Parallel ACO with a Ring Neighborhood for Dynamic TSP

The current paper introduces a new parallel computing technique based on ant colony optimization for a dynamic routing problem. In the dynamic traveling salesman problem the distances between cities as travel times are no longer fixed. The new technique uses a parallel model for a problem variant that allows a slight movement of nodes within their Neighborhoods. The algorithm is tested with success on several large data sets.Comment: 8 pages, 1 figure; accepted J. Information Technology Researc

Opportunistic Self Organizing Migrating Algorithm for Real-Time Dynamic Traveling Salesman Problem

Self Organizing Migrating Algorithm (SOMA) is a meta-heuristic algorithm based on the self-organizing behavior of individuals in a simulated social environment. SOMA performs iterative computations on a population of potential solutions in the given search space to obtain an optimal solution. In this paper, an Opportunistic Self Organizing Migrating Algorithm (OSOMA) has been proposed that introduces a novel strategy to generate perturbations effectively. This strategy allows the individual to span across more possible solutions and thus, is able to produce better solutions. A comprehensive analysis of OSOMA on multi-dimensional unconstrained benchmark test functions is performed. OSOMA is then applied to solve real-time Dynamic Traveling Salesman Problem (DTSP). The problem of real-time DTSP has been stipulated and simulated using real-time data from Google Maps with a varying cost-metric between any two cities. Although DTSP is a very common and intuitive model in the real world, its presence in literature is still very limited. OSOMA performs exceptionally well on the problems mentioned above. To substantiate this claim, the performance of OSOMA is compared with SOMA, Differential Evolution and Particle Swarm Optimization.Comment: 6 pages, published in CISS 201

An immune system based genetic algorithm using permutation-based dualism for dynamic traveling salesman problems

Copyright @ Springer-Verlag Berlin Heidelberg 2009.In recent years, optimization in dynamic environments has attracted a growing interest from the genetic algorithm community due to the importance and practicability in real world applications. This paper proposes a new genetic algorithm, based on the inspiration from biological immune systems, to address dynamic traveling salesman problems. Within the proposed algorithm, a permutation-based dualism is introduced in the course of clone process to promote the population diversity. In addition, a memory-based vaccination scheme is presented to further improve its tracking ability in dynamic environments. The experimental results show that the proposed diversification and memory enhancement methods can greatly improve the adaptability of genetic algorithms for dynamic traveling salesman problems.This work was supported by the Key Program of National Natural Science Foundation (NNSF) of China under Grant No. 70431003 and Grant No. 70671020, the Science Fund for Creative Research Group of NNSF of China under GrantNo. 60521003, the National Science and Technology Support Plan of China under Grant No. 2006BAH02A09 and the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant No. EP/E060722/1

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

ASAP: The After Salesman Problem

The customer contacts taking place after a sales transaction and the services involved are of increasing importance in contemporary business models. The responsiveness to service requests is a key dimension in service quality and therefore an important succes factor in this business domain. This responsiveness is of course highly dependent on the operational scheduling or dispatching decisions made in the often dynamic service settings. We consider the problem of optimizing responsiveness to service requests arriving in real time. We consider three models and formulations and present computational results on exact solution methods. The research is based on practical practical work done with the largest service organization in The Netherlands.operations research and management science;

Solving weighted and counting variants of connectivity problems parameterized by treewidth deterministically in single exponential time

It is well known that many local graph problems, like Vertex Cover and Dominating Set, can be solved in 2^{O(tw)}|V|^{O(1)} time for graphs G=(V,E) with a given tree decomposition of width tw. However, for nonlocal problems, like the fundamental class of connectivity problems, for a long time we did not know how to do this faster than tw^{O(tw)}|V|^{O(1)}. Recently, Cygan et al. (FOCS 2011) presented Monte Carlo algorithms for a wide range of connectivity problems running in time $c^{tw}|V|^{O(1)} for a small constant c, e.g., for Hamiltonian Cycle and Steiner tree. Naturally, this raises the question whether randomization is necessary to achieve this runtime; furthermore, it is desirable to also solve counting and weighted versions (the latter without incurring a pseudo-polynomial cost in terms of the weights). We present two new approaches rooted in linear algebra, based on matrix rank and determinants, which provide deterministic c^{tw}|V|^{O(1)} time algorithms, also for weighted and counting versions. For example, in this time we can solve the traveling salesman problem or count the number of Hamiltonian cycles. The rank-based ideas provide a rather general approach for speeding up even straightforward dynamic programming formulations by identifying "small" sets of representative partial solutions; we focus on the case of expressing connectivity via sets of partitions, but the essential ideas should have further applications. The determinant-based approach uses the matrix tree theorem for deriving closed formulas for counting versions of connectivity problems; we show how to evaluate those formulas via dynamic programming.Comment: 36 page