We present a fast and robust algorithm for solving biobjective mixed integer programs. The algorithm extends and merges ideas from two existing methods: the Boxed Line Method and the epsilon-Tabu Method. We demonstrate its efficacy in an extensive computational study. We also demonstrate that it is capable of producing a high-quality approximation of the nondominated … Read more
Set-valued optimization using the set approach is a research topic of high interest due to its practical relevance and numerous interdependencies to other fields of optimization. However, it is a very difficult task to solve these optimzation problems even for specific cases. In this paper we study set-valued optimization problems and develop a multiobjective optimization … Read more
In this paper, we study a first-order solution method for a particular class of set optimization problems where the solution concept is given by the set approach. We consider the case in which the set-valued objective mapping is identified by a finite number of continuously differentiable selections. The corresponding set optimization problem is then equivalent … Read more
The survey highlights some of the research topics which have attracted attention in the last two decades within the area of mathematical optimization of multiple objective functions. We give insights into topics where a huge progress can be seen within the last years. We give short introductions to the specific sub-fields as well as some … Read more
The recent success of bi-objective Branch-and-Bound (B&B) algorithms heavily relies on the efficient computation of upper and lower bound sets. Besides the classical dominance test, bound sets are used to improve the computational time by imposing inequalities derived from (partial) dominance in the objective space. This process is called objective branching since it is mostly … Read more
For a continuous multi-objective optimization problem, it is usually not a practical approach to compute all its nondominated points because there are infinitely many of them. For this reason, a typical approach is to compute an approximation of the nondominated set. A common technique for this approach is to generate a polyhedron which contains the … Read more
In supply chain optimization multiple objectives are considered simultaneously, for example to increase resilience and reduce costs. In this paper we discuss the corresponding bicriteria problems to find a good balance between these two objectives. We give a general model for supply chain resilience that integrates strategic decisions with the operational level. This modular model … Read more
Although many algorithms for multicriteria optimization provide good approximations, a precise control of their quality is challenging. In this paper we provide algorithmic tools to obtain exact approximation quality values for given approximations and develop a new method for multicriteria optimization guided by this quality. We show that the well-established “-indicator measure is NP-hard to … Read more
Derivatives are an important tool for single-objective optimization. In fact, it is commonly accepted that derivative-based methods present a better performance than derivative-free optimization approaches. In this work, we will show that the same does not apply to multiobjective derivative-based optimization, when the goal is to compute an approximation to the complete Pareto front of … Read more
We propose two Newton-type methods for solving (possibly) nonconvex unconstrained multiobjective optimization problems. The first is directly inspired by the Newton method designed to solve convex problems, whereas the second uses second-order information of the objective functions with ingredients of the steepest descent method. One of the key points of our approaches is to impose … Read more