A Parallelized Implementation of Cut-and-Solve and a Streamlined Mixed-Integer Linear Programming Model for Finding Genetic Patterns Optimally Associated with Complex Diseases

With the advent of genetic sequencing, there was much hope of finding the inherited elements underlying complex diseases, such as late-onset Alzheimer’s disease (AD), but it has been a challenge to fully uncover the necessary information hidden in the data. A likely contributor to this failure is the fact that the pathogenesis of most complex diseases does not involve single markers working alone, but patterns of genetic markers interacting additively or epistatically. But as we move upwards beyond patterns of size two, it quickly becomes computationally infeasible to examine all combinations in the solution space. A common solution to solving this type of combinatorial optimization problem is to model it as a mixed-integer linear program (MIP) and solve it using the algorithm branch-and-cut, implemented by a commercial solver. However, with the trend of using increasing numbers of computing cores to increase computational power, there is a need for a different approach to solving MIPs that can utilize parallel environments. Here we show how a parallelized implementation of an alternative algorithm, cut-and-solve, can be used to solve this genetics problem faster than CPLEX, one of the leading commercial MIP solvers

Integrating operations research into green logistics:A review

Logistical activities have a significant global environmental impact, necessitating the adoption of green logistics practices to mitigate environmental effects. The COVID-19 pandemic has further emphasized the urgency to address the environmental crisis. Operations research provides a means to balance environmental concerns and costs, thereby enhancing the management of logistical activities. This paper presents a comprehensive review of studies integrating operations research into green logistics. A systematic search was conducted in the Web of Science Core Collection database, covering papers published until June 3, 2023. Six keywords (green logistics OR sustainable logistics OR cleaner logistics OR green transportation OR sustainable transportation OR cleaner transportation) were used to identify relevant papers. The reviewed studies were categorized into five main research directions: Green waste logistics, the impact of costs on green logistics, the green routing problem, green transport network design, and emerging challenges in green logistics. The review concludes by outlining suggestions for further research that combines green logistics and operations research, with particular emphasis on investigating the long-term effects of the pandemic on this field.</p

A Branch-and-Price Algorithm Enhanced by Decision Diagrams for the Kidney Exchange Problem

Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter's co-registered patient, if any, also receives a kidney from a different donor. The kidney exchange problem (KEP) aims to find an optimal collection of kidney exchanges taking the form of cycles and chains. Existing exact solution methods for KEP either are designed for the case where only cyclic exchanges are considered, or can handle long chains but are scalable as long as cycles are short. We develop the first decomposition method that is able to deal with long cycles and long chains for large realistic instances. More specifically, we propose a branch-and-price framework, in which the pricing problems are solved (for the first time in packing problems in a digraph) through multi-valued decision diagrams. Also, we present a new upper bound on the optimal value of KEP, stronger than the one proposed in the literature, which is obtained via our master problem. Computational experiments show superior performance of our method over the state of the art by optimally solving almost all instances in the PrefLib library for multiple cycle and chain lengths

Decision Diagram-Based Branch-and-Bound with Caching for Dominance and Suboptimality Detection

The branch-and-bound algorithm based on decision diagrams introduced by Bergman et al. in 2016 is a framework for solving discrete optimization problems with a dynamic programming formulation. It works by compiling a series of bounded-width decision diagrams that can provide lower and upper bounds for any given subproblem. Eventually, every part of the search space will be either explored or pruned by the algorithm, thus proving optimality. This paper presents new ingredients to speed up the search by exploiting the structure of dynamic programming models. The key idea is to prevent the repeated expansion of nodes corresponding to the same dynamic programming states by querying expansion thresholds cached throughout the search. These thresholds are based on dominance relations between partial solutions previously found and on the pruning inequalities of the filtering techniques introduced by Gillard et al. in 2021. Computational experiments show that the pruning brought by this caching mechanism allows significantly reducing the number of nodes expanded by the algorithm. This results in more benchmark instances of difficult optimization problems being solved in less time while using narrower decision diagrams.Comment: Accepted to INFORMS Journal on Computin

Το Πρόβλημα του Περιοδεύοντος Πωλητή: Ανάλυση Ερευνητικού Πεδίου, Αλγόριθμοι Επίλυσης και Επιχειρησιακές Εφαρμογές

Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Τεχνο-Οικονομικά Συστήματα (ΜΒΑ)

Exact Algorithms for Mixed-Integer Multilevel Programming Problems

We examine multistage optimization problems, in which one or more decision makers solve a sequence of interdependent optimization problems. In each stage the corresponding decision maker determines values for a set of variables, which in turn parameterizes the subsequent problem by modifying its constraints and objective function. The optimization literature has covered multistage optimization problems in the form of bilevel programs, interdiction problems, robust optimization, and two-stage stochastic programming. One of the main differences among these research areas lies in the relationship between the decision makers. We analyze the case in which the decision makers are self-interested agents seeking to optimize their own objective function (bilevel programming), the case in which the decision makers are opponents working against each other, playing a zero-sum game (interdiction), and the case in which the decision makers are cooperative agents working towards a common goal (two-stage stochastic programming). Traditional exact approaches for solving multistage optimization problems often rely on strong duality either for the purpose of achieving single-level reformulations of the original multistage problems, or for the development of cutting-plane approaches similar to Benders\u27 decomposition. As a result, existing solution approaches usually assume that the last-stage problems are linear or convex, and fail to solve problems for which the last-stage is nonconvex (e.g., because of the presence of discrete variables). We contribute exact finite algorithms for bilevel mixed-integer programs, three-stage defender-attacker-defender problems, and two-stage stochastic programs. Moreover, we do not assume linearity or convexity for the last-stage problem and allow the existence of discrete variables. We demonstrate how our proposed algorithms significantly outperform existing state-of-the-art algorithms. Additionally, we solve for the first time a class of interdiction and fortification problems in which the third-stage problem is NP-hard, opening a venue for new research and applications in the field of (network) interdiction