Related papers: A linear programming based heuristic framework for…
We study a robust extensible bin packing problem with budgeted uncertainty, under a budgeted uncertainty model where item sizes are defined to lie in the intersection of a box with a one-norm ball. We propose a scenario generation algorithm…
Since the 1990s, considerable empirical work has been carried out to train statistical models, such as neural networks (NNs), as learned heuristics for combinatorial optimization (CO) problems. When successful, such an approach eliminates…
In this paper, we propose a fast method for exactly enumerating a very large number of all lower cost solutions for various combinatorial problems. Our method is based on backtracking for a given decision diagram which represents all the…
Heuristic algorithms such as simulated annealing, Concorde, and METIS are effective and widely used approaches to find solutions to combinatorial optimization problems. However, they are limited by the high sample complexity required to…
A popular approach for addressing uncertainty in variational inequality problems is by solving the expected residual minimization (ERM) problem. This avenue necessitates distributional information associated with the uncertainty and…
The aim of this paper is twofold. First, we introduce "resource constraints" as a general concept that covers many practical restrictions on experimental design. Second, for computing efficient exact designs of experiments under any…
This paper studies binary linear programming problems in the presence of uncertainties that may cause solution values to change during implementation. This type of uncertainty, termed implementation uncertainty, is modeled explicitly…
We study single-stage decision problems in which a subset of items with minimum total cost has to be selected at once from a given set of items, subject to two costs of each item -fixed and uncertain -and cardinality constraints for each…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
We use the technique of information relaxation to develop a duality-driven iterative approach to obtaining and improving confidence interval estimates for the true value of finite-horizon stochastic dynamic programming problems. We show…
We introduce the Discrete Min-Max Violation (DMMV) as a general optimization problem which seeks an assignment of discrete values to variables that minimizes the largest constraint violation. This context-free mathematical formulation is…
This paper studies the non-preemptive single-machine scheduling problem with heterogeneous release times and processing times, with the objective of minimizing total waiting time. The problem is known to be NP-hard. By modeling machine idle…
Reasoning models represent a significant advance in LLM capabilities, particularly for complex reasoning tasks such as mathematics and coding. Previous studies confirm that parallel test-time compute-sampling multiple solutions and…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
We study the stochastic shortest path (SSP) problem in reinforcement learning with linear function approximation, where the transition kernel is represented as a linear mixture of unknown models. We call this class of SSP problems as linear…
Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available…
In this paper, a robust optimization framework is developed to train shallow neural networks based on reachability analysis of neural networks. To characterize noises of input data, the input training data is disturbed in the description of…
We present a powerful general framework for designing data-dependent optimization algorithms, building upon and unifying recent techniques in adaptive regularization, optimistic gradient predictions, and problem-dependent randomization. We…
In decision-making under uncertainty, several criteria have been studied to aggregate the performance of a solution over multiple possible scenarios. This paper introduces a novel variant of ordered weighted averaging (OWA) for optimization…
Increasing the complexity of solving budgetary allocation (NP-hardness problem) has led a wide range of methods to minimize the costs. Metaheuristics and Linear Programming (LP) are the most optimization in this fields. Therefore, this…