Related papers: Branch-and-bound for biobjective mixed-integer lin…
A key ingredient in branch and bound (B&B) solvers for mixed-integer programming (MIP) is the selection of branching variables since poor or arbitrary selection can affect the size of the resulting search trees by orders of magnitude. A…
In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. The constrained problem is reduced to a discontinuous unconstrained problem…
Computing the exact optimal experimental design has been a longstanding challenge in various scientific fields. This problem, when formulated using a specific information function, becomes a mixed-integer nonlinear programming (MINLP)…
Dealing with multi-objective problems by using generation methods has some interesting advantages since it provides the decision-maker with the complete information about the set of non-dominated points (Pareto front) and a clear overview…
Most combinatorial optimization problems can be formulated as mixed integer linear programming (MILP), in which branch-and-bound (B\&B) is a general and widely used method. Recently, learning to branch has become a hot research topic in the…
Decision trees are powerful tools for classification and regression that attract many researchers working in the burgeoning area of machine learning. One advantage of decision trees over other methods is their interpretability, which is…
A hybrid framework combining the branch and bound method with multiobjective evolutionary algorithms is proposed for nonconvex multiobjective optimization. The hybridization exploits the complementary character of the two optimization…
Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split:…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. In this context, verification involves proving or disproving that an NN…
We present a branch-and-bound algorithm for globally solving parabolic optimal control problems with binary switches that have bounded variation and possibly need to satisfy further combinatorial constraints. More precisely, for a given…
Machine learning is increasingly used to guide branch-and-cut (B&C) for mixed-integer linear programming by learning score-based policies for selecting branching variables and cutting planes. Many approaches train on local signals from…
We propose an exact algorithm for solving biobjective integer programming problems, which arise in various applications of operations research. The algorithm is based on solving Pascoletti-Serafini scalarizations to search specified regions…
Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…
We present a simple and at the same time fficient algorithm to compute all nondominated extreme points in the outcome set of multi-objective mixed integer linear programmes in any dimension. The method generalizes the well-known dichotomic…
This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier…
Most state-of-the-art branch-and-bound solvers for mixed-integer linear programming rely on limited-precision floating-point arithmetic and use numerical tolerances when reasoning about feasibility and optimality during their search. While…
Branch-and-bound algorithms (B&B) and polynomial-time approximation schemes (PTAS) are two seemingly distant areas of combinatorial optimization. We intend to (partially) bridge the gap between them while expanding the boundary of…
Multi-objective optimization is a widely studied problem in diverse fields, such as engineering and finance, that seeks to identify a set of non-dominated solutions that provide optimal trade-offs among competing objectives. However, the…
Overparameterization and overfitting are common concerns when designing and training deep neural networks, that are often counteracted by pruning and regularization strategies. However, these strategies remain secondary to most learning…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…