Realistic decision problems are inherently multiobjective and uncertain. To manage both of these complexities, robust multiobjective optimization strives to aid the decision maker in finding a decision which is Pareto efficient and is hedged against the worst-case scenario. In this paper, we present a robustness approach which is grounded in the decision maker’s preferences by … Read more
One goal of multiobjective optimization is to approximate the nondominated set in the image space. One widely used approximation concept is that of enclosures. These are unions of closed boxes that cover the nondominated set. The bounds of these boxes form the lower and upper bound sets of the enclosure. The quality of an enclosure … Read more
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
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
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
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
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
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
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
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