Hybridized evolutionary local search algorithm for the team orienteering problem with time windows

The orienteering problem (OP) consists in finding an elementary path over a subset of vertices. Each vertex is associated with a profit that is collected on the visitor’s first visit. The objective is to maximize the collected profit with respect to a limit on the path’s length. The team orienteering problem (TOP) is an extension of the OP where a fixed number m of paths must be determined. This paper presents an effective hybrid metaheuristic to solve both the OP and the TOP with time windows. The method combines the greedy randomized adaptive search procedure (GRASP) with the evolutionary local search (ELS). ELS generates multiple distinct child solutions using a mutation mechanism. Each child solution is further improved by a local search procedure. GRASP provides multiple starting solutions to the ELS. The method is able to improve several best known results on available benchmark instances.     

Discrete particle swarm optimization for the team orienteering problem

Orienteering problem is a well researched routing problem which is a generalization of the traveling salesman problem. Team orienteering problem (TOP) is the extended version of the orienteering problem with more than one member in the team. In this paper the first known discrete particle swarm optimization (DPSO) algorithm has been developed for 2, 3 and 4-member TOP. In the DPSO meta-heuristic novel methods have been introduced for the initial particle generation process. Reduced variable neighborhood search and 2-opt were applied as the local search tools. The efficacy of the algorithm was tested using seven commonly used benchmark problem sets ranging in size from 21 to 102 nodes. The results of the DPSO algorithm were compared against seven other heuristic algorithms that have been developed for TOP. It was concluded that the developed DPSO algorithm for the TOP is competitive and robust across the benchmark problem sets.     

An effective PSO-inspired algorithm for the team orienteering problem

The Team Orienteering Problem (TOP) is a particular vehicle routing problem in which the aim is to maximize the profit gained from visiting customers without exceeding a travel cost/time limit. This paper proposes a new and fast evaluation process for TOP based on an interval graph model and a Particle Swarm Optimization inspired Algorithm (PSOiA) to solve the problem. Experiments conducted on the standard benchmark of TOP clearly show that our algorithm outperforms the existing solving methods. PSOiA reached a relative error of 0.0005% whereas the best known relative error in the literature is 0.0394%. Our algorithm detects all but one of the best known solutions. Moreover, a strict improvement was found for one instance of the benchmark and a new set of larger instances was introduced.     

An adaptive ejection pool with toggle-rule diversification approach for the capacitated team orienteering problem

In the capacitated team orienteering problem (CTOP), we are given a set of homogeneous vehicles and a set of customers each with a service demand value and a profit value. A vehicle can get the profit of a customer by satisfying its demand, but the total demand of all customers in its route cannot exceed the vehicle capacity and the length of the route must be within a specified maximum. The problem is to design a set of routes that maximizes the total profit collected by the vehicles. In this article, we propose a new heuristic algorithm for the CTOP using the ejection pool framework with an adaptive strategy and a diversification mechanism based on toggling between two priority rules. Experimental results show that our algorithm can match or improve all the best known results on the standard CTOP benchmark instances proposed by Archetti et al. (2008).     

A memetic algorithm for the orienteering problem with hotel selection

In this paper, a memetic algorithm is developed to solve the orienteering problem with hotel selection (OPHS). The algorithm consists of two levels: a genetic component mainly focuses on finding a good sequence of intermediate hotels, whereas six local search moves embedded in a variable neighborhood structure deal with the selection and sequencing of vertices between the hotels. A set of 176 new and larger benchmark instances of OPHS are created based on optimal solutions of regular orienteering problems. Our algorithm is applied on these new instances as well as on 224 benchmark instances from the literature. The results are compared with the known optimal solutions and with the only other existing algorithm for this problem. The results clearly show that our memetic algorithm outperforms the existing algorithm in terms of solution quality and computational time. A sensitivity analysis shows the significant impact of the number of possible sequences of hotels on the difficulty of an OPHS instance.     

Metaheuristics for the team orienteering problem

The Team Orienteering Problem (TOP) is the generalization to the case of multiple tours of the Orienteering Problem, known also as Selective Traveling Salesman Problem. A set of potential customers is available and a profit is collected from the visit to each customer. A fleet of vehicles is available to visit the customers, within a given time limit. The profit of a customer can be collected by one vehicle at most. The objective is to identify the customers which maximize the total collected profit while satisfying the given time limit for each vehicle. We propose two variants of a generalized tabu search algorithm and a variable neighborhood search algorithm for the solution of the TOP and show that each of these algorithms beats the already known heuristics. Computational experiments are made on standard instances.     

The Team Orienteering Problem with Time Windows: An LP-based Granular Variable Neighborhood Search

The Team Orienteering Problem (TOP) is a known NP-hard problem that typically arises in vehicle routing and production scheduling contexts. In this paper we introduce a new solution method to solve the TOP with hard Time Window constraints (TOPTW). We propose a Variable Neighborhood Search (VNS) procedure based on the idea of exploring, most of the time, granular instead of complete neighborhoods in order to improve the algorithm’s efficiency without loosing effectiveness. The method provides a general way to deal with granularity for those routing problems based on profits and complicated by time constraints. Extensive computational results are reported on standard benchmark instances. Performance of the proposed algorithm is compared to optimal solution values, when available, or to best known solution values obtained by state-of-the-art algorithms. The method comes out to be, on average, quite effective allowing to improve the best know values for 25 test instances.     

A guided local search metaheuristic for the team orienteering problem

In the team orienteering problem (TOP) a set of locations is given, each with a score. The goal is to determine a fixed number of routes, limited in length, that visit some locations and maximise the sum of the collected scores. This paper describes an algorithm that combines different local search heuristics to solve the TOP. Guided local search (GLS) is used to improve two of the proposed heuristics. An extra heuristic is added to regularly diversify the search in order to explore more areas of the solution space. The algorithm is compared with the best known heuristics of the literature and applied on a large problem set. The obtained results are almost of the same quality as the results of these heuristics but the computational time is reduced significantly. Applying GLS to solve the TOP appears to be a very promising technique. Furthermore, the usefulness of exploring more areas of the solution space is clearly demonstrated.     

An exact algorithm for large multiple knapsack problems

The Multiple Knapsack Problem (MKP) is the problem of assigning a subset of n items to m distinct knapsacks, such that the total profit sum of the selected items is maximized, without exceeding the capacity of each of the knapsacks. The problem has several applications in naval as well as financial management. A new exact algorithm for the MKP is presented, which is specially designed for solving large problem instances. The recursive branch-and-bound algorithm applies surrogate relaxation for deriving upper bounds, while lower bounds are obtained by splitting the surrogate solution into the m knapsacks by solving a series of Subset-sum Problems. A new separable dynamic programming algorithm is presented for the solution of Subset-sum Problems, and we also use this algorithm for tightening the capacity constraints in order to obtain better upper bounds. The developed algorithm is compared to the mtm algorithm by Martello and Toth, showing the benefits of the new approach. A surprising result is that large instances with n=100 000 items may be solved in less than a second, and the algorithm has a stable performance even for instances with coefficients in a moderately large range.     

A Particle Swarm Optimization Algorithm with Path Relinking for the Location Routing Problem

This paper introduces a new hybrid algorithmic nature inspired approach based on particle swarm optimization, for solving successfully one of the most popular logistics management problems, the location routing problem (LRP). The proposed algorithm for the solution of the location routing problem, the hybrid particle swarm optimization (HybPSO-LRP), combines a particle swarm optimization (PSO) algorithm, the multiple phase neighborhood search – greedy randomized adaptive search procedure (MPNS-GRASP) algorithm, the expanding neighborhood search (ENS) strategy and a path relinking (PR) strategy. The algorithm is tested on a set of benchmark instances. The results of the algorithm are very satisfactory for these instances and for six of them a new best solution has been found.      

An Algorithmic Framework for the Exact Solution of the Prize-Collecting Steiner Tree Problem

The Prize-Collecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of utility networks where profit generating customers and the network connecting them have to be chosen in the most profitable way. Our main contribution is the formulation and implementation of a branch-and-cut algorithm based on a directed graph model where we combine several state-of-the-art methods previously used for the Steiner tree problem. Our method outperforms the previously published results on the standard benchmark set of problems. We can solve all benchmark instances from the literature to optimality, including some of them for which the optimum was not known. Compared to a recent algorithm by Lucena and Resende, our new method is faster by more than two orders of magnitude. We also introduce a new class of more challenging instances and present computational results for them. Finally, for a set of large-scale real-world instances arising in the design of fiber optic networks, we also obtain optimal solution values. Received: April, 2004 This work has been partly supported by the RTNADONET, 504438, by the Doctoral Scholarship Program of the Austrian Academy of Sciences (DOC) and by CNR and MIUR, Italy.A preliminary version of this paper appeared as [21].     

An exact algorithm for minimizing resource availability costs in project scheduling

A new exact algorithm that solves the Resource Availability Cost Problem (RACP) in project scheduling is shown to yield a significant improvement over the existing algorithm in the literature. The new algorithm consists of a hybrid method where an initial feasible solution is found heuristically. The branching scheme solves a Resource-Constrained Project Scheduling Problem (RCPSP) at each node where the resources of the RACP are fixed. The knowledge of previously solved RCPSPs is used to produce cuts in the search tree. A worst-case-performance theorem is established for this new algorithm. Experiments are performed on instances adapted from the PSPLIB database. The new algorithm can be used to minimize any resource availability cost problem once a procedure for the underlying resource-constrained problem is available.     

The capacitated team orienteering problem with incomplete service

In this paper we study the capacitated version of the Team Orienteering Problem (TOP), that is the Capacitated TOP (CTOP) and the impact of relaxing the assumption that a customer, if served, must be completely served. We prove that the profit collected by the CTOP with Incomplete Service (CTOP-IS) may be as large as twice the profit collected by the CTOP. A computational study is also performed to evaluate the average increase of the profit due to allowing incomplete service. The results show that the increase of the profit strongly depends on the specific instance. On the tested instances the profit increase ranges between 0 and 50 %. We complete the computational study with the increase of the profit of the CTOP due to split deliveries, that is multiple visits to the same customer, and to split deliveries combined with incomplete service.     

A hybrid imperialist competitive algorithm for minimizing makespan in a multi-processor open shop

In this paper a new mixed-integer linear programming (MILP) model is proposed for the multi-processor open shop scheduling (MPOS) problems to minimize the makespan with considering independent setup time and sequence dependent removal time. A hybrid imperialist competitive algorithm (ICA) with genetic algorithm (GA) is presented to solve this problem. The parameters of the proposed algorithm are tuned by response surface methodology (RSM). The performance of the algorithm to solve small, medium and large sized instances of the problem is evaluated by introducing two performance metrics. The quality of obtained solutions is compared with that of the optimal solutions for small sized instances and with the lower bounds for medium sized instances. Also some computational results are presented for large sized instances.     

A fast solution method for the time-dependent orienteering problem

This paper introduces a fast solution procedure to solve 100-node instances of the time-dependent orienteering problem (TD-OP) within a few seconds of computation time. Orienteering problems occur in logistic situations were an optimal combination of locations needs to be selected and the routing between the selected locations needs to be optimized. In the time-dependent variant, the travel time between two locations depends on the departure time at the first location. Next to a mathematical formulation of the TD-OP, the main contribution of this paper is the design of a fast and effective algorithm to tackle this problem. This algorithm combines the principles of an ant colony system (ACS) with a time-dependent local search procedure equipped with a local evaluation metric. Additionally, realistic benchmark instances with varying size and properties are constructed. The average score gap with the known optimal solution on these test instances is only 1.4% with an average computation time of 0.5 seconds. An extensive sensitivity analysis shows that the performance of the algorithm is insensitive to small changes in its parameter settings.     

University course timetabling using hybridized artificial bee colony with hill climbing optimizer

University course timetabling is concerned with assigning a set of courses to a set of rooms and timeslots according to a set of constraints. This problem has been tackled using metaheuristics techniques. Artificial bee colony (ABC) algorithm has been successfully used for tackling uncapaciated examination and course timetabling problems. In this paper, a novel hybrid ABC algorithm based on the integrated technique is proposed for tackling the university course timetabling problem. First of all, initial feasible solutions are generated using the combination of saturation degree (SD) and backtracking algorithm (BA). Secondly, a hill climbing optimizer is embedded within the employed bee operator to enhance the local exploitation ability of the original ABC algorithm while tackling the problem. Hill climbing iteratively navigates the search space of each population member in order to reach a local optima. The proposed hybrid ABC technique is evaluated using the dataset established by Socha including five small, five medium and one large problem instances. Empirical results on these problem instances validate the effectiveness and efficiency of the proposed algorithm. Our work also shows that a well-designed hybrid technique is a competitive alternative for addressing the university course timetabling problem.     

An iterative three-component heuristic for the team orienteering problem with time windows

This paper studies the team orienteering problem with time windows, the aim of which is to maximize the total profit collected by visiting a set of customers with a limited number of vehicles. Each customer has a profit, a service time and a time window. A service provided to any customer must begin in his or her time window. We propose an iterative framework incorporating three components to solve this problem. The first two components are a local search procedure and a simulated annealing procedure. They explore the solution space and discover a set of routes. The third component recombines the routes to identify high quality solutions. Our computational results indicate that this heuristic outperforms the existing approaches in the literature in average performance by at least 0.41%. In addition, 35 new best solutions are found.     

最小化总反馈长度的耦合活动排程研究

耦合活动的排程直接影响新产品开发的周期和成本,因而受到了学者和研发管理人员的普遍关注。本文针对最小化总反馈长度这一耦合活动排程常用目标,将遗传算法与局部搜索算法相结合,提出了一种新的混合优化算法,并系统分析了参数对算法性能的影响。然后将算法应用到实际案例和大量随机算例中,实验结果表明混合优化算法较大幅度提高了现有局部搜索算法解的质量;同等情形下,混合优化算法所获得解比单纯运用遗传算法所获得解更好。     

Hybrid Genetic Algorithm for DNA Sequencing with Errors

In the paper, a new hybrid genetic algorithm solving the DNA sequencing problem with negative and positive errors is presented. The algorithm has as its input a set of oligonucleotides coming from a hybridization experiment. The aim is to reconstruct an original DNA sequence of a known length on the basis of this set. No additional information about the oligonucleotides nor about the errors is assumed. Despite that, the algorithm returns for computationally hard instances surprisingly good results, of a very high similarity to original sequences.     

军事定向越野路径优化问题建模及混合蚁群算法求解

军事定向越野运动中存在点位多、分布散、时间紧、得分要求高等条件,为在规定时间内找到一条得分高的行进线路,找到衡量和分析运动成绩好坏的标准,文中对军事定向越野中的路径优化问题进行了深入分析,建立了混合整数规划模型,设计了一种混合蚁群算法。算法中,首先由改进蚁群算法找到初始解,然后再利用选择、交叉和变异算子进行解的优化,通过仿真实验和算法对比验证了混合蚁群算法的可行性和优越性。