Optimal configurations for modular systems at the example of crane bridges

The aim of this paper is to optimize modular systems which cover the construction of products that can be assembled on a modular basis. Increasing the number of different variants of individual components on the one hand decreases the cost of oversizing the assembled product, while on the other hand the cost for maintaining the … Read more

Superadditive duality and convex hulls for mixed-integer conic optimization

We present an infinite family of linear valid inequalities for a mixed-integer conic program, and prove that these inequalities describe the convex hull of the feasible set when this set is bounded and described by integral data. The main element of our proof is to establish a new strong superadditive dual for mixed-integer conic programming … Read more

Linear-size formulations for connected planar graph partitioning and political districting

Motivated by applications in political districting, we consider the task of partitioning the n vertices of a planar graph into k connected components. We propose an extended formulation that has two desirable properties: (i) it uses just O(n) variables, constraints, and nonzeros, and (ii) it is perfect. To explore its ability to solve real-world problems, … Read more

D-optimal Data Fusion: Exact and Approximation Algorithms

We study the D-optimal Data Fusion (DDF) problem, which aims to select new data points, given an existing Fisher information matrix, so as to maximize the logarithm of the determinant of the overall Fisher information matrix. We show that the DDF problem is NP-hard and has no constant-factor polynomial-time approximation algorithm unless P = NP. … Read more

Computing Tchebychev weight space decomposition for multiobjective discrete optimization problems

Multiobjective discrete optimization (MODO) techniques, including weight space decomposition, have received increasing attention in the last decade. The primary weight space decomposition technique in the literature is defined for the weighted sum utility function, through which sets of weights are assigned to a subset of the nondominated set. Recent work has begun to study the … Read more

Copositive programming for mixed-binary quadratic optimization via Ising solvers

Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution of difficult optimization problems has spurred an increased interest in exploring methods to integrate Ising problems as part of their solution process, with existing … Read more

Multilinear formulations for computing Nash equilibrium of multi-player matrix games

We present multilinear and mixed-integer multilinear programs to find a Nash equilibrium in multi-player strategic-form games. We compare the formulations to common algorithms in Gambit, and conclude that a multilinear feasibility program finds a Nash equilibrium faster than any of the methods we compare it to, including the quantal response equilibrium method, which is recommended … 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

Cutting-plane algorithm for sparse estimation of the Cox proportional-hazards model

Survival analysis is a family of statistical methods for analyzing event occurrence times. In this paper, we address the mixed-integer optimization approach to sparse estimation of the Cox proportional-hazards model for survival analysis. Specifically, we propose a high-performance cutting-plane algorithm based on reformulation of bilevel optimization for sparse estimation. This algorithm solves the upper-level problem … Read more