13h30 - 13h55
A New Generation Approach for Multiobjective Programming
Generation (or a posteriori) methods in Multiobjective Programming (MOP) are the most computationally demanding category among the MOP approaches. Due to the dramatic increase in computational speed and the improvement of Mathematical Programming algorithms the generation methods become all the more attractive among today’s decision makers. In the present paper, an adapted method inspired by the epsilon constraint method is presented and applied to multiobjective optimization problems by solving a finite sequence of constrained single-objective problems. It’s a kind of lexicographic optimization on the original objective function. During the process of generating or approximating the Pareto set, we calculate the range of each objective function of the original problem. We generate the values of each objective function at feasible solutions encountered during various iterations of the mono-objective resolution. An exploitation of the set of all gathered information is applied via weights making it possible to deduce what is desired. The approach provides a new adaptive scheme generating an appropriate and satisfactory compromise solution to the Decision Maker. Some simple example problems are presented and their simulation results demonstrate the behavior of the method. The implementation can be general enough to handle arbitrarily many objective functions.
13h55 - 14h20
Bilevel Optimal Tolls Problems With Nonlinear Cost: A Heuristic Solution
The problem of assigning optimal tolls in a multi-commodity transportation network is formulated as a bilevel mathematical program. A heuristic algorithm based on the allowable ranges to stay optimal (ARSO) for quadratic programs is developed. In this way, one can analyze possible changes in the coefficients of some variables in the objective function within these allowed ranges without affecting the optimal solution. In addition, when stuck to a local maximum solution, a modified “filled function” technique helps one “jump” to another local maximum if such does exist; otherwise, the search is stopped. Numerical experiments confirm the robustness of our heuristics.
14h20 - 14h45
Solving Mixed-Integer Nonlinear Programs by the Metaheuristic Technique Generalized-CGRASP
Large-scale MINLP are difficult to address by classical combinatorial relaxation techniques due to the curse of dimensionality phenomenon. The Generalized-CGRASP method – a hybrid GRASP/C-GRASP metaheuristic – avoids many combinatorial difficulties doing an a priori random search in a discrete set. The random search and local improvement phases of Generalized-CGRASP independently use a discrete and a continuous set.
14h45 - 15h10
Finding a resilient communication network by Variable Neighborhood Search
Our goal is to find a network on 64 vertices with a small average distance and a bounded maximum degree, in order to design efficient data centers. Moreover, due to technical constraints, we need that the network possesses some robustness, especially after an edge or a vertex removal. First, we find some mathematical properties that have this class of desired graphs. From these properties, we conduct a Variable Neighborhood Search. Moreover, we explore different avenues to reach our goal. We present in this talk results of our current research.