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An algorithm for generating Lagrangian bound sets in Multiobjective Integer Programming

Categories Integer Programming, Multi-Criteria Optimization Tags , , ,

Lagrangian relaxation is a well-established technique for deriving strong bounds in single-objective discrete optimization. Its generalization to the multiobjective setting is not straightforward, as preserving the multiobjective structure leads to bound sets rather than scalar bounds. Recent studies show the existence of Lagrange multipliers that can yield tighter bound sets than those obtained from convex … Read more

Optimality Gap of Tailored Base-Surge Policies Decays Exponentially in Regular-Source Lead Times for Dual-Sourcing Models

Categories Dynamic Programming, Stochastic Programming, Supply Chain Management Tags , , , , ,

This paper resolves an open problem posed in the literature by proving that, in dual-sourcing inventory systems, the optimality gap of tailored base-surge (TBS) policies decays exponentially with the regular source lead time, with the express-source lead time fixed. In contrast to the existing approach, which relies on conditional Jensen inequalities and a vanishing-discount argument … Read more

Stochastic block coordinate and function alternation for multi-objective optimization and learning

Categories Multi-Criteria Optimization Tags , , ,

Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step, such methods require computing gradients with respect to all variables at every iteration, resulting in high computational costs in large-scale settings. In this work, we … Read more

A Binary Search-Based Criterion Space Algorithm for Solving Bi-Objective Integer Programs: The Quadtree Search Method

Categories Integer Programming, Multi-Criteria Optimization Tags , , , ,

We propose an exact binary search-based branch-and-bound algorithm, termed the Quadtree Search Method, for solving bi-objective integer programs. The existing literature on criterion space search methods for multi-objective optimization predominantly assumes that subproblems can be solved to optimality, an assumption that becomes computationally prohibitive for hard instances. In contrast, our approach departs from this assumption … Read more

Supervised feature selection via multiobjective programming and its application in the medical field

Categories Applications - OR and Management Sciences, Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization, Other Topics Tags , , , ,

In this study, we model the supervised feature selection problem using a novel approach: convex bi-objective optimization. Traditional methods have addressed this problem by maximizing relevance to class labels and minimizing redundancy among features. Recently, Wang et al. [30] formulated this problem as a single-objective convex optimization, yielding only a unique solution. Unlike that, we … Read more

Paving and computing the set of nondominated points for the bi-objective 0/1 uncapacitated facility location problem

Categories Combinatorial Optimization, Multi-Criteria Optimization Tags , , , , ,

The paper presents a three-phase algorithm to compute the set of nondominated points for the binary version of the uncapacitated facility location problem with two objectives. The first phase constructs a paving in objective space which is a collection of boxes that covers all nondominated points. The paving procedure is a branch and bound algorithm … Read more

An Interpretable Ensemble Heuristic for Principal-Agent Games with Machine Learning

Categories Applications - OR and Management Sciences, Game Theory, Optimization in Data Science

This paper addresses the challenge of enhancing public policy decision-making by efficiently solving principal-agent models (PAMs) for public-private partnerships, a critical yet computationally demanding problem. We develop a fast, interpretable, and generalizable approach to support policy decisions under these settings. We propose an interpretable ensemble heuristic (EH) that integrates Machine Learning (ML), Operations Research (OR), … Read more

Optimal Transport on Lie Group Orbits

Categories Infinite Dimensional Optimization, Other Topics

In its most general form, the optimal problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and formalize it using Lie group theory. Fixing a Lie group action and a reference distribution, we study optimal transport between measures in the same … Read more

On Stationary Conditions and the Convergence of Augmented Lagrangian methods for Generalized Nash Equilibrium Problems

Categories Constrained Nonlinear Optimization, Game Theory, Nonlinear Optimization Tags , , , ,

In this work, we study stationarity conditions and constraint qualifications (CQs) tailored to Generalized Nash Equilibrium Problems (GNEPs) and analyze their relationships and implications for the global convergence of algorithms. We recall that GNEPs generalize Nash Equilibrium Problems (NEPs) in that the feasible strategy set of each player depends on the strategies chosen by the … Read more

Solving Convex Quadratic Optimization with Indicators Over Structured Graphs

Categories (Mixed) Integer Nonlinear Programming, Dynamic Programming Tags ,

This paper studies convex quadratic minimization problems in which each continuous variable is coupled with a binary indicator variable. We focus on the structured setting where the Hessian matrix of the quadratic term is positive definite and exhibits sparsity. We develop an exact parametric dynamic programming algorithm whose computational complexity depends explicitly on the treewidth … Read more