Fuzzy-logic controlled genetic algorithm for the rail-freight crew-scheduling problem

AbstractThis article presents a fuzzy-logic controlled genetic algorithm designed for the solution of the crew-scheduling problem in the rail-freight industry. This problem refers to the assignment of train drivers to a number of train trips in accordance with complex industrial and governmental regulations. In practice, it is a challenging task due to the massive quantity of train trips, large geographical span and significant number of restrictions. While genetic algorithms are capable of handling large data sets, they are prone to stalled evolution and premature convergence on a local optimum, thereby obstructing further search. In order to tackle these problems, the proposed genetic algorithm contains an embedded fuzzy-logic controller that adjusts the mutation and crossover probabilities in accordance with the genetic algorithm’s performance. The computational results demonstrate a 10% reduction in the cost of the schedule generated by this hybrid technique when compared with a genetic algorithm with fixed crossover and mutation rates

Verifying integer programming results

Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic errors, motivating the desire for a way to produce independently verifiable certificates of claimed results. Due to the complex nature of state-of-the-art MIP solution algorithms, the ideal form of such a certificate is not entirely clear. This paper proposes such a certificate format designed with simplicity in mind, which is composed of a list of statements that can be sequentially verified using a limited number of inference rules. We present a supplementary verification tool for compressing and checking these certificates independently of how they were created. We report computational results on a selection of MIP instances from the literature. To this end, we have extended the exact rational version of the MIP solver SCIP to produce such certificates

The number of matchings of low order in hexagonal systems

AbstractA simple way to calculate the number of k-matchings, k ⩽ 5, in hexagonal systems is presented. Some relations between the coefficients of the characteristic polynomial of the adjacency matrix of a hexagonal system and the number of matchings are obtained

Separation algorithms for 0-1 knapsack polytopes

Valid inequalities for 0-1 knapsack polytopes often prove useful when tackling hard 0-1 Linear Programming problems. To generate such inequalities, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We present new exact and heuristic separation algorithms for several classes of inequalities, namely lifted cover, extended cover, weight and lifted pack inequalities. Moreover, we show how to improve a recent separation algorithm for the 0-1 knapsack polytope itself. Extensive computational results, on MIPLIB and OR Library instances, show the strengths and limitations of the inequalities and algorithms considered

The Number Of Matchings Of Low Order In Hexagonal Systems

. A simple way to calculate the number of k-matchings, k 5, in hexagonal systems is presented. Some relations between the coefficients of the characteristic polynomial of the adjacency matrix of a hexagonal system and the number of matchings are obtained. 1. Introduction A hexagonal system is a 2-connected plane graph G such that every interior face of G is a regular hexagon. A k-matching (or a matching of order k) of a graph G is a set of k pairwise nonadjacent edges of G. A hexagonal system has only vertices of degree 2 or 3. Note also that each hexagonal system H is a bipartite graph. It is also easy to see that H does not contain cycles of lengths 4; 8. Let G be a hexagonal system. Throughout the paper, n will denote the number of vertices whereas m will stand for the number of edges of G. By A = fa ij g n i;j=1 we will denote the adjacency matrix of G, that is a ij = ae 0; ij = 2 E (G) 1; ij 2 E (G) : Since every hexagonal system is bipartite, coefficients of the characte..

Heuristics for automated knowledge source integration and service composition

The NP-hard component set identification problem is a combinatorial problem arising in the context of knowledge discovery, information integration, and knowledge source/service composition. Considering a granular knowledge domain consisting of a large number of individual bits and pieces of domain knowledge (properties) and a large number of knowledge sources and services that provide mappings between sets of properties, the objective of the component set identification problem is to select a minimum cost combination of knowledge sources that can provide a joint mapping from a given set of initially available properties (initial knowledge) to a set of initially unknown proper-ties (target knowledge). We provide a general framework for heuristics and consider construction heuristics that are followed by local improvement heuristics. Computational results are reported on randomly generated problem instances. (C) 2006 Published by Elsevier Ltd.X11914sciescopu