Parallelized neural network system for solving Euclidean traveling salesman problem

We investigate a parallelized divide-and-conquer approach based on a self-organizing map (SOM) in order to solve the Euclidean traveling salesman problem (TSP). Our approach consists of dividing cities into municipalities, evolving the most appropriate solution from each municipality so as to find the best overall solution and, finally, joining neighborhood municipalities by using a blend operator to identify the final solution. We evaluate performance of parallelized approach over standard TSP test problems (TSPLIB) to show that our approach gives a better answer in terms of quality and time rather than the sequential evolutionary SOM.     

A self-organizing neural network approach for multiple traveling salesman and vehicle routing problems

This paper addresses several algorithms based on self-organizing neural network approach for routing problems. The algorithm for Traveling Salesman Problem is elaborated and the extension of the proposed algorithm to more complex problems namely, Multiple Traveling Salesmen and Vehicle Routing is discussed. In order to investigate the performance of the algorithms, a comprehensive empirical study has been provided. The simulations, which are conducted on standard data, evaluate the overall performance of this approach by comparing the results with the best known or the optimal solutions of the problems. The proposed algorithm shows significant advances in both qualities of the solution and computational efforts for most of the experimented data.     

An asynchronous recurrent linear threshold network approach to solving the traveling salesman problem

In this paper, an approach to solving the classical Traveling Salesman Problem (TSP) using a recurrent network of linear threshold (LT) neurons is proposed. It maps the classical TSP onto a single-layered recurrent neural network by embedding the constraints of the problem directly into the dynamics of the network. The proposed method differs from the classical Hopfield network in the update of state dynamics as well as the use of network activation function. Furthermore, parameter settings for the proposed network are obtained using a genetic algorithm, which ensure a stable convergence of the network for different problems. Simulation results illustrate that the proposed network performs better than the classical Hopfield network for optimization.     

Solving the traveling salesman problem using cooperative genetic ant systems

The travelling salesman problem (TSP) is a classic problem of combinatorial optimization and has applications in planning, scheduling, and searching in many scientific and engineering fields. Ant colony optimization (ACO) has been successfully used to solve TSPs and many associated applications in the last two decades. However, ACO has problem in regularly reaching the global optimal solutions for TSPs due to enormity of the search space and numerous local optima within the space. In this paper, we propose a new hybrid algorithm, cooperative genetic ant system (CGAS) to deal with this problem. Unlike other previous studies that regarded GA as a sequential part of the whole searching process and only used the result from GA as the input to subsequent ACO iterations, this new approach combines both GA and ACO together in a cooperative manner to improve the performance of ACO for solving TSPs. The mutual information exchange between ACO and GA in the end of the current iteration ensures the selection of the best solutions for next iteration. This cooperative approach creates a better chance in reaching the global optimal solution because independent running of GA maintains a high level of diversity in next generation of solutions. Compared with results from other GA/ACO algorithms, our simulation shows that CGAS has superior performance over other GA and ACO algorithms for solving TSPs in terms of capability and consistency of achieving the global optimal solution, and quality of average optimal solutions, particularly for small TSPs.     

一种求解TSP问题的ACO&SS算法设计

提出一种求解旅行商(TSP)问题的新型分散搜索算法.将蚁群算法(ACO)的构解方法引入分散搜索(SS)算法,在搜索过程中既考虑解的质量,又考虑解的分散性.采用一种将蚁群算法的信息素更新技术与分散搜索的组合机制相结合的新型子集组合成新解的构解机制,同时采用动态更新参考集与临界准则策略来加快收敛速度.实验结果表明,该算法优于其他现有的方法,获得了较好的结果.     

A parallel immune algorithm for traveling salesman problem and its application on cold rolling scheduling

Parallel computing provides efficient solutions for combinatorial optimization problem. However, since the communications among computing processes are rather cost-consuming, the actual parallel or distributed algorithm comes with substantial expenditures, such as, hardware, management, and maintenance. In this study, a parallel immune algorithm based on graphic processing unit (GPU) that originally comes to process the computer graphics in display adapter is proposed. Genetic operators and a structure of vaccine taboo list are designed, and the internal memory utility of GPU structure is optimized. To verify the effectiveness and efficiency of the proposed algorithm, various middle-scale traveling salesman problems (TSP) are employed to demonstrate the potential of the proposed techniques. The simulation examples demonstrate that the developed method can greatly improve the computing efficiency for solving the TSP, and the results are more remarkable when the scale of TSP becomes higher. Furthermore, the derived algorithm is verified by a practical application in steel industry that arranges the cold rolling scheduling of a batch of steel coils.     

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 novel discretization scheme for the close enough traveling salesman problem

This paper addresses a variant of the Euclidean traveling salesman problem in which the traveler visits a node if it passes through the neighborhood set of that node. The problem is known as the close-enough traveling salesman problem. We introduce a new effective discretization scheme that allows us to compute both a lower and an upper bound for the optimal solution. Moreover, we apply a graph reduction algorithm that significantly reduces the problem size and speeds up computation of the bounds. We evaluate the effectiveness and the performance of our approach on several benchmark instances. The computational results show that our algorithm is faster than the other algorithms available in the literature and that the bounds it provides are almost always more accurate.     

The hybrid genetic algorithm with two local optimization strategies for traveling salesman problem

Traveling salesman problem (TSP) is proven to be NP-complete in most cases. The genetic algorithm (GA) is improved with two local optimization strategies for it. The first local optimization strategy is the four vertices and three lines inequality, which is applied to the local Hamiltonian paths to generate the shorter Hamiltonian circuits (HC). After the HCs are adjusted with the inequality, the second local optimization strategy is executed to reverse the local Hamiltonian paths with more than 2 vertices, which also generates the shorter HCs. It is necessary that the two optimization strategies coordinate with each other in the optimization process. The two optimization strategies are operated in two structural programs. The time complexity of the first and second local optimization strategies are O(n) and O(n³), respectively. The two optimization strategies are merged into the traditional GA. The computation results show that the hybrid genetic algorithm (HGA) can find the better approximate solutions than the GA does within an acceptable computation time.     

Runtime reduction techniques for the probabilistic traveling salesman problem with deadlines

The probabilistic traveling salesman problem with deadlines (PTSPD) is an extension of the well-known probabilistic traveling salesman problem in which, in addition to stochastic presence, customers must also be visited before a known deadline. For realistically sized instances, the problem is impossible to solve exactly, and local-search methods struggle due to the time required to evaluate the objective function. Because computing the deadline violations is the most time consuming part of the objective, we focus on developing approximations for the computation of deadline violations. These approximations can be imbedded in a variety of local-search methods, and we perform experiments comparing their performance using a 1-shift neighborhood. These computational experiments show that the approximation methods lead to significant runtime improvements without loss in quality.     

基于自适应继承策略的帝国竞争算法求解旅行商问题

针对帝国竞争算法在求解旅行商问题时局部搜索能力不强和容易陷入局部最优的缺陷,提出一种基于自适应继承策略的帝国竞争算法.该算法采用自适应继承策略的启发式交叉算子、单点局部插入策略和固定邻域的2-opt算子来增强算法的局部优化能力,并加入帝国精英解集以保持种群的多样性.通过标准实例测试,验证了所提出的改进策略的优越性,与基于启发式交叉算子和帝国主义算法为框架的其他算法进行对比,实验结果表明,该算法求解中小规模的解旅行商问题具有较高的求解精度和较快的收敛速度.     

A new formulation and approach for the black and white traveling salesman problem

This paper proposes a new formulation and a column generation approach for the black and white traveling salesman problem. This problem is an extension of the traveling salesman problem in which the vertex set is divided into black vertices and white vertices. The number of white vertices visited and the length of the path between two consecutive black vertices are constrained. The objective of this problem is to find the shortest Hamiltonian cycle that covers all vertices satisfying the cardinality and the length constraints. We present a new formulation for the undirected version of this problem, which is amenable to the Dantzig–Wolfe decomposition. The decomposed problem which is defined on a multigraph becomes the traveling salesman problem with an extra constraint set in which the variable set is the feasible paths between pairs of black vertices. In this paper, a column generation algorithm is designed to solve the linear programming relaxation of this problem. The resulting pricing subproblem is an elementary shortest path problem with resource constraints, and we employ acceleration strategies to solve this subproblem effectively. The linear programming relaxation bound is strengthened by a cutting plane procedure, and then column generation is embedded within a branch-and-bound algorithm to compute optimal integer solutions. The proposed algorithm is used to solve randomly generated instances with up to 80 vertices.     

一种求解TSP问题的离散蝙蝠算法

蝙蝠算法是一种新型的群智能优化算法,在求解连续域优化问题上取得了较好的优化效果,但在离散优化领域的应用较少。研究了求解TSP问题的离散蝙蝠算法,设计了相关操作算子实现算法的离散化,并引入逆序操作使算法跳出局部最优。对TSPLIB标准库中若干经典实例进行测试并与粒子群和遗传算法进行对比分析,结果表明设计的离散蝙蝠算法无论在求解质量还是求解效率上都有明显优势,是一种高效的优化算法。     

The double traveling salesman problem with multiple stacks: A variable neighborhood search approach

The double traveling salesman problem with multiple stacks (DTSPMS) is a vehicle routing problem that consists on finding the minimum total length tours in two separated networks, one for pickups and one for deliveries. A set of orders is given, each one consisting of a pickup location and a delivery location, and it is required to send an item from the former location to the latter one. Repacking is not allowed, but collected items can be packed in several rows in such a way that each row must obey the LIFO principle. In this paper, a variable neighborhood search approach using four new neighborhood structures is presented to solve the problem.     

A hybrid GRASP/VND heuristic for the one-commodity pickup-and-delivery traveling salesman problem

We address in this paper the one-commodity pickup-and-delivery traveling salesman problem, which is characterized by a set of customers, each of them supplying (pickup customer) or demanding (delivery customer) a given amount of a single product. The objective is to design a minimum cost Hamiltonian route for a capacitated vehicle in order to transport the product from the pickup to the delivery customers. The vehicle starts the route from a depot, and its initial load also has to be determined. We propose a hybrid algorithm that combines the GRASP and VND metaheuristics. Our heuristic is compared with other approximate algorithms described in Hernández-Pérez and Salazar-González [Heuristics for the one-commodity pickup-and-delivery traveling salesman problem. Transportation Science 2004;38:245–55]. Computational experiments on benchmark instances reveal that our hybrid method yields better results than the previously proposed approaches.     

A modified ant system to achieve better balance between intensification and diversification for the traveling salesman problem

This paper presents a new variant of Ant Colony Optimization (ACO) for the Traveling Salesman Problem (TSP). ACO has been successfully used in many combinatorial optimization problems. However, ACO has a problem in reaching the global optimal solutions for TSPs, and the algorithmic performance of ACO tends to deteriorate significantly as the problem size increases. In the proposed modification, adaptive tour construction and pheromone updating strategies are embedded into the conventional Ant System (AS), to achieve better balance between intensification and diversification in the search process. The performance of the proposed algorithm is tested on randomly generated data and well-known existing data. The computational results indicate the proposed modification is effective and efficient for the TSP and competitive with Ant Colony System (ACS), Max-Min Ant System (MMAS), and Artificial Bee Colony (ABC) Meta-Heuristic.     

Neurodynamic programming: a case study of the traveling salesman problem

The paper focuses on the study of solving the large-scale traveling salesman problem (TSP) based on neurodynamic programming. From this perspective, two methods, temporal difference learning and approximate Sarsa, are presented in detail. In essence, both of them try to learn an appropriate evaluation function on the basis of a finite amount of experience. To evaluate their performances, some computational experiments on both the Euclidean and asymmetric TSP instances are conducted. In contrast with the large size of the state space, only a few training sets have been used to obtain the initial results. Hence, the results are acceptable and encouraging in comparisons with some classical algorithms, and further study of this kind of methods, as well as applications in combinatorial optimization problems, is worth investigating.     

Metaheuristics for the traveling salesman problem with pickups, deliveries and handling costs

This paper studies the Traveling Salesman Problem with Pickups, Deliveries, and Handling Costs. The subproblem of minimizing the handling cost for a fixed route is analyzed in detail. It is solved by means of an exact dynamic programming algorithm with quadratic complexity and by an approximate linear time algorithm. Three metaheuristics integrating these solution methods are developed. These are based on tabu search, iterated local search and iterated tabu search. The three heuristics are tested and compared on instances adapted from the related literature. The results show that the combination of tabu search and exact dynamic programming performs the best, but using the approximate linear time algorithm considerably decreases the CPU time at the cost of slightly worse solutions.     

一种求解旅行商问题的离散状态转移算法

本文提出了一种求解旅行商问题的离散状态转移算法,设计了交换、平移、对称等3种转移算子,讨论了算法的收敛性和时间复杂度等问题,研究了参数对算法的影响.实验结果表明,与模拟退火算法及蚁群算法等经典组合优化算法相比,该算法具有耗时短、寻优能力强等优点,这也表明了状态转移算法的适应性很好.