20,093 research outputs found
A 2.75-Approximation Algorithm for the Unconstrained Traveling Tournament Problem
A 2.75-approximation algorithm is proposed for the unconstrained traveling
tournament problem, which is a variant of the traveling tournament problem. For
the unconstrained traveling tournament problem, this is the first proposal of
an approximation algorithm with a constant approximation ratio. In addition,
the proposed algorithm yields a solution that meets both the no-repeater and
mirrored constraints. Computational experiments show that the algorithm
generates solutions of good quality.Comment: 12 pages, 1 figur
Fitness Uniform Optimization
In evolutionary algorithms, the fitness of a population increases with time
by mutating and recombining individuals and by a biased selection of more fit
individuals. The right selection pressure is critical in ensuring sufficient
optimization progress on the one hand and in preserving genetic diversity to be
able to escape from local optima on the other hand. Motivated by a universal
similarity relation on the individuals, we propose a new selection scheme,
which is uniform in the fitness values. It generates selection pressure toward
sparsely populated fitness regions, not necessarily toward higher fitness, as
is the case for all other selection schemes. We show analytically on a simple
example that the new selection scheme can be much more effective than standard
selection schemes. We also propose a new deletion scheme which achieves a
similar result via deletion and show how such a scheme preserves genetic
diversity more effectively than standard approaches. We compare the performance
of the new schemes to tournament selection and random deletion on an artificial
deceptive problem and a range of NP-hard problems: traveling salesman, set
covering and satisfiability.Comment: 25 double-column pages, 12 figure
Reachability cuts for the vehicle routing problem with time windows
This paper introduces a class of cuts, called reachability cuts, for the Vehicle Routing Problem with Time Windows (VRPTW). Reachability cuts are closely related to cuts derived from precedence constraints in the Asymmetric Traveling Salesman Problem with Time Windows and to k-path cuts for the VRPTW. In particular, any reachability cut dominates one or more k-path cuts. The paper presents separation procedures for reachability cuts and reports computational experiments on well-known VRPTW instances. The computational results suggest that reachability cuts can be highly useful as cutting planes for certain VRPTW instances.Routing; time windows; precedence constraints
The linearization problem of a binary quadratic problem and its applications
We provide several applications of the linearization problem of a binary
quadratic problem. We propose a new lower bounding strategy, called the
linearization-based scheme, that is based on a simple certificate for a
quadratic function to be non-negative on the feasible set. Each
linearization-based bound requires a set of linearizable matrices as an input.
We prove that the Generalized Gilmore-Lawler bounding scheme for binary
quadratic problems provides linearization-based bounds. Moreover, we show that
the bound obtained from the first level reformulation linearization technique
is also a type of linearization-based bound, which enables us to provide a
comparison among mentioned bounds. However, the strongest linearization-based
bound is the one that uses the full characterization of the set of linearizable
matrices. Finally, we present a polynomial-time algorithm for the linearization
problem of the quadratic shortest path problem on directed acyclic graphs. Our
algorithm gives a complete characterization of the set of linearizable matrices
for the quadratic shortest path problem
Referee assignment in the Chilean football league using integer programming and patterns
This article uses integer linear programming to address the referee assignment problem in the First Division of the Chilean professional football league. The proposed approach considers balance in the number of matches each referee must officiate, the frequency of each referee being assigned to a given team, the distance each referee must travel over the course of a season, and the appropriate pairings of referee experience or skill category with the importance of the matches. Two methodologies are studied, one traditional and the other a pattern-based formulation inspired by the home-away patterns for scheduling season match calendars. Both methodologies are tested in real-world and experimental instances, reporting results that improve significantly on the manual assignments. The pattern-based formulation attains major reductions in execution times, solving real instances to optimality in just a few seconds, while the traditional one takes anywhere from several minutes to more than an hour.Fil: Alarcón, Fernando. Universidad de Chile; ChileFil: Duran, Guillermo Alfredo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Guajardo, Mario. Norwegian School of Economics; Norueg
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