Hypervolume is most likely the most often used set quality indicator in (evolutionary) multi-objective optimization. It may be used to compare the quality of solution sets whose images in the objective space are approximations of the true Pareto front. Although in this way we may compare two or more approximations, our knowledge is limited without … Read more
In this paper, we investigate solution approaches in set optimization that are based on so-called vectorization strategies. Thereby, the original set-valued problems are reformulated as multi-objective optimization problems, whose optimal solution sets approximate those of the original ones in a certain sense. We consider both infinite-dimensional and finite-dimensional vectorization approaches. In doing so, we collect … Read more
We consider an unconstrained multi-criteria optimization problem with finite sum objective functions. The proposed algorithm belongs to a non-monotone trust-region framework where additional sampling approach is used to govern the sample size and the acceptance of a candidate point. Depending on the problem, the method can result in a mini-batch or an increasing sample size … Read more
When dealing with a multi-objective optimization problem, obtaining a comprehensive representation of the Pareto front can be computationally expensive. Furthermore, identifying the most representative Pareto solutions can be difficult and sometimes ambiguous. A popular selection are the so-called Pareto knee solutions, where a small improvement in any objective leads to a large deterioration in at … Read more
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 considered is a multi-objective optimization problem, 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 functions and … 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
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
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