Multi-stage robust optimization, in which decisions are taken sequentially as new information becomes available about the uncertain problem parameters, is a very versatile yet computationally challenging paradigm for decision-making under uncertainty. In this paper, we propose a new model and solution approach for multi-stage robust mixed-integer programs, which may contain both continuous and discrete decisions … Read more
A suitable set of test instances, also known as benchmark problems, is a key ingredient to systematically evaluate numerical solution algorithms for a given class of optimization problems. While in recent years several solution algorithms for the class of multiobjective mixed-integer nonlinear optimization problems have been proposed, there is a lack of a well-established set … Read more
The issue of characterizing completely efficient (Pareto) solutions to a fractional vector (multiobjective or multicriteria) minimization problem, where the involved functions are convex, has not been addressed previously. Thanks to an earlier characterization of weak efficiency in difference vector optimization by El Maghri, we get a vectorial necessary and sufficient condition given in terms of … Read more
We propose in this paper a Polak-Ribière-Polyak conjugate gradient type method for solving bicriteria optimization problems by avoiding scalarization techniques. Two particular advantages in this contribution are to be noted. First, the suggested descent direction common to both criteria may be directly computed by a given formula without solving any intermediate subproblem. Second, the descent … Read more
We propose an algorithm which appears to be the first bridge between the fields of conditional gradient methods and abs-smooth optimization. Our problem setting is motivated by various applications that lead to nonsmoothness, such as $\ell_1$ regularization, phase retrieval problems, or ReLU activation in machine learning. To handle the nonsmoothness in our problem, we propose … Read more
More and more people order products online and have parcels delivered to their homes. This leads to more congestion, negatively impacting the environment, public health, and safety. Carriers can use parcel lockers to consolidate and serve their customers to reduce these negative impacts. The implementation of a locker network can, however, be financially challenging. To … Read more
In this article we introduce an algorithm that approximates Pareto fronts of multiobjective mixed-integer convex optimization problems. The algorithm constructs an inner and outer approximation of the front exploiting the convexity of the patches and is applicable to problems with an arbitrary number of criteria. In the algorithm, the problem is decomposed into patches, which … Read more
We introduce a column elimination procedure for the capacitated vehicle routing problem. Our procedure maintains a decision diagram to represent a relaxation of the set of feasible routes, over which we define a constrained network flow. The optimal solution corresponds to a collection of paths in the decision diagram and yields a dual bound. The … Read more
We investigate a class of generalized Nash equilibrium problems (GNEPs) in which the objectives of the individuals are interdependent and the shared constraint consists of a system of partial differential equations. This setup is motivated by the modeling of strategic interactions of competing firms, which explicitly take into account the dynamics of transporting a commodity, … Read more
In this study, we investigate the connection between the efficient frontier (EF) of a general multiobjective mixed integer linear optimization problem (MILP) and the so-called restricted value function (RVF) of a closely related single-objective MILP. In the first part of the paper, we detail the mathematical structure of the RVF, including characterizing the set of … Read more