Perfect Edge-Transmitting Recombination of Permutations

Crossover is the process of recombining the genetic features of two parents. For many applications where crossover is applied to permutations, relevant genetic features are pairs of adjacent elements, also called edges in the permutation order. Recombination of edges without errors is thought to be an NP-hard problem, typically approximated by heuristics that either introduce new edges or are only able to produce a small variety of offspring. Here, we derive an algorithm for crossover of permutations that achieves perfect transmission of edges and produces a uniform sampling of all possible offspring, in quadratic average computation time. The algorithm and its derivation reveal a link between cycle crossover (CX) and edge assembly crossover (EAX), offering a new perspective on these well-established algorithms. We also describe a modification of the algorithm that generates the mathematically optimal offspring for the asymmetric travelling salesman problem

Developing Programming Tools to Handle Traveling Salesman Problem by the Three Object-Oriented Languages

The traveling salesman problem (TSP) is one of the most famous problems. Many applications and programming tools have been developed to handle TSP. However, it seems to be essential to provide easy programming tools according to state-of-theart algorithms. Therefore, we have collected and programmed new easy tools by the three object-oriented languages. In this paper, we present ADT (abstract data type) of developed tools at first; then we analyze their performance by experiments. We also design a hybrid genetic algorithm (HGA) by developed tools. Experimental results show that the proposed HGA is comparable with the recent state-of-the-art applications

An investigation of models for identifying critical components in a system.

Lai, Tsz Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (leaves 193-207).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Overview --- p.1Chapter 1.2 --- Contributions --- p.2Chapter 1.3 --- Organization --- p.2Chapter 2 --- Literature Review --- p.4Chapter 2.1 --- Taxonomy --- p.4Chapter 2.2 --- Design of Infrastructure --- p.6Chapter 2.2.1 --- Facility Location Models --- p.7Chapter 2.2.1.1 --- Random Breakdowns --- p.7Chapter 2.2.1.2 --- Deliberate Attacks --- p.8Chapter 2.2.2 --- Network Design Models --- p.9Chapter 2.3 --- Protection of Existing Components --- p.10Chapter 2.3.1 --- Interdiction Models --- p.11Chapter 2.3.2 --- Facility Location Models --- p.12Chapter 2.3.2.1 --- Random Breakdowns --- p.12Chapter 2.3.2.2 --- Deliberate Attacks --- p.12Chapter 2.3.3 --- Network Design Models --- p.14Chapter 3 --- Identifying Critical Facilities: Median Problem --- p.16Chapter 3.1 --- Introduction --- p.16Chapter 3.2 --- Problem Formulation --- p.18Chapter 3.2.1 --- The p-Median Problem --- p.18Chapter 3.2.1.1 --- A Toy Example --- p.19Chapter 3.2.1.2 --- Problem Definition --- p.21Chapter 3.2.1.3 --- Mathematical Model --- p.22Chapter 3.2.2 --- The r-Interdiction Median Problem --- p.24Chapter 3.2.2.1 --- The Toy Example --- p.24Chapter 3.2.2.2 --- Problem Definition --- p.27Chapter 3.2.2.3 --- Mathematical Model --- p.28Chapter 3.2.3 --- The r-Interdiction Median Problem with Fortification --- p.29Chapter 3.2.3.1 --- The Toy Example --- p.30Chapter 3.2.3.2 --- Problem Definition --- p.32Chapter 3.2.3.3 --- Mathematical Model --- p.33Chapter 3.2.4 --- The r-Interdiction Median Problem with Fortification (Bilevel Formulation) --- p.35Chapter 3.2.4.1 --- Mathematical Model --- p.36Chapter 3.3 --- Solution Methodologies --- p.38Chapter 3.3.1 --- Model Reduction --- p.38Chapter 3.3.2 --- Variable Consolidation --- p.40Chapter 3.3.3 --- Implicit Enumeration --- p.45Chapter 3.4 --- Results and Discussion --- p.48Chapter 3.4.1 --- Data Sets --- p.48Chapter 3.4.1.1 --- Swain --- p.48Chapter 3.4.1.2 --- London --- p.49Chapter 3.4.1.3 --- Alberta --- p.49Chapter 3.4.2 --- Computational Study --- p.50Chapter 3.4.2.1 --- The p-Median Problem --- p.50Chapter 3.4.2.2 --- The r-Interdiction Median Problem --- p.58Chapter 3.4.2.3 --- The r-Interdiction Median Problem with Fortification --- p.63Chapter 3.4.2.4 --- The r-Interdiction Median Problem with Fortification (Bilevel Formulation) --- p.68Chapter 3.5 --- Summary --- p.76Chapter 4 --- Hybrid Approaches --- p.79Chapter 4.1 --- Framework --- p.80Chapter 4.2 --- Tabu Assisted Heuristic Search --- p.81Chapter 4.2.1 --- A Tabu Assisted Heuristic Search Construct --- p.83Chapter 4.2.1.1 --- Search Space --- p.84Chapter 4.2.1.2 --- Initial Trial Solution --- p.85Chapter 4.2.1.3 --- Neighborhood Structure --- p.85Chapter 4.2.1.4 --- Local Search Procedure --- p.86Chapter 4.2.1.5 --- Form of Tabu Moves --- p.88Chapter 4.2.1.6 --- Addition of a Tabu Move --- p.88Chapter 4.2.1.7 --- Maximum Size of Tabu List --- p.89Chapter 4.2.1.8 --- Termination Criterion --- p.89Chapter 4.3 --- Hybrid Simulated Annealing Search --- p.90Chapter 4.3.1 --- A Hybrid Simulated Annealing Construct --- p.91Chapter 4.3.1.1 --- Random Selection of Immediate Neighbor --- p.92Chapter 4.3.1.2 --- Cooling Schedule --- p.93Chapter 4.3.1.3 --- Termination Criterion --- p.94Chapter 4.4 --- Hybrid Genetic Search Algorithm --- p.95Chapter 4.4.1 --- A Hybrid Genetic Search Construct --- p.99Chapter 4.4.1.1 --- Search Space --- p.99Chapter 4.4.1.2 --- Initial Population --- p.100Chapter 4.4.1.3 --- Selection --- p.104Chapter 4.4.1.4 --- Crossover --- p.105Chapter 4.4.1.5 --- Mutation --- p.106Chapter 4.4.1.6 --- New Population --- p.108Chapter 4.4.1.7 --- Termination Criterion --- p.109Chapter 4.5 --- Further Assessment --- p.109Chapter 4.6 --- Computational Study --- p.114Chapter 4.6.1 --- Parameter Selection --- p.115Chapter 4.6.1.1 --- Tabu Assisted Heuristic Search --- p.115Chapter 4.6.1.2 --- Hybrid Simulated Annealing Approach --- p.121Chapter 4.6.1.3 --- Hybrid Genetic Search Algorithm --- p.124Chapter 4.6.2 --- Expected Performance --- p.128Chapter 4.6.2.1 --- Tabu Assisted Heuristic Search --- p.128Chapter 4.6.2.2 --- Hybrid Simulated Annealing Approach --- p.138Chapter 4.6.2.3 --- Hybrid Genetic Search Algorithm --- p.146Chapter 4.6.2.4 --- Overall Comparison --- p.150Chapter 4.7 --- Summary --- p.153Chapter 5 --- A Special Case of the Median Problems --- p.156Chapter 5.1 --- Introduction --- p.157Chapter 5.2 --- Problem Formulation --- p.158Chapter 5.2.1 --- The r-Interdiction Covering Problem --- p.158Chapter 5.2.1.1 --- Problem Definition --- p.159Chapter 5.2.1.2 --- Mathematical Model --- p.160Chapter 5.2.2 --- The r-Interdiction Covering Problem with Fortification --- p.162Chapter 5.2.2.1 --- Problem Definition --- p.163Chapter 5.2.2.2 --- Mathematical Model --- p.164Chapter 5.2.3 --- The r-Interdiction Covering Problem with Fortification (Bilevel Formulation) --- p.167Chapter 5.2.3.1 --- Mathematical Model --- p.168Chapter 5.3 --- Theoretical Relationship --- p.170Chapter 5.4 --- Solution Methodologies --- p.172Chapter 5.5 --- Results and Discussion --- p.175Chapter 5.5.1 --- The r-Interdiction Covering Problem --- p.175Chapter 5.5.2 --- The r-Interdiction Covering Problem with Fortification --- p.178Chapter 5.5.3 --- The r-Interdiction Covering Problem with Fortification (Bilevel Formulation) --- p.182Chapter 5.6 --- Summary --- p.187Chapter 6 --- Conclusion --- p.189Chapter 6.1 --- Summary of Our Work --- p.189Chapter 6.2 --- Future Directions --- p.19