Solving the robust shortest path problem with interval data using a probabilistic metaheuristic approach

This paper addresses the robust shortest path problem with interval data, i.e. the case of classical shortest path problem with given source and sink when arc weights are not fixed but take their values from some intervals associated with arcs. The problem consists in finding a shortest path that minimizes so called robust deviation, i.e. deviation from an optimal solution under the worst case realization of interval weights. As it was proven in [9], the problem is NP-hard, therefore it is of great interest to tackle it with some metaheuristic approach, namely simulated annealing, in order to calculate an approximate solution for the large scale instances efficiently. We describe theoretical aspects and present the results of computational experiments. To the best of our knowledge, this is the first attempt to develop metaheuristic approach for solving the robust shortest path problem

Simulated annealing algorithm for the robust spanning tree problem

This paper addresses the robust spanning tree problem with interval data, i.e. the case of classical minimum spanning tree problem when edge weights are not fixed but take their values from some intervals associated with edges. The problem consists in finding a spanning tree that minimizes so-called robust deviation, i.e. deviation from an optimal solution under the worst case realization of interval weights. As it was proven in [8], the problem is NP-hard, therefore it is of great interest to tackle it with some metaheuristic approach, namely simulated annealing, in order to calculate an approximate solution for large scale instances efficiently. We describe theoretical aspects and present the results of computational experiments. To the best of our knowledge, this is the first attempt to develop a metaheuristic approach for solving the robust spanning tree problem

Robustness in combinatorial optimization and scheduling theory: An extended annotated bibliography

This work is an up-to-date-extension of a previous annotated bibliography (2004) which covered 40 references only. It focuses on what has been published during the last ten years in the area of combinatorial optimization and scheduling theory concerning robustness and other similar techniques dealing with worst case optimization under uncertainty and non-accuracy of problem data

Robustness in combinatorial optimization and scheduling theory: An annotated bibliography

This short annotated bibliography focuses on what has been published during the last ten years in the area of combinatorial optimization and scheduling theory concerning robustness and other similar techniques that deal with worst case optimization under uncertainty and non-accuracy of problem data

Fuzzy multicriteria flight gate assignment

This paper addresses the multiple criteria flight gate assignment problem under uncertainty, which is naturally modeled by fuzzy numbers. The problem examined is a special kind of multicriteria multi-mode resource-constrained project scheduling problem with generalized precedence constraints or time windows. Fuzziness is introduced for basic problem parameters, that is, arrival and departure times, in order to cover possible earliness and tardiness of flights. We solve the problem directly by a special multicriteria metaheuristic, known as fuzzy Pareto simulated annealing, in order to get a representative approximation of the Pareto front

Flight gate scheduling: State-of-the-art and recent developments

This paper surveys a large variety of mathematical models and up-to-date solution techniques developed for solving a general flight gate scheduling problem that deals with assigning different aircraft activities (arrival, departure and intermediate parking) to distinct aircraft stands or gates. The aim of the work is both to present various models and solution techniques which are available in nowadays literature and to give a general idea about new open problems that arise in practise. We restrict the scope of the paper to flight gate management without touching scheduling of ground handling operations.

Strong stability measures for multicriteria quadratic integer programming problem of finding extremum solutions

We consider a wide class of quadratic optimization problems with integer and Boolean variables. In this paper, the lower and upper bounds on the strong stability radius of the set of extremum solutions are obtained in the situation where solution space and criterion space are endowed with various Hölder's norms. </p

Stability kernel in finite games with perturbed payoffs

The parametric concept of equilibrium in a finite cooperative game of several players in a normal form is introduced. This concept is defined by the partitioning of a set of players into coalitions. Two extreme cases of such partitioning correspond to Pareto optimal and Nash equilibrium outcomes, respectively. The game is characterized by its matrix, in which each element is a subject for independent perturbations., ie a set of perturbing matrices is formed by a set of additive matrices, with two arbitrary Hölder norms specified independently in the outcome and criterion spaces. We undertake post-optimal analysis for the so-called stability kernel. The analytical expression for supreme levels of such perturbations is found. Numerical examples illustrate some of the pertinent cases.</p

On one type of stability for multiobjective integer linear programming problem with parameterized optimality

A multiobjective problem of integer linear programming with parametric optimality is addressed. The parameterization is introduced by dividing a set of objectives into a family of disjoint subsets, within each Pareto optimality is used to establish dominance between alternatives. The introduction of this principle allows us to connect such classical optimality sets as extreme and Pareto. The admissible perturbation in such problem is formed by a set of additive matrices, with arbitrary H\"{o}lder's norms specified in the solution and criterion spaces. The lower and upper bounds for the radius of strong stability are obtained with some important corollaries concerning previously known results.</p