# Tutorials

### Practical Guidelines for Solving Difficult Mixed Integer Programs, Version 2.0

The paper “Practical Guidelines for Solving Difficult Mixed Integer Programs” by Klotz and Newman was written in 2012, and significant parts of that material first appeared in 2007. Since then, mixed-integer solvers have evolved significantly. Two of the three models the paper describes were unsolvable at the time, but some solvers now handle them easily, as of the last five years. This tutorial will provide an update to the guidelines. We will consider additional functionality in the solvers and look at a new set of challenging models.

• Alexandra Newman is a professor in the Mechanical Engineering Department at the Colorado School of Mines (CSM). Prior to joining CSM, she was a research assistant professor at the Naval Postgraduate School in the Operations Research Department. She obtained her BS in applied mathematics at the University of Chicago and her PhD in industrial engineering and operations research at the University of California at Berkeley. She specializes in deterministic optimization modeling, especially as it applies to energy and mining systems, and to logistics, transportation, and routing. She received a Fulbright Fellowship to work with industrial engineers on mining problems at the University of Chile in 2010 and was awarded the Institute for Operations Research and the Management Sciences (INFORMS) Prize for the Teaching of Operations Research and Management Science Practice in 2013.

### Stochastic Failure Models for Network Analysis

Risk-awareness in the design and operation of networks need to systematically consider the performance of the network and consider investment to extend it to face the new challenge to provide their service. In general networks are subject to a trade-off between a low probability of unavailability of the service they provide and the very high cost associated with the impossibility of providing service in that event. Providers, users and regulators wish to understand how to better operate and redesign these networks, so researcher have developed techniques to evaluate their performance and study their stability. To analyze network failures attention must be paid to three important aspects: first to choose a failure model that is complex enough to capture the interaction between components but, at the same time simple to calibrate with the available information; second study the performance, this means that given a model we need to develop methodology to compute the performance of the network, and third to compare network designs and chose according to a budget constraint those which perform better.

In this tutorial we will discuss new failure models that are appearing to capture dependence in components and how to estimate performance metrics considering simulation techniques. We will finish with some comment on the network design problem.

• Javiera Barrera is an assistant professor at the Faculty of Engineering and Science, Universidad Adolfo Ibáñez. She obtained her undergraduate degree in mathematical engineering at Universidad de Chile. She earned simultaneously her PhD in mathematics at the Laboratoire MAP5 of  l’Université Paris Descartes and at the School of Engineering of Universidad de Chile. She specializes in asymptotic convergence of Markov chains and in stochastic optimization methods for networks design. Her most recent research has developed models to incorporate failure dependency in the networks reliability analysis.

### Mariel Lavieri

University of Michigan, USA

### Medical Decision Making; The Past, the Present, and the Future

Abstract to come

• Mariel Lavieri is an Associate Professor in the School of Industrial and Operations Engineering at the University of Michigan. In her work, she applies operations research to healthcare topics. Her most recent research focuses on medical decision making, in particular on determining optimal screening, monitoring and treatment by explicitly modeling the stochastic disease progression. She has also developed models for health workforce planning, which take into account training requirements, workforce attrition, capacity planning, promotion rules and learning. Among others, Mariel is the recipient of the MICHR Distinguished Mentor Award, the National Science Foundation CAREER Award, the International Conference on Operations Research Young Participant with Most Practical Impact Award, and the Bonder Scholarship. She has also received the Pierskalla Best Paper Award, and an honorary mention in the George B. Dantzig Dissertation Award. She has been selected to participate in the Frontiers of Engineering Symposium organized by the National Academy of Engineering. Mariel has guided work that won, among others, the Medical Decision Making Lee Lusted Award, the INFORMS Doing Good with Good OR Award, and the Production and Operations Management Society College of Healthcare Operations Management Best Paper Award.

### Andre Luiz Diniz

Eletrobras Cepel, Brazil

### OR in Energy Planning: Modeling Strategies, Solving Techniques and Practical Aspects

Energy planning is a fertile field for the application of operations research techniques and mathematical programming tools. There are a lot of interesting problems, ranging from long-term planning to day-ahead or intra-day scheduling tools. Despite the improvement in commercial packages to solve LP, MILP or MINLP problems, extensive expertise is still required to model, decompose and solve such problems in an efficient way, in order to derive tools that provide implementable results as closest as possible to reality, in reasonable CPU times.

One of the main challenges in these types of problems is how to handle uncertainty. In the past, this issue was mainly addressed in long-term problems, with the application of stochastic programming techniques such as SDDP to represent uncertainty in some crucial input variables such as hydro inflows to reservoirs. In modern power systems, the large increase in intermittent generation has forced unit commitment and short-term scheduling tools to also address this issue, leading to different ways to model here and now/wait and see decisions, and favoring the application of alternative techniques such as robust optimization. In addition, the modeling of hourly operation aspects in long-term planning tools is becoming more and more important, posing a big challenge in handling the trade-off between accuracy in system representation and computational time.

Besides providing an overview of decomposition techniques and solving strategies to tackle power generation planning and scheduling problems, this talk also briefly discusses alternative approaches to model different aspects of system operation, such as power flows in the electrical network, dynamic thermal unit commitment characteristics and nonconvex/time linking constraints for the operation of hydro and pumped storage plants, always with a look at practical applications in large-scale systems.

• Andre Luiz Diniz received the BSc in Civil Engineering in 1996, the MSc in Operations Research in 2000, and the DSc in optimization in 2007 at the Federal University of Rio de Janeiro (UFRJ). In 2014 he was on leave for a 3-month post-doctoral at the Weierstrass Institute for Applied Analysis and Stochastics in Berlin. Since 1998 he has been a researcher at CEPEL, the Brazilian Electric Energy Research Center, working in the development of optimization models for power generation planning and also as a project manager. Since 2017 he is the head of the Optimization and Environment Department (DEA) of CEPEL. He is also an assistant professor of the Institute of Mathematics and Statistics at the State University of Rio de Janeiro (UERJ), where he teaches courses on probability, statistics and decision making. He is a Senior Member of IEEE and is currently vice-chair of the Power System Economics subcommittee. He has a large experience in several subjects related to optimization, such as linear, dynamic and stochastic programming, as well as application of decomposition methods such as Benders decomposition, Lagrangian Relaxation and Stochastic dual dynamic programming to real large scale problems in the power industry. He has published over 75 papers in local and international conferences and journals, and has been working as a reviewer for several conferences and journals on electrical engineering and operations research.

SEIO

### A Few Links Between Mathematical Optimization and Data Science

Abstract to come

• Emilio Carrizosa, President of SEIO, the Spanish Stats & OR Society, Professor of Statistics and Operations Research and Director of IMUS – the Institute of Mathematics of the University of Seville, Spain. In his career, he has combined academic research (he has published more than 100 papers on Mathematical Optimization and its Applications to Data Science) with OR and Data Science industrial activities.

### Ivan Contreras

Ivan Contreras is an Associate Professor and Research Chair in Transportation and Logistics Network Optimization in the Mechanical, Industrial, and Aerospace Engineering Department at Concordia University, Canada. He is a regular member of the Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT). He obtained his B.Sc. and M.Sc. in Industrial Engineering from the University of Americas, Mexico, and his Ph.D. in Operations Research from the Technical University of Catalonia, Spain. His research focuses on the development of models and algorithms for large-scale optimization problems arising in transportation and logistics, scheduling and production, and health-care planning. In 2015, he was awarded the Institute for Operations Research and the Management Sciences (INFORMS) Chuck ReVelle Rising Star Award for his contributions to location science.

MIT, USA

### The JuMP Ecosystem for Mathematical Optimization

JuMP is a multi-award-winning domain-specific language for mathematical optimization. JuMP has already been successfully used in academic and industrial problems related to marketing, causal inference, daily fantasy sports, optimal control of aerial drones, machine learning, school bus routing, sustainable power systems expansion, and decarbonization of electrical networks. The JuMP ecosystem gives access to a wide range of highly-effective commercial and open-source optimization tools in a natural syntax that requires only a basic knowledge of mathematical optimization. JuMP provides this access with a performance that matches or exceeds those of commercial and open-source alternatives, as well as unparalleled versatility and extensibility allowed by the advanced features of the Julia programming language. In particular, JuMP and its infrastructure was used to develop the solver Pajarito.jl, which is currently the state-of-the-art for the mixed-integer conic optimization problems. In this tutorial, we begin with basic syntax and features of JuMP and associated packages assuming no previous knowledge of JuMP and only an elementary knowledge of mathematical optimization. We then cover more advanced features, give performance tips, and cover the recent improvements to JuMP. Finally, we demo some state-of-the-art features, including showing how various packages in the rich Julia ecosystem can be seamlessly combined to provide simple solutions to complicated problems in the optimal control of aerial drones.

• Juan Pablo Vielma is the Richard S. Leghorn (1939) Career Development Associate Professor at MIT Sloan School of Management and is affiliated to MIT’s Operations Research Center. Dr. Vielma has a B.S. in Mathematical Engineering from University of Chile and a Ph.D. in Industrial Engineering from the Georgia Institute of Technology. His current research interests include the theory and practice of mixed-integer mathematical optimization and applications in energy, natural resource management, marketing and statistics. In January of 2017 he was named by President Obama as one of the recipients of the Presidential Early Career Award for Scientists and Engineers (PECASE). Some of his other recognitions include the NSF CAREER Award and the INFORMS Computing Society Prize. He is currently an associate editor for Operations Research and Operations Research Letters, a member of the board of directors of the INFORMS Computing Society, and a member of the NumFocus steering committee for JuMP.

### Martin Savelsbergh

Georgia Tech, USA

### Criterion Space Search Algorithms for Multi-objective Mixed Integer Programming

Multi-objective optimization problems are pervasive in practice. In contrast to single-objective optimization, the goal in multi-objective optimization is to generate a set of solutions that induces the Pareto front, i.e., the set of all nondominated points. A nondominated point is a vector of objective function values evaluated at a feasible solution, with the property that there exists no other feasible solution that is at least as good in all objective function values and better in one or more of them. Recently, criterion space search algorithms, in which the search for the Pareto front takes place in the space of the vectors of objective function values, i.e., the criterion space, have gained in popularity. These methods exploit the advances in single-objective optimization solvers, since they repeatedly solve single-objective optimization problems. We will introduce and discuss criterion space search algorithms for both pure and mixed multi-objective integer programs.

• Martin Savelsbergh is a logistics and optimization specialist with over 25 years of experience in mathematical modeling, operations research, optimization methods, algorithm design, performance analysis, transport, supply chain management, and production planning. He has published over 160 research papers in many of the top operations research and optimization journals and has supervised more than 30 Ph.D. students. Martin has a track record of creating innovative techniques for solving large-scale optimization problems in a variety of areas, ranging from service network design, to last-mile and crowdsourced delivery, to ridesharing.  He has demonstrated an ability to design and implement highly sophisticated and effective optimization algorithms as well as an ability to analyze practical decision problems and translate the insights obtained into optimal business solutions.  Martin holds the James C. Edenfield Chair in the H. Milton Stewart School of Industrial and Systems Engineering (ISyE) at Georgia Institute of Technology. He is co-director of The Supply Chain and Logistics Institute (SCL). SCL coordinates all supply chain and logistics activities on the Georgia Tech campus.  Martin Savelsbergh is Editor-in-Chief of Transportation Science, one of the most prestigious academic journals in the area of transportation science and logistics.

### Meisam Razaviyayn

University of Southern California, USA

### Solving “Nice” Non-Convex Optimization Problems and its Connections to Training Deep Neural Networks

When is solving a non-convex optimization problem easy? Despite significant research efforts to answer this question, most existing results are problem specific and cannot be applied even with simple changes in the objective function. In this talk, we provide theoretical insights to this question by answering two related questions: 1) Are all local optima of a given non-convex optimization problem globally optimal? 2) When can we compute a local optimum of a given non-convex constrained optimization problem efficiently?  In the first part of the talk, motivated by the non-convex training problem of deep neural networks, we provide simple sufficient conditions under which any local optimum of a given highly composite optimization problem is globally optimal. Unlike existing results in the literature, our sufficient condition applies to many non-convex optimization problems such as training problem of non-convex multi-linear neural networks and non-linear neural networks with pyramidal structures.

In the second part of the talk, we consider the problem of finding a local optimum of a constrained non-convex optimization problem under strict saddle point property. We show that, unlike the unconstrained scenario, the vanilla projected gradient descent algorithm fails to escape saddle points even in the presence of a single linear constraint. We then propose a trust region algorithm which converges to second order stationary points for optimization problems with small number of linear constraints. Our algorithm is the first optimization procedure, with polynomial per-iteration complexity, which converges to $\epsilon$-first order stationary points of a non-manifold constrained optimization problem in $O(\epsilon^{-3/2})$ iterations, and at the same time can escape saddle points under strict saddle property.

• Meisam Razaviyayn is an assistant professor at the department of Industrial and Systems Engineering at the University of Southern California. Prior to joining USC, he was a postdoctoral research fellow in the Department of Electrical Engineering at Stanford University. He received his PhD in Electrical Engineering with minor in Computer Science at the University of Minnesota under the supervision of Professor Tom Luo. He obtained his MS degree in Mathematics under the supervision of Professor Gennady Lyubeznik. Meisam Razaviyayn is the recipient of the Signal Processing Society Young Author Best Paper Award in 2014 and the finalist for Best Paper Prize for Young Researcher in Continuous Optimization in 2013 and 2016. His research interests include the design and analysis of large scale optimization algorithms arise in modern data science era.