Multi-Criteria Optimization – Optimization Online

A Decision-Support Framework for Structuring and Reducing Large Multi-Objective Solution Sets via Clustering: An Application to Proton Therapy

Published: 2026/08/17

nicole

(Mixed) Integer Linear Programming, Biomedical Applications, Multi-Criteria Optimization clustering, decision support, extended goal programming, goal programming, intensity modulated proton therapy, multi-criteria decision analysis, multi-objective optimization, multiobjective optimization, OR for medicine, Pareto set reduction, radiotherapy treatment planning, representative selection.

This paper proposes a four-stage decision-support framework for structuring and reducing large multi-objective solution sets into compact and interpretable collections of representative alternatives. The methodology combines: (Phase 1) systematic solution generation through extended goal programming and structured preference exploration; (Phase 2) robustness-aware enrichment and profiling under weight sensitivity analysis; (Phase 3) filtering and dominance-based reduction … Read more

Attainability of properly efficient points via weighted norm scalarization

Published: 2026/08/07

Multi-Criteria Optimization multiobjective optimization, proper efficiency, supportedness, trade-off bound, weighted norm scalarization

We show that efficient points can be obtained with the weighted norm scalarization under assumptions less restrictive than in the existing literature. For properly efficient points with a given trade-off bound, we provide an easy-to-compute lower bound on the norm parameter that allows the approximation of the desired points within a specified tolerance. We apply … Read more

Exact Branch-and-Price Algorithm for Live Operating Room Reoptimization

Published: 2026/07/31

(Mixed) Integer Linear Programming, Multi-Criteria Optimization, Scheduling branch-and-price, column generation, completion bounds, multi-criteria optimization, Operating Theatre Scheduling

Live reoptimization of operating room schedules is required to cope with disruptions such as emergency arrivals and deviations in surgery durations under strict time limits. The resulting problem can be formulated as a large-scale Resource Constrained Project Scheduling Problem (RCPSP). While exact optimization methods are attractive in this context due to their ability to provide … Read more

Convexlikeness and Supportedness in Quadratic Multiobjective Optimization

Published: 2026/07/19

Multi-Criteria Optimization, Quadratic Programming convexlikeness, hidden convexity, multiobjective optimization, nonconvex optimization, nonconvex quadratic programming, s-lemma, supportedness, Weighted sum scalarization

This paper studies geometric and structural properties of quadratic multiobjective optimization problems. Thereby, a multiobjective optimization problem is called convexlike if the upper image, i.e., the image set plus the nonnegative orthant, is a convex set. Moreover, we say that a feasible point is supported in case it is a minimal solution of a weighted … Read more

Exploring polynomial models in the Search Step of Direct Multisearch

Published: 2026/07/14

Multi-Criteria Optimization, Nonlinear Optimization derivative-free optimization, direct-search methods, multiobjective optimization, Pareto front approximation, quadratic interpolation

Direct Multisearch (DMS) is a class of direct-search algorithms designed for multiobjective derivative-free optimization. Its framework consists of an optional search step and a poll step, the latter ensuring the corresponding theoretical convergence properties. Recently, a search strategy based on the minimization of quadratic polynomial models, constructed from previously evaluated points, was proposed to improve … Read more

An algorithm for generating Lagrangian bound sets in Multiobjective Integer Programming

Published: 2026/05/24

Integer Programming, Multi-Criteria Optimization bound sets, branch and bound algorithm, lagrangian relaxation, Multiobjective Discrete Optimization

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

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

Published: 2026/05/14

Multi-Criteria Optimization Alternating Optimization, block coordinate descent method, multi-objective optimization, stochastic optimization

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

Published: 2026/05/07

Integer Programming, Multi-Criteria Optimization approximation, Bi-Objective Integer Programming, Binary Search, Branch-and-Bound, Criterion Space Search Method

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

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

Published: 2026/04/18

Combinatorial Optimization, Multi-Criteria Optimization Allocation problem, bound sets, branch and bound algorithm, labeling algorithm, multi-objective combinatorial optimization, Uncapacited facility location problem

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

Objective-Function Free Multi-Objective Optimization: Rate of Convergence and Performance of an Adagrad-like algorithm

Published: 2026/02/02

Multi-Criteria Optimization, Unconstrained Optimization Adagrad-like algorithm, multi-objective optimization, objective-function-free optimization

We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not rely on the dominance property to accept new iterates, which allows for a flexible and function-free optimization framework. New points are obtained using an … Read more