We present two novel applications of symmetries for mixed-integer linear programming. First we propose two variants of a new heuristic to improve the objective value of a feasible solution using symmetries. These heuristics can use either the actual permutations or the orbits of the variables to find better feasible solutions. Then we introduce a new … Read more
We consider a class of multicriteria stochastic optimization problems that features benchmarking constraints based on conditional value-at-risk and second-order stochastic dominance. We develop alternative mixed-integer programming formulations and solution methods for cut generation problems arising in optimization under such multivariate risk constraints. We give the complete linear description of two non-convex substructures appearing in these … Read more
We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic integer programming proposed by Buchheim, Caprara and Lodi to the presence … Read more
This note presents a theoretical analysis of disjunctive constraints featuring unbounded variables. In this framework, classical modeling techniques, including big-M approaches, are not applicable. We introduce a lifted second-order cone formulation of such on/off constraints and discuss related constraint qualification issues. A solution is proposed to avoid solvers’ failure. Citation H. L. Hijazi and L.Liberti … Read more
In this paper, we study bilevel mixed integer programming (MIP) problem and present a novel computing scheme based on reformulations and decomposition strategy. By converting bilevel MIP into a constrained mathematical program, we present its single-level reformulations that are friendly to perform analysis and build insights. Then, we develop a decomposition algorithm based on column-and-constraint … Read more
Mixed-integer quadratic programming (MIQP) is the problem of optimizing a quadratic function over points in a polyhedral set where some of the components are restricted to be integral. In this paper, we prove that the decision version of mixed-integer quadratic programming is in NP, thereby showing that it is NP-complete. This is established by showing … Read more
Many dynamic decision problems involving uncertainty can be appropriately modeled as multi-stage stochastic programs. However, most practical instances are so large and/or complex that it is impossible to solve them on a single computer, especially due to memory limitations. Extending the work of Sandikci et al. (2013) on two-stage stochastic mixed-integer-programs (SMIPs), this paper develops … Read more
In Pareto bi-objective integer optimization the optimal result corresponds to a set of non- dominated solutions. We propose a generic bi-objective branch-and-bound algorithm that uses a problem-independent branching rule exploiting available integer solutions, and cutting plane generation taking advantage of integer objective values. The developed algorithm is applied to the bi-objective team orienteering problem with … Read more
This paper provides the convex hull description for the basic operation of slow- and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are: 1) generation limits and 2) minimum up and down times. Apart from this, the startup and shutdown processes are also … Read more
This paper provides the convex hull description for the following basic operating constraints of a single power generation unit in Unit Commitment (UC) problems: 1) generation limits, 2) startup and shutdown capabilities, and 3) minimum up and down times. Although the model does not consider some crucial constraints, such as ramping, the proposed constraints can … Read more