Related papers: Branch-and-bound for biobjective mixed-integer lin…

We consider bi-objective ranking and selection problems, where the goal is to correctly identify the Pareto optimal solutions among a finite set of candidates for which the two objective outcomes have been observed with uncertainty (e.g.,…

We consider the problem of optimally designing a system for repeated use under uncertainty. We develop a modeling framework that integrates design and operational phases, which are represented by a mixed-integer program and discounted-cost…

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural…

In this work, the author presents a novel method for finding descent directions shared by two or more differentiable functions defined on the same unconstrained domain space. Then, the author illustrates an alternative Multiple-Gradient…

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include…

Mixed Integer Programming (MIP) solvers rely on an array of sophisticated heuristics developed with decades of research to solve large-scale MIP instances encountered in practice. Machine learning offers to automatically construct better…

In this paper, an exact method is proposed to optimize two fractional linear functions over the efficient set of a fractional multiobjective linear problem (MOILFP). This type of problems is encountered when there are two decision makers…

We develop a branch-and-bound algorithm for the integer D-optimality problem, a central problem in statistical design theory, based on two convex relaxations, employing variable-bound tightening and fast local-search procedures, testing our…

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the…

The Branch-and-bound (B&B) algorithm is the main solver for Mixed Integer Linear Programs (MILPs), where the selection of branching variable is essential to computational efficiency. However, traditional heuristics for branching often fail…

In this paper, we propose a new descent method, termed as multiobjective memory gradient method, for finding Pareto critical points of a multiobjective optimization problem. The main thought in this method is to select a combination of the…

Multi-agent optimization problems with many objective functions have drawn much interest over the past two decades. Many works on the subject minimize the sum of objective functions, which implicitly carries a decision about the problem…

Memory bandwidth regulation and cache partitioning are widely used techniques for achieving predictable timing in real-time computing systems. Combined with partitioned scheduling, these methods require careful co-allocation of tasks and…

Machine learning is increasingly used to improve decisions within branch-and-bound algorithms for mixed-integer programming. Many existing approaches rely on deep learning, which often requires very large training datasets and substantial…

We consider the problem of finding a fixed point of a nonexpansive mapping, which is also a solution of a pseudo-monotone equilibrium problem, where the bifunction in the equilibrium problem is the sum of two ones. We propose a splitting…

Due to the expected disparity in quantum vs. classical clock speeds, quantum advantage for branch and bound algorithms is more likely achievable in settings involving large search trees and low operator evaluation costs. Therefore, in this…

We propose a mixed-integer quadratic programming (QP) solver that is suitable for use in embedded applications, for example, hybrid model predictive control (MPC). The solver is based on the branch-and-bound method, and uses a recently…

One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very…

In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…

Machine learning components commonly appear in larger decision-making pipelines; however, the model training process typically focuses only on a loss that measures accuracy between predicted values and ground truth values. Decision-focused…