Contributions to the solution of the symmetric travelling salesman problem

Imperial Users onl

Hyper‐Heuristics and Metaheuristics for Selected Bio‐Inspired Combinatorial Optimization Problems

Many decision and optimization problems arising in bioinformatics field are time demanding, and several algorithms are designed to solve these problems or to improve their current best solution approach. Modeling and implementing a new heuristic algorithm may be time‐consuming but has strong motivations: on the one hand, even a small improvement of the new solution may be worth the long time spent on the construction of a new method; on the other hand, there are problems for which good‐enough solutions are acceptable which could be achieved at a much lower computational cost. In the first case, specially designed heuristics or metaheuristics are needed, while the latter hyper‐heuristics can be proposed. The paper will describe both approaches in different domain problems

TSP and its variants : use of solvable cases in heuristics

This thesis proposes heuristics motivated by solvable cases for the travelling salesman problem (TSP) and the cumulative travelling salesman path problem (CTSPP). The solvable cases are investigated in three aspects: specially structured matrices, special neighbourhoods and small-size problems. This thesis demonstrates how to use solvable cases in heuristics for the TSP and the CTSPP and presents their promising performance in theoretical research and empirical research. Firstly, we prove that the three classical heuristics, nearest neighbour, double-ended nearest neighbour and GREEDY, have the theoretical property of obtaining the permutation for permuted strong anti-Robinson matrices for the TSP such that the renumbered matrices satisfy the anti-Robinson conditions. Inspired by specially structured matrices, we propose Kalmanson heuristics, which not only have the theoretical property of solving permuted strong Kalmanson matrices to optimality for the TSP, but also outperform their classical counterparts for general cases. Secondly, we propose three heuristics for the CTSPP. The pyramidal heuristic is motivated by the special pyramidal neighbourhood. The chains heuristic and the sliding window heuristic are motivated by solvable small-size problems. The experiments suggest the proposed heuristics outperform the classical GRASP-2-opt on general cases for the CTSPP. Thirdly, we conduct both theoretical and empirical research on specially structured cases for the CTSPP. Theoretically, we prove the solvability of Line- CTSPP on more general cases and the time complexity of the CTSPP on SUM matrices. We also conjecture that the CTSPP on two rays is NP-hard. Empirically, we propose three heuristics, which perform well on specially structured cases. The Line heuristic, based on Line-CTSPP, performs better than GRASP-2-opt when nodes are distributed on two close parallel lines. The Up-Down heuristic is inspired by the Up-Down structure in solvable Path TSP and outperforms GRASP-2-opt in convex-hull cases and close-to-convex-hull cases. The Two-Ray heuristic combines the path structures in the first two heuristics and obtains high-quality solutions when nodes are along two rays

The Plant Propagation Algorithm for Discrete Optimisation

The thesis is concerned with novel Nature-Inspired heuristics for the so called NP-hard problems of optimisation. A particular algorithm which has been recently introduced and shown to be effective in continuous optimisation is the Plant Propagation Algorithm or PPA. Here, we intend to extend it to cope with combinatorial optimisation. In order to show that our extension is viable and effective, we consider three types of problems which are good representatives of the whole topic. These are the Travelling Salesman Problem or TSP, the Knapsack Problem or KP and the scheduling problem of Berth Allocation as arises in container ports or BAP. Because PPA is a population-based search heuristic, we devote a chapter to the important issue of generating good and yet computationally relatively light initial populations of solutions to kick start the search process. In the case of the TSP we revisit and extend the Strip Algorithm (SA). We introduce the 2-Part SA and show that it is better than the classical SA. We also introduce new variants such as the Adaptive SA and the Spiral SA which cope with clustered cities and instances with cities concentrated around the center of the unit square, respectively. In the case of KP we adapt the Roulette Wheel selection approach to generate solutions to start with PPA. And in the case of BAP, we introduce a number of simple heuristics which consider a schedule as a flat box with one side being the processing time and the other the position of vessels on the wharf. The heuristics try to generate schedules by avoiding overlap as much as possible. All approaches and algorithms are implemented and tested against well established algorithms. The results are recorded and discussed extensively. The thesis ends with a conclusion and ideas for further research

Traveling Salesman Problem

This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering

Twin-constrained Hamiltonian paths on threshold graphs: an approach to the minimum score separation problem

The Minimum Score Separation Problem (MSSP) is a combinatorial problem that has been introduced in JORS 55 as an open problem in the paper industry arising in conjunction with the cutting-stock problem. During the process of producing boxes, áat papers are prepared for folding by being scored with knives. The problem is to determine if and how a given production pattern of boxes can be arranged such that a certain minimum distance between the knives can be kept. While it was originally suggested to analyse the MSSP as a specific variant of a Generalized Travelling Salesman Problem, the thesis introduces the concept of twin-constrained Hamiltonian cycles and models the MSSP as the problem of finding a twin-constrained Hamiltonian path on a threshold graph (threshold graphs are a specific type of interval graphs). For a given undirected graph G(N,E) with an even node set N and edge set E, and a bijective function b on N that assigns to every node i in N a "twin node" b(i)6=i, we define a new graph G'(N,E') by adding the edges {i,b(i)} to E. The graph G is said to have a twin-constrained Hamiltonian path with respect to b if there exists a Hamiltonian path on G' in which every node has its twin node as its predecessor (or successor). We start with presenting some general Öndings for the construction of matchings, alternating paths, Hamiltonian paths and alternating cycles on threshold graphs. On this basis it is possible to develop criteria that allow for the construction of twin-constrained Hamiltonian paths on threshold graphs and lead to a heuristic that can quickly solve a large percentage of instances of the MSSP. The insights gained in this way can be generalized and lead to an (exact) polynomial time algorithm for the MSSP. Computational experiments for both the heuristic and the polynomial-time algorithm demonstrate the efficiency of our approach to the MSSP. Finally, possible extensions of the approach are presented

A vision-based optical character recognition system for real-time identification of tractors in a port container terminal

Automation has been seen as a promising solution to increase the productivity of modern sea port container terminals. The potential of increase in throughput, work efficiency and reduction of labor cost have lured stick holders to strive for the introduction of automation in the overall terminal operation. A specific container handling process that is readily amenable to automation is the deployment and control of gantry cranes in the container yard of a container terminal where typical operations of truck identification, loading and unloading containers, and job management are primarily performed manually in a typical terminal. To facilitate the overall automation of the gantry crane operation, we devised an approach for the real-time identification of tractors through the recognition of the corresponding number plates that are located on top of the tractor cabin. With this crucial piece of information, remote or automated yard operations can then be performed. A machine vision-based system is introduced whereby these number plates are read and identified in real-time while the tractors are operating in the terminal. In this paper, we present the design and implementation of the system and highlight the major difficulties encountered including the recognition of character information printed on the number plates due to poor image integrity. Working solutions are proposed to address these problems which are incorporated in the overall identification system.postprin