is a combinatorial optimization problem belonging to the class of NP-hard problems. This study proposes a novel self-adaptive check and repair operator (SACRO) combined with particle swarm optimization (PSO) to solve the MKP. The traditional check and repair operator (CRO) uses a unique pseudo-utility ratio, whereas SACRO dynamically and automatically changes the alternative pseudo-utility ratio as the PSO algorithm runs. Two existing PSO algorithms are used as the foundation to support the novel SACRO methods, the proposed SACRO-based algorithms were tested using 137 benchmark problems from the OR-Library to validate and demonstrate the efficiency of SACRO idea. The results were compared with those of other population-based algorithms. Simulation and evaluation results show that SACRO is more competitive and robust than the traditional CRO. The proposed SACRO-based algorithms rival other state-of-the-art PSO and other algorithms. Therefore, changing different types of pseudo-utility ratios produces solutions with better results in solving MKP. Moreover, SACRO can be combined with other population-based optimization algorithms to solve constrained optimization problems.     

求解背包问题的更贪心粒子群算法

将粒子群算法与贪心思想相融合,提出一种用于求解0/1背包问题的更贪心混合粒子群算法。对超过背包重量约束的粒子的处理措施是去掉已经装进去且性价比最差的物品,直至满足重量约束为止,这种思想在改善粒子质量的同时避免了通常罚函数方法中敏感的参数选择问题;对当前可行粒子的处理措施是将还未装入背包且性价比最好的物品装进背包,直至不能装为止。通过与文献中基于经典算例的计算结果比较表明,更贪心粒子群算法无论在寻优能力、计算速度和稳定性方面都超过了文献中提到的混合遗传算法（HGA）、贪心遗传算法（GGA）和混合粒子群算法（GBPSOA）。     

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.     

An improved binary particle swarm optimization for unit commitment problem

This paper proposes a new improved binary PSO (IBPSO) method to solve the unit commitment (UC) problem, which is integrated binary particle swarm optimization (BPSO) with lambda-iteration method. The IBPSO is improved by priority list based on the unit characteristics and heuristic search strategies to repair the spinning reserve and minimum up/down time constraints. To verify the advantages of the IBPSO method, the IBPSO is tested and compared to the other methods on the systems with the number of units in the range of 10–100. Numerical results demonstrate that the IBPSO is superior to other methods reported in the literature in terms of lower production cost and shorter computational time.