Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.

Objective Selection for Cancer Treatment: An Inverse Optimization Approach

The quality of radiation therapy treatment plans and the efficiency of the planning process are heavily affected by the choice of planning objectives. Although simple objectives enable efficient treatment planning, the resulting treatment quality might not be clinically acceptable; complex objectives can generate high-quality treatment, yet the planning process becomes computationally prohibitive. In “Objective Selection for Cancer Treatment: An Inverse Optimization Approach,” by integrating inverse optimization and feature selection techniques, Ajayi, Lee, and Schaefer propose a novel objective selection method that uses historical radiation therapy treatment data to infer a set of planning objectives that are tractable and parsimonious yet clinically effective. Although the objective selection problem is a large-scale bilevel mixed-integer program, the authors propose various solution approaches inspired by feature selection greedy algorithms and patient-specific anatomical characteristics.

Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming

Although inverse linear programming (LP) has received increasing attention as a technique to identify an LP that can reproduce observed decisions that are originally from a complex system, the performance of the linear objective function inferred by existing inverse LP methods is often highly sensitive to noise, errors, and uncertainty in the underlying decision data. Inspired by robust regression techniques that mitigate the impact of noisy data on the model fitting, in “Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming,” Shahmoradi and Lee propose a notion of stability in inverse LP and develop an inverse optimization model that identities objective functions that are stable against data imperfection. Although such a stability consideration renders the inverse model a large-scale mixed-integer program, the authors analyze the connection between the model and well-known biclique problems and propose an efficient exact algorithm as well as heuristics.

A Neural Network Inverse Optimization Procedure for Constitutive Parameter Identification and Failure Mode Estimation of Laterally Loaded Unreinforced Masonry Walls

A new Neural Network Optimization (NNO) algorithm for constitutive material parameter identification based on inverse analysis of experimental tests of small-scale masonry prisms under compressive loads is presented. The Concrete Damaged Plasticity (CDP) constitutive model is used for the brick and mortar of the Unreinforced Masonry (URM) walls. By comparisons with experimental data taken from laboratory tests, it is demonstrated that the constitutive parameters calibrated by application of the proposed inverse optimization procedure on the small-scale (prism) experimental results are sufficiently accurate to allow for the prediction of the mechanical response of large-scale URM walls subject to compressive and lateral loads. This eliminates the need for large-scale URM wall experimental tests for the identification of their material properties, making the calibration process more economic. After verifying the accuracy of the calibrated constitutive parameters based on the above comparisons, a numerical parametric study is performed for the investigation of the effect of material behavior and geometrical aspect ratios on the failure mechanisms of large-scale URM walls.

An Inverse Optimization Approach to Measuring Clinical Pathway Concordance

Clinical pathways outline standardized processes in the delivery of care for a specific disease. Patient journeys through the healthcare system, however, can deviate substantially from these pathways. Given the positive benefits of clinical pathways, it is important to measure the concordance of patient pathways so that variations in health system performance or bottlenecks in the delivery of care can be detected, monitored, and acted upon. This paper proposes the first data-driven inverse optimization approach to measuring pathway concordance in any problem context. Our specific application considers clinical pathway concordance for stage III colon cancer. We develop a novel concordance metric and demonstrate using real patient data from Ontario, Canada that it has a statistically significant association with survival. Our methodological approach considers a patient’s journey as a walk in a directed graph, where the costs on the arcs are derived by solving an inverse shortest path problem. The inverse optimization model uses two sources of information to find the arc costs: reference pathways developed by a provincial cancer agency (primary) and data from real-world patient-related activity from patients with both positive and negative clinical outcomes (secondary). Thus, our inverse optimization framework extends existing models by including data points of both varying “primacy” and “alignment.” Data primacy is addressed through a two-stage approach to imputing the cost vector, whereas data alignment is addressed by a hybrid objective function that aims to minimize and maximize suboptimality error for different subsets of input data. This paper was accepted by Chung Piaw Teo, Special Issue on Data-Driven Prescriptive Analytics.

AN INVERSE OPTIMIZATION PROBLEM OF HEAT TRANSFER IN THE MACHINING PROCESS – A REVIEW

This paper reports on the results of research on thermal aspects in the process of material removal by inverse heat transfer problem. The research focuses on the identification, modeling and optimization of machining process based on the measured temperature at a particular point of the workpiece. The inverse approach determines the overall temperature distribution of the workpiece and the unknown heat flux at the tool/workpiece interface in machining. By introducing and minimizing an objective function based on the heat flux function, relationship of the heating power and duration on the surface layer of the workpiece is optimized. In this way, the most favourable machining conditions are determined in order to achieve high productivity and quality levels. The inverse optimization problem is solved by using the analytical, numerical and regularization methods. Formulation, application and analysis of the inverse optimization problem of heat transfer are shown on the example of creep-feed grinding. The creep-feed grinding process is a widely used abrasive machining process that is characterized by high thermal load of the workpiece. The results of the inverse optimization problem were verified by a series of experiments under different machining conditions.