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Abstract. The Traveling Salesman Problem with a Drone (Tbr-lJ) is a hybrid truck and drone model of delivery, in which the drone rides on the truck and launches from the [...]

Abstract. The consistent traveling salesman problem aims to identify minimum-cost routes to be followed by a single vehicle so as to provide a set of customers with service that adheres [...]

Abstract. Carrier-vehicle systems generally consist of a slow carrier (e.g., a ship) with a long operational range and a faster vehicle (e.g., an aircraft) with a limited operational range. The [...]

This paper addresses the close-enough traveling salesman problem. In this problem, rather than visiting the vertex (customer) itself, the salesman must visit a specific region containing such vertex. To solve [...]

In the Hamiltonian p-median problem (HpMP), the target is to find p cycles that partition a given undirected graph with the objective of minimizing the total sum of the costs [...]

The capacitated vehicle routing problem (CVRP) involves distributing identical items from a depot to a set of demand locations using a single capacitated vehicle. We introduce the heterogeneous capacitated vehicle [...]

In this paper, we study the classical no-wait flowshop scheduling problem with makespan objective (F|no-wait| [C.sub.max in the standard three-field notation). This problem is well known to be a special [...]

The Canadian traveler problem (CTP) is a simple, yet challenging, stochastic optimization problem wherein an agent is given a graph where some edges are blocked with certain probabilities and the [...]

We address a variant of the Euclidean traveling salesman problem known as the close-enough traveling salesman problem (CETSP), where the traveler visits a node if it enters a compact neighborhood [...]

The double traveling salesman problem with multiple stacks is a variant of the pickup and delivery traveling salesman problem in which all pickups must be completed before any delivery. In [...]

The traveling salesman problem with time windows (TSPTW) is the problemof finding in a weighted digraph a least-cost tour starting from a selected vertex, visiting each vertex of the graph [...]

The traveling salesman problem with time windows (TSPTW) is the problem of finding a minimum-cost path visiting a set of cities exactly once, where each city must be visited within [...]

This research presents an attempt to solve a logistic company's problem of delivering petrol to petrol station in the state of Johor. This delivery system is formulated as a travelling salesman problem (TSP). TSP involves finding an optimal route for visiting stations and returning to point of origin, where the inter-station distance is symmetric and known. This real world application is a deceptive simple combinatorial problem and our approach is to develop solutions based on the idea of local search and meta-heuristics. As a standard problem, we have chosen a solution is a deceptively simple combinatorial problem and we defined it simply as the time spends or distance travelled by salesman visiting n cities (or nodes) cyclically. In one tour the vehicle visits each station just once and finishes up where he started. As standard problems, we have chosen TSP with different stations visited once. This research presents the development of solution engine based on local search method known as Greedy Method and with the result generated as the initial solution, Simulated Annealing (SA) and Tabu Search (TS) further used to improve the search and provide the best solution. A user friendly optimization program developed using Microsoft C++ to solve the TSP and provides solutions to future TSP which may be classified into daily or advanced management and engineering problems. Key words: Heuristic method, tabu search, simulated annealing, travelling salesman problem and greedy search, INTRODUCTION The present society are built on infrastructure of information technology (IT) comprised of computers and systems of communication. Nowadays, societies worldwide are fed with terms such information society is [...]

We consider a problem in which we are given a domain, a cost function which depends on position at each point in the domain, and a subset of points ('cities') in the domain. The goal is to determine the cheapest closed path that visits each city in the domain once. This can be thought of as a version of the traveling salesman problem, in which an underlying known metric determines the cost of moving through each point of the domain, but in which the actual shortest path between cities is unknown at the outset. We describe algorithms for both a heuristic and an optimal solution to this problem. The complexity of the heuristic algorithm is at worst case M.N log N, where M is the number of cities, and N the size of the computational mesh used to approximate the solutions to the shortest paths problems. The average runtime of the heuristic algorithm is linear in the number of cities and O(N log N) in the size N of the mesh. Eikonal equation | geodesics

A method for tackling the traveling salesman problem, using 2-p-opt and 1-shift algorithm, is presented.

In this paper, we introduce the concept of fine-tuned learning which relies on the notion of data approximation followed by sequential data refinement. We seek to determine whether fine-tuned learning is a viable approach to use when trying to solve combinatorial optimization problems. In particular, we conduct an extensive computational experiment to study the performance of fine-tuned-learning-based heuristics for the traveling salesman problem (TSP). We provide important insight that reveals how fine-tuned learning works and why it works well, and conclude that it is a meritorious concept that deserves serious consideration by researchers solving difficult problems.

A tabu search method based on ejection chain procedures is used to solve the cardinality-constrained Traveling Salesman Problem (TSP), a special TSP problem that determines a node simple path that maximizes the sum of weights of nodes passed by, subject to lower and upper bounds on the inclusive nodes. Short term tabu search is found to improve the power of the ejection chain, while random restarting should be used conditionally rather than unconditionally to obtain optimal results. The method has also been used to seek a profitable column in a column generation procedure for solving fractional covering problems. Computational experiments confirm the importance of advanced ejection chain rules for deriving robust solutions to complicated problems.

Efficient interprocessor duplicate pruning methods were developed. The methods were applied in parallel A* algorithms to obtain high speedup over sequential A* graph search. It was found that for graphical search spaces, duplicate pruning is essential for a good performance. A graph formulation of the search space was superior to a tree formulation since the formulation enables the detection and pruning of duplicates.

Choice constraints and exclusion constraints were used to characterize and solve, via integer programming, NP-hard finite constraint satisfaction problems. The solution approach is illustrated through its applications to the n-size conjunctive normal form satisfaction problem, propositional satisfiability (SAT) problem, the quadratic assignment problem, the traveling salesman problem, and the minimal set covering problem.

A new stochastic and dynamic routing model, the generation policy, for solving the Dynamic Traveling Repairman Problem in Euclidean service space is introduced. The new policy, which was evaluated in both low and heavy traffic conditions 'using results from branching processes with state dependent immigration,' is optimal because it generates a new routing schedule immediately after a generation of demands is serviced on a first-come first-serve basis.

Genetic algorithms (GA) have features that can effectively provide good quality scheduling solutions for the service level based vehicle scheduling problem. These include ease of implementation through efficient coding of solution alternatives, simultaneous emphasis on global and local search and the use of randomization in the search process. A GA is usually associated with interactive methods by replicating the positive attributes of existing solutions in the search process.

This paper presents a robust tabu search approach to the traveling-salesman problem with time windows. The approach uses a two-level tour hashing scheme within a reactive tabu search procedure to detect unique repeated solutions and to promote a more diverse search. Strong feasibility conditions restrict the neighborhood of candidate solutions. The search returns optimal, or near-optimal, solutions within a fraction of the time required by optimal methods. The algorithm's search neighborhood is not restricted to feasible solutions, and superior marginally infeasible solutions are reported to enhance the decision making process. The paper presents computational results for 145 problems from the literature., 1. Introduction This paper presents a tabu search approach to solving the traveling-salesman problem with time windows (TSPTW) as defined by Baker (1983) Dumas et al. (1993) and Desrosiers et [...]

The performance of two local search methods for combinatorial optimization problems are investigated. Specifically, the first-improving and best-improving pivot rules for choosing a neighboring point with an improved objective function are evaluated within the context of a random model and a structured model, respectively. Numerical experiments with the travelling salesman problem and the quadratic assignment problem using a variant of the two pivot rules are also carried out.

The vehicle routing problem (VRP) continues to be a topic of interest among operational researchers. The problem, which involves minimizing the total costs for the route assignments of vehicles going to and coming back from a depot, is usually solved using a chance constrained program or a stochastic program with recourse. At present, variants of the VRP include the traveling salesman problem with stochastic customers and stochastic travel times, respectively, as well as the VRP problem with stochastic demands and customers, respectively.

Probabilistic combinatorial optimization (PCO) problems refer to the class of optimization problems with random data due to uncertainty or unreliable predictions. At present, it is a new field of study in operations research and as such, many methodological and conceptual problems still exist. One examples include the definition of functionals for minimization PCOs. This is evident in the analysis of PCOs defined on graphs such as the traveling salesman problem, minimum spanning tree problem and vehicle routing problem.

The problem of planning the daily delivery of gas cylinders within Hungary was solved and a Borland C++ implementation of the solution developed for Primagaz-Hungaria. It pertains to the minimum-cost scheduling and routing of trucks as well as assignment of capacities to filling stations. The solution recasts the problem as a linear integer optimization problem which may be further decomposed into a linear optimization and a travelling-salesman problem.

A parallel simulated annealing algorithm based on E.E. Witte, R.D. Chamberlain and M.A. Franklin's speculative computation approach is introduced. Unlike the original procedure, however, it has minimal communications traffic due to its problem independence. Its applicability and efficiency is illustrated in two examples, namely, the traveling salesman problem and a task scheduling problem.

The simulated annealing algorithm is extended into a heuristic procedure for solving 0-1 optimization problems. The method, which has a higher convergence speed, approximates the anticipated variable values for given temperatures to enable the problem size to be compressed in proportion with the temperature. Its use in solving the traveling salesman and the minimization of an unconstrained 0-1 quadratic function is discussed.

The concept of local search, a heuristic for solving combinatorial optimization problems, is developed. To this end, a new technique, known as sacrificing, is introduced to enhance the conventional local improvement algorithm without compromising its running time. This improvement can be seen in the derived solutions for the Dial-A-Ride problem, another version of the Traveling Salesman problem.

Several formulations of the time-dependent traveling salesman problem are investigated with respect to older versions of the classical problem. The formulations include one based on a linearized quadratic assignment model and 3-index formulations based on the work of J.C. Picard, M. Queyranne, K.R. Fox, B. Gavish and S. Graves. The problem, which has many real-world applications, pertains to situations where arc costs are 'dependent on their position in the tour.'

Several algorithms for the rapid solving of fractional packing and covering problems are introduced. The algorithms, which use the Lagrangian relaxation technique, are based on an extension to a method for deriving approximate solutions for multicommodity flow problems. They may be applied to job shop scheduling, the Held-Karp bound for the traveling salesman problem, network embedding problems and the minimum-cost multicommodity flow problem.

The traveling salesman problem with pick-up and delivery is considered. The routing problem pertains to the minimization of a single vehicle's route for doing pick-ups and deliveries such that its tour begins and ends at a specified location. To facilitate a heuristic solution, it is compared to the traveling salesman problem. Another heuristic, known as the 'cheapest insertion,' is likewise employed to derive a second solution procedure.

Two bicriterion touring problems, the median tour problem (MTP) and the maximal covering tour problem (MCTP), are proposed to minimize total tour length and maximize access to the tour for the nodes not directly on it. The access objective in the MTP is to minimize total travel distance necessary for demand at the nodes to reach their nearest stop on the tour, while that in the MCTP is to maximize the total demand within a pre-determined maximal travel distance from a tour stop. Solution methods formulated for the MTP may also be used to solve the MCTP.

How can a knight be moved on a chessboard so that the knight visits each square once and only once and goes back to the starting square? The earliest serious attempt to find a knight's tour on the chessboard was made by L. Euler in 1759. In this correspondence, a parallel algorithm based on the hysteresis McCulloch-Pitts neurons is proposed to solve the knight's tour problem. The relation between the traveling salesman problem and the knight's tour problem is also discussed. A large number of simulation runs were performed to investigate the behavior of the hysteresis McCulloch-Pitts neural model. The purpose of this correspondence is to present a case study - how to successfully represent the combinatorial optimization problems by means of neural network.

A demonstration of the relationship between the subtour elimination algorithm of Gilmore and Gomory for the large travelling salesman problem (TSP) and Gabovich's algorithm for the small TSP is presented with mathematical calculations. The problem is applied to machine scheduling theory as an example. The recognition problem for these two types of matrices is solved by using Deineko and Filonenko's algorithm for recognizing permuted distribution matrices.

The integrability conditions devised by Beardwood et al for unbounded support in the Euclidean traveling salesperson problem are shown to be insufficient. Instead, a strongercondition is formulated. This result is optimal but not necessary, thus indicating the need for a more appropriate condition. This study also observed the problem's asymptotic behavior to fully understand the possibility of extending length of the shortest tour to distributions with unbounded support.

A study is conducted to examine the maximum benefit Chinese postman problem (MBCPP) and the maximum benefit traveling salesman problem (MBTSP). The study considers benefits for the MBCPP for each traversal of a directed graph link while a benefit is considered for MBSTP when a node is visited and link traversal yields costs. Results show that a solution algorithm based on a branch and bound procedure exhibits repetitive solutions for the studied problems.

Probabilistic combinatorial optimization problems, which are known to explicitly include probabilistic elements in their definitions, are given a rigorous treatment. The focus is on the general finite-sized bounds and limit theorems of the traveling salesman and minimum spanning tree problems, both probabilistic. Moreover, the asymptotic results from this study can be generalized if the points are independently and uniformly distributed over (0,t)squared. However, only some issues regarding the two problems' individual convergences and extensions are finalized.

A traveling salesman problem with a symmetric matrix and entries of either one or two is studied. Subtour patching is used to devise for this problem a polynomial-time approximation algorithm with a worst-case ratio of 7/6 and accuracy better than 3/2. Moreover, a separate algorithm with a worst-case ratio of 11/9 is combined with a third algorithm that obtains the optimum triangle-free two-matching of a graph to result in a bound of 7/6. However, this special traveling salesman case is MAX SNP-hard, thus making it possible to have no polynomial-time approximation scheme.