An efficient hybrid algorithm for the Traveling Car Renter Problem

This paper tackles a Traveling Salesman Problem variant called Traveling Car Renter Problem, where one car renter desires to travel among cities using a rented vehicle. Basically, the car renter has two options when he/she arrives in a city: to return the vehicle and rent another one or to keep the same car until the next city. Every time a car is delivered in a city, a return fee must be paid. Travel cost between any pair of cities also depends on the chosen car. The objective is to establish a Hamiltonian cycle minimizing the travel costs and returning fees. An evolutionary algorithm (EA) and a hybrid method called Adaptive Local Search Procedure (ALSP) are proposed for this problem. Both were compared to the best known algorithm in literature and obtained better results for non-Euclidean instances. Such algorithms compose an efficient model for a better exploration of the problem solutions space. From the expert system point-of-view, we propose a novel inference engine with minimized results error.     

Honey bees mating optimization algorithm for the Euclidean traveling salesman problem

This paper introduces a new hybrid algorithmic nature inspired approach based on Honey Bees Mating Optimization for successfully solving the Euclidean Traveling Salesman Problem. The proposed algorithm for the solution of the Traveling Salesman Problem, the Honey Bees Mating Optimization (HBMOTSP), combines a Honey Bees Mating Optimization (HBMO) algorithm, the Multiple Phase Neighborhood Search-Greedy Randomized Adaptive Search Procedure (MPNS-GRASP) algorithm and the Expanding Neighborhood Search Strategy. Besides these two procedures, the proposed algorithm has, also, two additional main innovative features compared to other Honey Bees Mating Optimization algorithms concerning the crossover operator and the workers. The main contribution of this paper is that it shows that the HBMO can be used in hybrid synthesis with other metaheuristics for the solution of the TSP with remarkable results both to quality and computational efficiency. The proposed algorithm was tested on a set of 74 benchmark instances from the TSPLIB and in all but eleven instances the best known solution has been found. For the rest instances the quality of the produced solution deviates less than 0.1% from the optimum.     

A framework for developing a daily activity and multimodal travel planner

There is a need to further explore ways to use Advanced Traveler Information Systems (ATIS) to encourage transit and ridesharing. One mechanism is to provide convenient travel itinerary information, not just for one trip, but for a day's travel. The formulation should consider time constraints, activity needs, real transit service parameters and the actual street system. Basic algorithmic development is needed to spur the private sector interest in such a product by demonstrating its utility. The activity travel planner will aid its user in planning his daily itinerary by arranging the sequence of stops, suggesting and possibly selecting stop locations, providing transit route and schedule information, and suggesting travel routes. This paper develops a framework for solving the Travel Itinerary Planning Problem (TIPP) which is a variant of the Traveling Salesman Problem (TSP). Implementation of the solution algorithm would be used to develop and test a prototype for an activity and travel planner.     

Heuristics for the probabilistic traveling salesman problem with deadlines based on quasi-parallel Monte Carlo sampling

The Probabilistic Traveling Salesman Problem with Deadlines (PTSPD) is a Stochastic Vehicle Routing Problem with a computationally demanding objective function. In this work we propose an approximation for that objective function based on Monte Carlo Sampling and using the novel approach of quasi-parallel evaluation of samples. We perform comprehensive computational studies that reveal the efficiency of this approximation. Additionally, we examine different Local Search Algorithms and present a Random Restart Local Search Algorithm for solving the PTSPD together with an extensive computational study on a large set of benchmark instances.     

Algorithms for the On-Line Quota Traveling Salesman Problem

The Quota Traveling Salesman Problem is a generalization of the well-known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of sales, minimizing the amount of time. In this paper we address the on-line version of the problem, where requests are given over time. We present algorithms for various metric spaces, and analyze their performance in the usual framework of competitive analysis. In particular we present a 2-competitive algorithm that matches the lower bound for general metric spaces. In the case of the halfline metric space, we show that it is helpful not to move at full speed, and this approach is also used to derive the best on-line polynomial time algorithm known so far for the On-Line TSP (in the homing version).     

考虑时间窗与随机航行时间的船舶航线规划

良好的航线设计是船运公司降低运营成本,提高服务质量的关键。船舶运输中存在航行时间不确定,码头资源稀缺等特点,基于此将其航线问题抽象为考虑时间窗与随机旅行时间的多重流动旅行商问题。针对航行时间的随机性,设计了线性近似方法,提出了虚拟时间窗的概念,构建了初始模型与修正模型;给出了该问题的一个算例,验证了模型与算法的有效性和合理性。     

A competitive neural network algorithm for solving vehicle routing problem

This paper describes a self organization Neural Network algorithm for a class of Vehicle Routing Problems. Motivated by the outstanding performance of adaptive Neural Network approach in the Traveling Salesman Problem, we devised an algorithm to extend the domain of applicability of this approach to more complex problems. First, relevant adaptation is proposed to refine the model for the Multiple Traveling Salesman Problem. Then, an additional mechanism to satisfy further constraints are embodied into the algorithm. The effectiveness of the proposed algorithm is evaluated by considering a series of standard problems from the literature. The results show that the algorithm can yield solutions within a few percent of optimality.     

A combined multistart random constructive heuristic and set partitioning based formulation for the vehicle routing problem with time dependent travel times

Although the Vehicle Routing Problem (VRP) has been broadly addressed in the literature, most of the works consider constant travel times. This is a strong simplification that does not allow to correctly model real world applications. In fact, nowadays, travel times sensibly change, across the day, due to congestion phenomena. Therefore, to actually represent the reality, it is necessary to consider time dependent travel times. In this paper, the VRP with Time Dependent Travel Times, service times at nodes, and limit on the maximum route duration, is addressed. The objective function consists into minimizing the total travel time. A Multistart Random Constructive Heuristic, (MRCH), in which congestion level is considered, is proposed. The routes obtained by the MRCH are then used as columns in a Set Partitioning formulation. Computational results, carried out on instances derived by VRP instances taken from the literature, show the efficiency and effectiveness of the proposed approach.     

A Memetic Algorithm with a large neighborhood crossover operator for the Generalized Traveling Salesman Problem

The Generalized Traveling Salesman Problem (GTSP) is a generalization of the well-known Traveling Salesman Problem (TSP), in which the set of cities is divided into mutually exclusive clusters. The objective of the GTSP consists in visiting each cluster exactly once in a tour, while minimizing the sum of the routing costs. This paper addresses the solution of the GTSP using a Memetic Algorithm. The originality of our approach rests on the crossover procedure that uses a large neighborhood search. This algorithm is compared with other algorithms on a set of 54 standard test problems with up to 217 clusters and 1084 cities. Results demonstrate the efficiency of our algorithm in both solution quality and computation time.     

一种改进的求解TSP问题的近似算法

旅行商问题(TSP)是典型的具有NPC复杂性的组合优化问题。在现有求解TSP问题的2-近似算法closest-point算法基础上,通过对插入点的插入位置进行改进,提出了一种有效的近似算法最近点前后插入法(CPBOA),并采用TSPLIB中的一些典型实例对该算法进行了测试,同时与典型的常数近似比算法MST-PRIM算法和closest-point算法进行了比较。实验结果表明,该算法在求解质量上与closest-point和MST-PRIM算法相比都有很大的改进,而且速度也很快。     

– Ant System

Ant System, the first Ant Colony Optimization algorithm, showed to be a viable method for attacking hard combinatorial optimization problems. Yet, its performance, when compared to more fine-tuned algorithms, was rather poor for large instances of traditional benchmark problems like the Traveling Salesman Problem. To show that Ant Colony Optimization algorithms could be good alternatives to existing algorithms for hard combinatorial optimization problems, recent research in this area has mainly focused on the development of algorithmic variants which achieve better performance than Ant System.In this paper, we present – Ant System ( ), an Ant Colony Optimization algorithm derived from Ant System. differs from Ant System in several important aspects, whose usefulness we demonstrate by means of an experimental study. Additionally, we relate one of the characteristics specific to — that of using a greedier search than Ant System — to results from the search space analysis of the combinatorial optimization problems attacked in this paper. Our computational results on the Traveling Salesman Problem and the Quadratic Assignment Problem show that is currently among the best performing algorithms for these problems.     

The online Prize-Collecting Traveling Salesman Problem

We study the online version of the Prize-Collecting Traveling Salesman Problem (PCTSP), a generalization of the Traveling Salesman Problem (TSP). In the TSP, the salesman has to visit a set of cities while minimizing the length of the overall tour. In the PCTSP, each city has a given weight and penalty, and the goal is to collect a given quota of the weights of the cities while minimizing the length of the tour plus the penalties of the cities not in the tour. In the online version, cities are disclosed over time. We give a 7/3-competitive algorithm for the problem, which compares with a lower bound of 2 on the competitive ratio of any deterministic algorithm. We also show how our approach can be combined with an approximation algorithm in order to obtain an O(1)-competitive algorithm that runs in polynomial time.     

A Hybrid Multi-Swarm Particle Swarm Optimization algorithm for the Probabilistic Traveling Salesman Problem

The Probabilistic Traveling Salesman Problem (PTSP) is a variation of the classic Traveling Salesman Problem (TSP) and one of the most significant stochastic routing problems. In the PTSP, only a subset of potential customers need to be visited on any given instance of the problem. The number of customers to be visited each time is a random variable. In this paper, a new hybrid algorithmic nature inspired approach based on Particle Swarm Optimization (PSO), Greedy Randomized Adaptive Search Procedure (GRASP) and Expanding Neighborhood Search (ENS) Strategy is proposed for the solution of the PTSP. The proposed algorithm is tested on numerous benchmark problems from TSPLIB with very satisfactory results. Comparisons with the classic GRASP algorithm, the classic PSO and with a Tabu Search algorithm are also presented. Also, a comparison is performed with the results of a number of implementations of the Ant Colony Optimization algorithm from the literature and in 13 out of 20 cases the proposed algorithm gives a new best solution.     

Global migration strategy with moving colony for hierarchical distributed evolutionary algorithms

In the established hierarchical distributed evolutionary algorithms (HDEAs), object of global migration is individual. To obtain better solutions of concrete problems, global migration strategy with moving colony is proposed in this paper. In global migration based on the proposed strategy, migration object is subpopulation which moves between groups. Such global migration can increase the efficiency of thereafter local migration. Moreover, realizing it even needs no communication because it can be executed by regrouping subpopulations. In our experiments, the basement of parallelism is an EA for the Traveling Salesman Problem. Outcomes of HDEAs based on proposed scheme which have different global migration topology are compared with those of traditional ones on nine benchmark instances. The results show that a HDEA based on the proposed strategy having the ring global topology performs better than traditional HDEAs for high difficulty instances. However, the advantage of that having the random global topology is not so significant because of conflicting migrations arisen from this topology.     

An application of the self-organizing map in the non-Euclidean Traveling Salesman Problem

An application of the self-organizing map (SOM) to the Traveling Salesman Problem (TSP) has been reported by many researchers, however these approaches are mainly focused on the Euclidean TSP variant. We consider the TSP as a problem formulation for the multi-goal path planning problem in which paths among obstacles have to be found. We apply a simple approximation of the shortest path that seems to be suitable for the SOM adaptation procedure. The approximation is based on a geometrical interpretation of SOM, where weights of neurons represent nodes that are placed in the polygonal domain. The approximation is verified in a set of real problems and experimental results show feasibility of the proposed approach for the SOM based solution of the non-Euclidean TSP.     

遗传算法在旅行商问题中的实践与探究

TSP问题是组合优化领域的经典问题之一,旨在求出遍历若干个城市的最短路径。本文通过遗传算法GA的选择和变异算子的确定和、交叉算子的改进,并在TSP问题中的实践来探索这个经典的NP(Nondeterministic Polynomial)难题。     

TSP问题的算法与应用的研究

TSP问题是一个典型的组合优化问题.针对TSP问题的两种主要算法:遗传算法和蚁群算法,进行了分析和研究.并且提出了网络浏览器运行的实现方法,给出了系统实现的B/S三层架构.最后,运用本算法和实现的技术,作为应用实例实现了ERP物流配送路径决策支持系统的原型.     

GRASP with path relinking for the symmetric Euclidean clustered traveling salesman problem

In this paper, we propose new heuristics using several path-relinking strategies to solve the Clustered Traveling Salesman Problem (CTSP). The CTSP is a generalization of the Traveling Salesman Problem (TSP) in which the set of vertices is partitioned into clusters and the objective is to find a minimum cost Hamiltonian cycle such that the vertices of each cluster are visited continuously. A comparison among the performance of the several different adopted path-relinking strategies is presented using instances with up to 2000 vertices and clusters varying between 4 and 150 vertices. Also computational experiments were performed to compare the performance of the proposed heuristics with an exact algorithm and a Genetic Algorithm. The obtained computational results showed that the proposed heuristics were able to obtain competitive results related to the quality of the solutions and computational execution time.     

A correction algorithm for token-passing sequences in mobile communication networks

We present a distributed approximation algorithm for the Traveling Salesman Problem (TSP) in networks that use a broadcast, multiaccess communication channel. The application for which the algorithm was originally designed is maintaining a short token-passing path (which means low scheduling overhead) in radio networks with mobile nodes. The algorithm is adaptive in the sense that it shifts gradually between performing a slight correction of an existing tour and recomputing one “from scratch.” It can thus be viewed as a generalization, or extension, of conventional TSP algorithms. The proposed algorithm guarantees the same worst-case tour length as the one guaranteed by any conventional “from scratch” algorithm, yet it is capable of taking advantage of certain node layouts (e.g., geographically clustered nodes) to reduce the cost of computing the path. The correction algorithm is suitable for dynamic graphs with slowly changing edge weights, and for which a Traveling Salesman tour (optimal or approximate) has previously been computed and is “deteriorating” with time due to the weight changes. The algorithm can be used to “refresh” the tour whenever it deteriorates beyond a given level, and thus maintain a reasonable average tour length at relatively low computation and communication costs. For a Euclidean graph withn nodes laid out in a bounded area with diameterD, the maximal length of the tour produced by the algorithm is proportional toD√n, like the maximal length of an optimal tour in that graph (the two differ by a factor of 2 at the worst case).     

\epsilon- DANTE : an ant colony oriented depth search procedure

The e\epsilon-Depth ANT Explorer (e\epsilon- DANTE ) algorithm applied to a multiple objective optimization problem is presented in this paper. This method is a hybridization of the ant colony optimization algorithm with a depth search procedure, putting together an oriented/limited depth search. A particular design of the pheromone set of rules is suggested for these kinds of optimization problems, which are an adaptation of the single objective case. Six versions with incremental features are presented as an evolutive path, beginning in a single colony approach, where no depth search is applied, to the final e\epsilon- DANTE . Versions are compared among themselves in a set of instances of the multiple objective Traveling Salesman Problem. Finally, our best version of e\epsilon- DANTE is compared with several established heuristics in the field showing some promising results.