On solving the MAX-SAT using sum of squares

We consider semidefinite programming (SDP) approaches for solving the maximum satisfiabilityproblem (MAX-SAT) and the weighted partial MAX-SAT. It is widely known that SDP is well-suitedto approximate the (MAX-)2-SAT. Our work shows the potential of SDP also for other satisfiabilityproblems, by being competitive with some of the best solvers in the yearly MAX-SAT competition.Our solver combines … Read more

Semi-Infinite Generalized Disjunctive and Mixed Integer Convex Programs with(out) Uncertainty

In this paper, we introduce semi-infinite generalized disjunctive programs that are defined by logical propositions along with disjunctions of sets of logical equations and infinite number of algebraic inequalities. We denote these programs by SIGDPs. For SIGDPs with linear and convex inequalities, we present new reformulations: semi-infinite mixed-binary/disjunctive linear programs and semi-infinite mixed-binary/disjunctive convex programs, … Read more

Recognition of Facets for Knapsack Polytope is DP-complete

DP¬† is a complexity class that is the class of all languages that are the intersection of a language in NP and a language in co-NP, as coined by Papadimitriou and Yannakakis. In this paper, we will establish that, recognizing a facet for the knapsack polytope is DP-complete, as conjectured by Hartvigsen and Zemel in … Read more

The Largest Unsolved QAP Instance Tai256c Can Be Converted into A 256-dimensional Simple BQOP with A Single Cardinality Constraint

Tai256c is the largest unsolved quadratic assignment problem (QAP) instance in QAPLIB; a 1.48\% gap remains between the best known feasible objective value and lower bound of the unknown optimal value. This paper shows that the instance can be converted into a 256 dimensional binary quadratic optimization problem (BQOP) with a single cardinality constraint which … Read more

A binary linear programming approach for supporting administrative territorial consolidation

The objective of this paper is to develop a scalable binary linear programming model for finding the optimal aggregation of communes into spatially contiguous administrative territorial units (ATUs) constrained on certain balancing criteria. The requirement for the ATUs to be contiguous represents the main computational bottleneck and, therefore, it prevents one from using such models … Read more

Revisiting local branching with a machine learning lens

Finding high-quality solutions to mixed-integer linear programming problems (MILPs) is of great importance for many practical applications. In this respect, the refinement heuristic local branching (LB) has been proposed to produce improving solutions and has been highly influential for the development of local search methods in MILP. The algorithm iteratively explores a sequence of solution … Read more

Relaxations and Cutting Planes for Linear Programs with Complementarity Constraints

We study relaxations for linear programs with complementarity constraints, especially instances whose complementary pairs of variables are not independent. Our formulation is based on identifying vertex covers of the conflict graph of the instance and generalizes the extended reformulation-linearization technique of Nguyen, Richard, and Tawarmalani to instances with general complementarity conditions between variables. We demonstrate … Read more

Using Multiple Reference Vectors and Objective Scaling in the Feasibility Pump

The Feasibility Pump (FP) is one of the best-known primal heuristics for mixed-integer programming (MIP): more than 15 papers suggested various modifications of all of its steps. So far, no variant considered information across multiple iterations, but all instead maintained the principle to optimize towards a single reference integer point. In this paper, we evaluate … Read more

Solving large-scale unit-commitment problems using dual dynamic programming and open-source solvers

The astonishing dimensions and complexity of power systems render them impossible to be managed without the help of cutting-edge software. Due to a lack of scalable, reliable and well documented free and open-source solutions, system operators, regulators, and government agencies often rely on proprietary software to provide them information that ultimately will be used to … Read more