In this paper, we investigate two known solution approaches for set-valued optimization problems, both of which are based on so-called vectorization strategies. These strategies consist of deriving a parametric family of multi-objective optimization problems whose optimal solution sets approximate those of the original set-valued problem with arbitrary accuracy in a certain sense. Thus, these approaches … Read more
The problem we consider is a multi-objective optimization prob- lem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust region framework with probabilistic model functions, able to cope with noisy problems, using inaccurate … Read more
In this article, we present several examples of special nonlinear conjugate gradient directions for nonlinear (non-convex) multi-objective optimization. These directions provide a descent direction for the objectives, independent of the line-search. This way, we can provide an algorithm with simple, Armijo-like backtracking and prove convergence to first-order critical points. In contrast to other popular conjugate … Read more
In this work we propose a general nonmonotone line-search method for nonconvex multi-objective optimization problems with convex constraints. At the \(k\)th iteration, the degree of nonmonotonicity is controlled by a vector \(\nu_{k}\) with nonnegative components. Different choices for \(\nu_{k}\) lead to different nonmonotone step-size rules. Assuming that the sequence \(\left\{\nu_{k}\right\}_{k\geq 0}\) is summable, and that … Read more
Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for multiobjective optimization converge slowly, even for well-conditioned problems, due to the objective imbalances. To address this limitation, we incorporate curvature information to scale each objective within … Read more
We present an algorithm for triobjective nonlinear integer programs that combines the epsilon-constrained method with available oracles for biobjective integer programs. We prove that our method is able to detect the nondominated set within a finite number of iterations. Specific strategies to avoid the detection of weakly nondominated points are devised. The method is then … Read more
This paper is devoted to the Truck-to-dock Door Assignment Problem. Two integer programming formulations introduced after 2009 are examined. Our review of the literature takes note of the criticisms and limitations addressed to the seminal work of 2009. Although the published adjustments that followed present strong argument and technical background, we have identified several errors, … Read more
Motivated by our collaboration with a residency program at an academic health system, we propose new integer programming (IP) approaches for the resident-to-rotation assignment problem (RRAP). Given sets of residents, resident classes, and departments, as well as a block structure for each class, staffing needs, rotation requirements for each class, program rules, and resident vacation … Read more
In this work, we present an algorithm for computing an enclosure for multi-objective mixed-integer nonconvex optimization problems. In contrast to existing solvers for this type of problem, this algorithm is not based on a branch-and-bound scheme but rather relies on a relax-and-refine approach. While this is an established technique in single-objective optimization, several adaptions to … Read more
We consider a two-stage stochastic multi-objective linear program (TSSMOLP) which is a natural generalization of the well-studied two-stage stochastic linear program (TSSLP) allowing modelers to specify multiple objectives in each stage. The second-stage recourse decision is governed by an uncertain multi-objective linear program (MOLP) whose solution maps to an uncertain second-stage nondominated set. The TSSMOLP … Read more