1,643 research outputs found
An Optimal Control Theory for the Traveling Salesman Problem and Its Variants
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
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
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
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)
Optimizing production scheduling of steel plate hot rolling for economic load dispatch under time-of-use electricity pricing
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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