In this we paper we define a new class of the team orienteering problem; the cooperative orienteering problem with time windows (COPTW). The COPTW is a generalisation of the TOPTW, which requires multiple vehicles to cooperatively collect the reward from a location. The COPTW is demonstrated with the aid of a wildfire scenario in South … Read more
Let $A$ be an element of the copositive cone $\mathcal{COP}^n$. A zero $\mathbf{u}$ of $A$ is a nonnegative vector whose elements sum up to one and such that $\mathbf{u}^TA\mathbf{u} = 0$. The support of $\mathbf{u}$ is the index set $\mathrm{supp}\mathbf{u} \subset \{1,\dots,n\}$ corresponding to the nonzero entries of $\mathbf{u}$. A zero $\mathbf{u}$ of $A$ is … Read more
In a recent Math. Program. paper, Eckstein and Silva proposed a new error criterion for the approximate solutions of augmented Lagrangian subproblems. Based on a saddle-point formulation of the primal and dual problems, they proved that dual sequences generated by augmented Lagrangians under this error criterion are bounded and that theirs limit points are dual … Read more
We consider the problem of scheduling jobs on a single machine to minimize the total electricity cost of processing these jobs under time-of-use electricity tariffs. We consider both uniform-speed and speed-scalable machine environments. For the uniform-speed case, we prove that this problem is strongly NP-hard, and in fact inapproximable within a constant factor, unless P … Read more
In this paper, following the ideas presented in Attouch et al. (Math. Program. Ser. A, 137: 91-129, 2013), we present an inexact version of the proximal point method for nonsmoth functions, whose regularization is given by a generalized perturbation term. More precisely, the new perturbation term is defined as a “curved enough” function of the … Read more
The paper deals with the definition and the computation of surrogate upper bound sets for the bi-objective bi-dimensional binary knapsack problem. It introduces the Optimal Convex Surrogate Upper Bound set, which is the tightest possible definition based on the convex relaxation of the surrogate relaxation. Two exact algorithms are proposed: an enumerative algorithm and its … Read more
This note studies compact representations of linear on/off constraints in mixed-integer linear optimization. A characterization of the convex hull of linear disjunctions is given in the space of original variables. This result can improve formulations of mixed-integer linear programs featuring on/off constraints by reducing the integrality gap in a Branch and Bound approach. Citation @article{, … Read more
Duality theory is pervasive in finite dimensional optimization. There is growing interest in solving infinite-dimensional optimization problems and hence a corresponding interest in duality theory in infinite dimensions. Unfortunately, many of the intuitions and interpretations common to finite dimensions do not extend to infinite dimensions. In finite dimensions, a dual solution is represented by a … Read more
Inexact Restoration methods have been proved to be effective to solve constrained optimization problems in which some structure of the feasible set induces a natural way of recovering feasibility from arbitrary infeasible points. Sometimes natural ways of dealing with minimization over tangent approximations of the feasible set are also employed. A recent paper [N. Banihashemi … Read more
Various journal-ranking algorithms have been proposed, most of them based on citation counts. This article introduces a new approach based on the reciprocal direct influence of all pairs of a list of journals. The proposed method is assessed against an opinion-based ranking published in 2005 for 25 operations research and management science (OR/MS) journals, and … Read more