Related papers: The multiobjective multidimensional knapsack probl…
Tasks in multi-task learning often correlate, conflict, or even compete with each other. As a result, a single solution that is optimal for all tasks rarely exists. Recent papers introduced the concept of Pareto optimality to this field and…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
We present a Reinforcement Learning (RL) solution to the view planning problem (VPP), which generates a sequence of view points that are capable of sensing all accessible area of a given object represented as a 3D model. In doing so, the…
The Multidimensional Assignment Problem (MAP) (abbreviated s-AP in the case of s dimensions) is an extension of the well-known assignment problem. The most studied case of MAP is 3-AP, though the problems with larger values of s also have a…
Multi-objective combinatorial optimization problems (MOCOP) frequently arise in practical applications that require the simultaneous optimization of conflicting objectives. Although traditional evolutionary algorithms can be effective, they…
In this paper, we study the following knapsack problem: Given a list of squares with profits, we are requested to pack a sublist of them into a rectangular bin (not a unit square bin) to make profits in the bin as large as possible. We…
Bayesian Optimization (BO) is a powerful tool for optimizing expensive black-box objective functions. While extensive research has been conducted on the single-objective optimization problem, the multi-objective optimization problem remains…
This paper addresses a generalization of the well known multi-agent path finding (MAPF) problem that optimizes multiple conflicting objectives simultaneously such as travel time and path risk. This generalization, referred to as…
Multimodality is one of the biggest difficulties for optimization as local optima are often preventing algorithms from making progress. This does not only challenge local strategies that can get stuck. It also hinders meta-heuristics like…
We consider the product knapsack problem, which is the variant of the classical 0-1 knapsack problem where the objective consists of maximizing the product of the profits of the selected items. These profits are allowed to be positive or…
In this paper, we introduce several new quasi-Newton methods for the composite multiobjective optimization problems (in short, CMOP) with Armijo line search. These multiobjective versions of quasi-Newton methods include BFGS quasi-Newnon…
The labeled MRPP (Multi-Robot Path Planning) problem involves routing robots from start to goal configurations efficiently while avoiding collisions. Despite progress in solution quality and runtime, its complexity and industrial relevance…
K-Means algorithm is a popular clustering method. However, it has two limitations: 1) it gets stuck easily in spurious local minima, and 2) the number of clusters k has to be given a priori. To solve these two issues, a multi-prototypes…
In this article we propose a descent method for equality and inequality constrained multiobjective optimization problems (MOPs) which generalizes the steepest descent method for unconstrained MOPs by Fliege and Svaiter to constrained…
Creating meaningful interpretations for black-box machine learning models involves balancing two often conflicting objectives: accuracy and explainability. Exploring the trade-off between these objectives is essential for developing…
We consider the chance-constrained binary knapsack problem (CKP), where the item weights are independent and normally distributed. We introduce a continuous relaxation for the CKP, represented as a non-convex optimization problem, which we…
The Time-Invariant Incremental Knapsack problem (IIK) is a generalization of Maximum Knapsack to a discrete multi-period setting. At each time, capacity increases and items can be added, but not removed from the knapsack. The goal is to…
This paper presents an algorithm for solving multiobjective optimization problems involving composite functions, where we minimize a quadratic model that approximates $F(x) - F(x^k)$ and that can be derivative-free. We establish theoretical…
Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization. As solving large-scale combinatorial optimization problems is challenging, primal heuristics have been developed to quickly…
Multi-Objective Optimization (MOO) is very difficult for expensive functions because most current MOO methods rely on a large number of function evaluations to get an accurate solution. We address this problem with surrogate approximation…