Natashia Lesley Boland
Frontiers of Integer Programming
Optimization problems in which some or all of the variables are constrained to take integer values are applicable in a many fields, ranging from medicine and healthcare to banking and finance to environmental management and conservation. Over recent decades, exact algorithms for their solution have become faster and more efficient, culminating in a variety of commercial software packages and public domain codes that provide exceptional capability for solving practical problems to optimality. This has opened up new frontiers.
Many decision makers, in practice, consider multiple, competing objectives. In medicine, radiation oncologists seek to minimize the damage to a critical organ while maximizing the damage to a cancerous tumor. In environmental management, the health of populations of competing, threatened species must be maximized. Leveraging the power of exact integer programming solvers, algorithms that compute the optimal trade-off curve, also known as the Pareto frontier, for integer programming problems with multiple objectives, have been developed in recent years. These greatly enhance what optimization can offer the decision-maker, giving them a complete picture of the options available to them, and allowing them to exercise their experience and expertise in selecting the solution to implement.
The astonishing capabilities of exact solvers has only increased the appetite of practitioners to solve ever-larger problems, which challenges the state-of-the-art. These solver capabilities have been achieved by decades of research enhancing the “divide-and-conquer” branch-and-bound method that lies at the heart of all exact solvers. Yet one key element of this method has remained largely untouched since it was first presented in the 1960’s: the branching rule, by which the solution space is divided. Recent work has shown that for problems with decomposable structure, new branching rules, developed to exploit that structure, can have dramatic effects on the performance of the branch-and-bound method.
In this talk, we will discuss both these developments, at the frontiers of integer programming research, and, in the process, identify further research opportunities for the field.
J. Cole Smith
The Applications, Mathematics, and Algorithms of Two-Player Optimization Problems
The optimization fields of bilevel programming, interdiction, and robust optimization have become vital areas of study over the past few decades. Problems in these fields typically involve two players making decisions in turn, where each player’s actions affect each other’s objectives and/or resources. These models increasingly important relevance in protecting critical infrastructure, determining vulnerabilities in complex systems, and analyzing how systems can be designed to achieve desired outcomes for the players. This lecture will discuss some of the applications that inspired developments in these areas, and will contrast the models used to represent the different games. Despite the variations in algorithms designed to solve these models, there are many commonalities as well. This talk will discuss, in a lightly technical manner, the commonalities of these approaches and how advances in one research area benefits the development of algorithms in the other areas. Finally, I will discuss some emerging research areas and opportunities for future research in this field.
Will Artificial Intelligence Kill Markowitz?
In the aftermath of the 2007 financial crisis, many specialists blamed Modern Portfolio Theory (MPT) for the chaos. While some of the critics to MPT have solid bases, many also defend the ideas of Markowitz. MPT is not about fancy financial engineering, algorithms or forecasting; it really is about the creation of investment portfolios that maximize expected return for each level of risk. The simplest, yet the most unquestionable rule of finance, is that if on average you want higher returns, you will have to accept greater risk in your portfolio.
In this talk, we will discuss how to combine machine learning algorithms and modern portfolio theory to make investment decisions. The speaker manages the first artificial intelligence driven fund in Latin America.
Alice E. Smith
Decision Science Inspired by Nature
This talk will put forth several straightforward but successful implementations of analytical approaches inspired by natural systems. These nature-based paradigms range in fidelity with their natural systems origins but all seek to leverage the structures and operations of nature doing what it does best – novelty detection, system optimization, adaptability to dynamic environments, robustness, and flexibility. More specifically, the well-known, but often misunderstood and misused, natural system computational paradigms of artificial neural networks, fuzzy logic, and evolutionary algorithms will be considered for use in decision science. Used judiciously and knowledgeably these approaches can offer significant advantages in diverse decision environments. A curated selection of diverse applications from the speaker’s more than 25 years of experience in this field will be explained and objectively analyzed. The applications are (1) quality and process improvement of large-scale ceramic casting, (2) real-time placement of drones for ad hoc network connectivity, (3) continuous monitoring of vehicles for predictive maintenance, (4) the location of semi-obnoxious facilities in municipalities considering transport costs and social costs, and (5) the design of large order picking warehouses considering travel distance.
Revisiting Some Location/routing Problems
Location/routing problems (LRPs) is the term generally used to refer to a large family of problems, combining location and routing decisions, which have become classical in combinatorial optimization. In practice, this family contains problems, which, depending on the modeling assumptions, can be of very diverse nature. Aspects that may affect substantially the characteristics of the resulting LRP include, in addition to the type of network where the problem is stated, the placement and features of the demand that has to be served, or potential specific requirements on the service facilities or the service routes. In this talk we mainly focus on two such aspects, namely whether service demand is placed at the nodes or the edges of the network, and whether or not all users with demand have to be served. Alternative techniques are discussed, leading to improved formulations or solution algorithms for some LRPs.
Advances in Exact Algorithms for Vehicle Routing
The Vehicle Routing Problem (VRP) is among the most widely studied problems in the fields of operations research and combinatorial optimization. Its relevance stems from its direct application in the real world systems that distribute goods and provide services, vital to the modern economies. Reflecting the large variety of conditions present in those systems, the VRP literature is spread into dozens of variants. For example, there are variants that consider time windows, multiple depots, mixed vehicle fleet, split deliveries, pickups and deliveries, precedences, etc. The currently best exact VRP algorithms are based on the combination of column generation and cut separation, in the so called Branch-Cut-and-Price (BCP) algorithms. This talk surveys significant recent contributions by several authors. In particular, it presents the concept of cuts with limited-memory (Pecin et al. 2014), a technique that represented a breakthrough on some of the most classical VRP variants, allowing the optimal solution of instances with up to a few hundreds points. The talk also presents the ongoing efforts for creating the first effective generic exact VRP algorithms. They should be suited to many distinct variants and still have a good performance.