The minimum $k$-enclosing ball problem seeks the ball with smallest radius that contains at least $k$ of $m$ given points in a general $n$-dimensional Euclidean space. This problem is NP-hard. We present a branch-and-bound algorithm on the tree of the subsets of $k$ points to solve this problem. The nodes on the tree are ordered … Read more
Christofides and Hadjiconstantinou introduced a dynamic programming state space relaxation for obtaining upper bounds for the Constrained Two-dimensional Guillotine Cutting Problem. The quality of those bounds depend on the chosen item weights, they are adjusted using a subgradient-like algorithm. This paper proposes Algorithm X, a new weight adjusting algorithm based on integer programming that provably … Read more
We present sufficient conditions under which thermal generators can be aggregated in mixed-integer linear programming (MILP) formulations of the unit commitment (UC) problem, while maintaining feasibility and optimality for the original disaggregated problem. Aggregating thermal generators with identical characteristics (e.g., minimum/maximum power output, minimum up/down-time, and cost curves) into a single unit reduces redundancy in … Read more
We propose a nested decomposition scheme for infinite-horizon stochastic linear programs. Our approach can be seen as a provably convergent extension of stochastic dual dynamic programming to the infinite-horizon setting: we explore a sequence of finite-horizon problems of increasing length until we can prove convergence with a given confidence level. The methodology alternates between a … Read more
Demand for healthcare services is growing rapidly in Australia and across the world, and rising healthcare expenditure is increasing pressure on sustainability of government-funded healthcare systems. In Australia, elective surgery waiting lists are growing and hospitals are struggling with a capacity shortage. To keep up with the rising demand, we need to be more efficient … Read more
In the literature, packing and partitioning orbitopes were discussed to handle symmetries that act on variable matrices in certain binary programs. In this paper, we extend this concept by restrictions on the number of 1-entries in each column. We develop extended formulations of the resulting polytopes and present numerical results that show their effect on … Read more
In this paper we consider energy management optimization problems in a future wherein an interaction with micro-grids has to be accounted for. We will model this interaction through a set of contracts between the generation companies owning centralized assets and the micro-grids. We will formulate a general stylized model that can, in principle, account for … Read more
Process systems engineers have long recognized the importance of both logic and optimization for automated decision-making. But modern challenges in process systems engineering could strongly benefit from methodological contributions in computer science. In particular, we propose satisfiability modulo theories (SMT) for process systems engineering applications. We motivate SMT using a series of test beds and … Read more
Motivated by recent advances in solution methods for mixed-integer convex optimization (MICP), we study the fundamental and open question of which sets can be represented exactly as feasible regions of MICP problems. We establish several results in this direction, including the first complete characterization for the mixed-binary case and a simple necessary condition for the … Read more
In this paper, we consider the well-known constant-batch lot-sizing problem, which we refer to as the single module capacitated lot-sizing (SMLS) problem, and multi-module capacitated lot-sizing (MMLS) problem. We provide sufficient conditions under which the (k,l,S,I) inequalities of Pochet and Wolsey (Math of OR 18: 767-785, 1993), the mixed (k,l,S,I) inequalities, derived using mixing procedure … Read more