Zahed Shahmoradi | Searcharxiv

arXiv2021

Optimality-Based Clustering: An Inverse Optimization Approach

We propose a new clustering approach, called optimality-based clustering, that clusters data points based on their latent decision-making preferences. We assume that each data point is a decision generated by a decision-maker who (approximately) solves an optimization problem and cluster the data points by identifying a common objective function of the optimization problems for each cluster such that the worst-case optimality error is minimized. We propose three different clustering models and test them in the diet recommendation application.

math.OC↗

arXiv2020

Quantile Inverse Optimization: Improving Stability in Inverse Linear Programming

Inverse linear programming (LP) has received increasing attention due to its potential to generate efficient optimization formulations that can closely replicate the behavior of a complex system. However, inversely inferred parameters and corresponding forward solutions from the existing inverse LP method can be highly sensitive to noise, errors, and uncertainty in the input data, limiting its applicability in data-driven settings. We introduce the notion of inverse and forward stability in inverse LP and propose a novel inverse LP method that determines a set of objective functions that are stable under data imperfection and generate solutions close to the relevant subset of the data. We formulate the inverse model as a mixed-integer program and elucidate its connection to bi-clique problems, which we exploit to develop efficient heuristics. We also show how this method can be used for online learning. We numerically evaluate the stability of the proposed method and demonstrate its practical use in the diet recommendation and transshipment applications.

math.OC↗