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In this paper, we consider the classic stochastic (dynamic) knapsack problem, a fundamental mathematical model in revenue management, with general time-varying random demand. Our main goal is to study the optimal policies, which can be…

Optimization and Control · Mathematics 2018-07-19 Yingdong Lu

The submodular knapsack problem (SKP), which seeks to maximize a submodular set function by selecting a subset of elements within a given budget, is an important discrete optimization problem. The majority of existing approaches to solving…

Data Structures and Algorithms · Computer Science 2025-07-16 Yimin Hao , Yi Zhou , Chao Xu , Zhang-Hua Fu

Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…

Data Structures and Algorithms · Computer Science 2019-08-07 Brian Brubach , Karthik Abinav Sankararaman , Aravind Srinivasan , Pan Xu

We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…

Optimization and Control · Mathematics 2017-12-20 Ewa M. Bednarczuk , Janusz Miroforidis , Przemysław Pyzel

This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…

Optimization and Control · Mathematics 2016-10-31 Insoon Yang , Samuel A. Burden , Ram Rajagopal , S. Shankar Sastry , Claire J. Tomlin

In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…

Data Structures and Algorithms · Computer Science 2020-12-22 Wenxin Li

Since its inception in the mid-60s, the inventory staggering problem has been explored and exploited in a wide range of application domains, such as production planning, stock control systems, warehousing, and aerospace/defense logistics.…

Data Structures and Algorithms · Computer Science 2025-06-13 Noga Alon , Danny Segev

Quality diversity (QD) algorithms have been shown to be very successful when dealing with problems in areas such as robotics, games and combinatorial optimization. They aim to maximize the quality of solutions for different regions of the…

Neural and Evolutionary Computing · Computer Science 2022-07-29 Adel Nikfarjam , Anh Viet Do , Frank Neumann

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…

Optimization and Control · Mathematics 2024-03-12 Junyoung Kim , Kyungsik Lee

Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…

Optimization and Control · Mathematics 2024-01-30 Alexander Engelmann , Maisa B. Bandeira , Timm Faulwasser

The area of parameterized approximation seeks to combine approximation and parameterized algorithms to obtain, e.g., (1+eps)-approximations in f(k,eps)n^{O(1)} time where k is some parameter of the input. We obtain the following results on…

Data Structures and Algorithms · Computer Science 2019-06-27 Fabrizio Grandoni , Stefan Kratsch , Andreas Wiese

This work proposes an efficient parallel algorithm for non-monotone submodular maximization under a knapsack constraint problem over the ground set of size $n$. Our algorithm improves the best approximation factor of the existing parallel…

Artificial Intelligence · Computer Science 2024-09-09 Tan D. Tran , Canh V. Pham , Dung T. K. Ha , Phuong N. H. Pham

We consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack, while the follower chooses a feasible packing maximizing his own profit. The leader's aim is to optimize a linear objective function…

Data Structures and Algorithms · Computer Science 2022-07-19 Christoph Buchheim , Dorothee Henke , Jannik Irmai

We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…

Data Structures and Algorithms · Computer Science 2026-01-01 Danny Hermelin , Danny Segev , Dvir Shabtay

We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…

Data Structures and Algorithms · Computer Science 2008-10-29 Marek Cygan , Lukasz Kowalik , Marcin Pilipczuk , Mateusz Wykurz

In the knapsack problem under explorable uncertainty, we are given a knapsack instance with uncertain item profits. Instead of having access to the precise profits, we are only given uncertainty intervals that are guaranteed to contain the…

Data Structures and Algorithms · Computer Science 2025-07-04 Jens Schlöter

The knapsack problem is one of the classical problems in combinatorial optimization: Given a set of items, each specified by its size and profit, the goal is to find a maximum profit packing into a knapsack of bounded capacity. In the…

Data Structures and Algorithms · Computer Science 2020-12-02 Susanne Albers , Arindam Khan , Leon Ladewig

Most exact algorithms for general partially observable Markov decision processes (POMDPs) use a form of dynamic programming in which a piecewise-linear and convex representation of one value function is transformed into another. We examine…

Artificial Intelligence · Computer Science 2013-02-08 Anthony R. Cassandra , Michael L. Littman , Nevin Lianwen Zhang

In this focused technical paper, we present long-awaited algorithmic advances toward the efficient construction of near-optimal replenishment policies for a true inventory management classic, the economic warehouse lot scheduling problem.…

Data Structures and Algorithms · Computer Science 2026-01-23 Danny Segev

Combinatorial optimization has wide applications from industry to natural science. Ising machines bring an emerging computing paradigm for efficiently solving a combinatorial optimization problem by searching a ground state of a given Ising…

Statistical Mechanics · Physics 2024-07-16 Kentaro Ohno , Tatsuhiko Shirai , Nozomu Togawa