1,643 research outputs found

    An Optimal Control Theory for the Traveling Salesman Problem and Its Variants

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    We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space of measurable functions to the field of real numbers. Many variants of the TSP, such as those with neighborhoods, with forbidden neighborhoods, with time-windows and with profits, can all be framed under this construct. In sharp contrast to their discrete-optimization counterparts, the modeling constructs presented in this paper represent a fundamentally new domain of analysis and computation for TSPs and their variants. Beyond its apparent mathematical unification of a class of problems in graph theory, the main advantage of the new approach is that it facilitates the modeling of certain application-specific problems in their home space of measurable functions. Consequently, certain elements of economic system theory such as dynamical models and continuous-time cost/profit functionals can be directly incorporated in the new optimization problem formulation. Furthermore, subtour elimination constraints, prevalent in discrete optimization formulations, are naturally enforced through continuity requirements. The price for the new modeling framework is nonsmooth functionals. Although a number of theoretical issues remain open in the proposed mathematical framework, we demonstrate the computational viability of the new modeling constructs over a sample set of problems to illustrate the rapid production of end-to-end TSP solutions to extensively-constrained practical problems.Comment: 24 pages, 8 figure

    The multi-path Traveling Salesman Problem with stochastic travel costs

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    Given a set of nodes, where each pair of nodes is connected by several paths and each path shows a stochastic travel cost with unknown probability distribution, the multi-path Traveling Salesman Problem with stochastic travel costs aims at finding an expected minimum Hamiltonian tour connecting all nodes. Under a mild assumption on the unknown probability distribution, a deterministic approximation of the stochastic problem is given. The comparison of such approximation with a Monte Carlo simulation shows both the accuracy and the efficiency of the deterministic approximation, with a mean percentage gap around 2% and a reduction of the computational times of two orders of magnitude

    Dynamic vehicle routing problems: Three decades and counting

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    Since the late 70s, much research activity has taken place on the class of dynamic vehicle routing problems (DVRP), with the time period after year 2000 witnessing a real explosion in related papers. Our paper sheds more light into work in this area over more than 3 decades by developing a taxonomy of DVRP papers according to 11 criteria. These are (1) type of problem, (2) logistical context, (3) transportation mode, (4) objective function, (5) fleet size, (6) time constraints, (7) vehicle capacity constraints, (8) the ability to reject customers, (9) the nature of the dynamic element, (10) the nature of the stochasticity (if any), and (11) the solution method. We comment on technological vis-à-vis methodological advances for this class of problems and suggest directions for further research. The latter include alternative objective functions, vehicle speed as decision variable, more explicit linkages of methodology to technological advances and analysis of worst case or average case performance of heuristics.© 2015 Wiley Periodicals, Inc

    The Eco-Friendly Intermodal Delivery Network

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    The design of the distribution process is a strategic issue for almost every company. As the use of advanced technology and automation increases in manufacturing and logistics, the implementation of autonomous and electrical transportation, such as driverless vehicles and electric trucks, has become an interesting topic of study within the last few years, with the main objective of minimizing distribution costs and delivery times. The purpose of this research is to prove that intermodal delivery networks, which may combine a train and several electric vehicles, are more efficient and environmentally friendly than unimodal networks for high volume and long haul transportation, regardless of the customers’ distribution. This is only applicable if demand does not fall within the capacity restriction of road transportation vehicles. To do so, this paper utilizes an optimization algorithm that consists of a feedback mechanism between K-means and a genetic algorithm, which finds the optimal routes between distribution centers and surrounding customers as a multiple traveling salesman problem (mTSP)

    Vehicle routing and location routing with intermediate stops:A review

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    Optimizing production scheduling of steel plate hot rolling for economic load dispatch under time-of-use electricity pricing

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    Time-of-Use (TOU) electricity pricing provides an opportunity for industrial users to cut electricity costs. Although many methods for Economic Load Dispatch (ELD) under TOU pricing in continuous industrial processing have been proposed, there are still difficulties in batch-type processing since power load units are not directly adjustable and nonlinearly depend on production planning and scheduling. In this paper, for hot rolling, a typical batch-type and energy intensive process in steel industry, a production scheduling optimization model for ELD is proposed under TOU pricing, in which the objective is to minimize electricity costs while considering penalties caused by jumps between adjacent slabs. A NSGA-II based multi-objective production scheduling algorithm is developed to obtain Pareto-optimal solutions, and then TOPSIS based multi-criteria decision-making is performed to recommend an optimal solution to facilitate filed operation. Experimental results and analyses show that the proposed method cuts electricity costs in production, especially in case of allowance for penalty score increase in a certain range. Further analyses show that the proposed method has effect on peak load regulation of power grid.Comment: 13 pages, 6 figures, 4 table
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