Optimization problems involving two decision makers at two different decision levels are referred to as bilevel programming problems. In this work, we present a novel algorithm for the exact and global solution of two classes of bi-level programming problems, namely (i) bi-level mixed-integer linear programming problems (B-MILP) and (ii) bi-level mixed-integer quadratic programming problems (B-...

We use logic-based Benders decomposition to minimize tardiness in single-facility scheduling problems with many jobs and long time horizons. Release dates and due dates are given. A mixed integer linear programming (MILP) based master problem allocates jobs to segments of the time horizon, and a constraint programming (CP) based subproblem schedules the jobs in each segment.

Linear programming problems with alternate solutions are challenging due to the choice of multiple strategiesresulting in the same optimal value of the objective function. However, searching for these solutions is atedious task, especially when using mixed integer linear programming (MILP), as previously applied tometabolic models. Therefore, judgment on plurality of optimal m...

This paper presents an efficient solution approach to tackle large-scale singlefloor process plant layout problems. Based on the mixed integer linear programming (MILP) model proposed by Papageorgiou and Rotstein [1], the final layout (i.e. coordinates and dimensions) is determined from an initial feasible solution by an iterative improvement procedure using mixed integer optimisation. The appl...

This paper addresses the globally optimal solution of the network-constrained unit commitment (NCUC) problem incorporating a nonlinear alternating current (AC) model of the transmission network. We formulate the NCUC as a mixed-integer quadratically constrained quadratic programming (MIQCQP) problem. A global optimization algorithm is developed based on a multi-tree approach that iterates betwe...

Given a mixed-integer linear programming (MILP) model and an optimal basis of the associated linear programming relaxation, the Gomory’s corner relaxation is obtained by dropping nonnegativity constraints on the basic variables. Although this relaxation received a considerable attention in the literature in the last 40 years, the crucial issue of evaluating the practical quality of the corner-r...

The paper focuses on the solution of the minimum loss reconfiguration problem of distribution networks, including embedded generation, by means of a mixed integer linear programming (MILP) model. The proposed model takes into account typical operating constraints of distribution networks (radial configuration, branch ampacity limits and bus voltage requirements). The accuracy of the results and...

Two new Mixed Integer Linear Programming (MILP) formulations for modeling a univariate piecewise linear function f were introduced in Li et al. (2008). The first formulation (given by (1)–(3) in Li et al.) uses “Big-M” type constraints, so we denote it by LiBigM. The second formulation (given by (23)–(33) in Li et al.) uses a number of binary variables that is logarithmic in the number of segme...

This paper presents results from recent hardware experiments using two forms of on-line Mixed-integer Linear Programming (MILP). The demonstrations were performed on wheeled ground vehicles, with a view to future use on autonomous teams of UAVs. The first experiment uses MILP at a high-level to account for a limited detection horizon while maneuvering in the presence of obstacles. The second pe...