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Evolutionary algorithms for the chance-constrained knapsack problem

Yue Xie, Oscar Harper, Hirad Assimi, Aneta Neumann, Frank Neumann
2019 Proceedings of the Genetic and Evolutionary Computation Conference on - GECCO '19  
Evolutionary algorithms have been widely used for a range of stochastic optimization problems. In most studies, the goal is to optimize the expected quality of the solution.  ...  Motivated by real-world problems where constraint violations have extremely disruptive effects, we consider a variant of the knapsack problem where the profit is maximized under the constraint that the  ...  Acknowledgments This work has been supported by the Australian Research Council through grant DP160102401 and by the South Australian Government through the Research Consortium "Unlocking Complex Resources  ... 
doi:10.1145/3321707.3321869 dblp:conf/gecco/XieHAN019 fatcat:thisiy7y3bamzkzpybi527cgka

A cross entropy algorithm for the Knapsack problem with setups

M. Caserta, E. Quiñonez Rico, A. Márquez Uribe
2008 Computers & Operations Research  
In this article we propose a new metaheuristic-based algorithm for the Integer Knapsack Problem with Setups.  ...  This problem is a generalization of the standard Integer Knapsack Problem, complicated by the presence of setup costs in the objective function as well as in the constraints.  ...  Perrot and Vanderbeck [12] proposed a dynamic programming scheme for IKPS that is a generalization of the standard dynamic programming for the integer Knapsack problem.  ... 
doi:10.1016/j.cor.2006.02.028 fatcat:c7jopdypf5geboato6p45imzfy

Evolutionary Algorithms for the Chance-Constrained Knapsack Problem [article]

Yue Xie, Oscar Harper, Hirad Assimi, Aneta Neumann, Frank Neumann
2021 arXiv   pre-print
The problem aims to maximize the profit of selected items under a constraint that the knapsack capacity bound is violated with a small probability.  ...  Evolutionary algorithms have been applied to a wide range of stochastic problems.  ...  Moreover, evolutionary algorithms have been used for various stochastic problems such as the stochastic job shop problem [16] , the stochastic chemical batch scheduling problem [41] , and other dynamic  ... 
arXiv:1902.04767v3 fatcat:3mh2o7dwmbftdkkfjkmplbekxy

Recoverable Robustness by Column Generation [chapter]

P. C. Bouman, J. M. van den Akker, J. A. Hoogeveen
2011 Lecture Notes in Computer Science  
We show our approach on two example problems: the size robust knapsack problem, in which the knapsack size may get reduced, and the demand robust shortest path problem, in which the sink is uncertain and  ...  In this paper, we apply the technique of column generation to find solutions to recoverable robustness problems. We consider two types of solution approaches: separate recovery and combined recovery.  ...  We use column generation for recoverable robust optimization. We will present column generation models for the size robust knapsack problem and for the demand robust shortest path problem.  ... 
doi:10.1007/978-3-642-23719-5_19 fatcat:xelcwsylu5foheyeclldfew32q

A Shortest-Path-Based Approach for the Stochastic Knapsack Problem with Non-Decreasing Expected Overfilling Costs

Troels Martin Range, Dawid Kozlowski, Niels Christian Petersen
2017 Social Science Research Network  
We formulate the SKP as a network problem and demonstrate that it can be solved by a label-setting dynamic programming approach for the Shortest Path Problem with Resource Constraint (SPPRC).  ...  The knapsack problem (KP) is concerned with the selection of a subset of multiple items with known positive values and weights such that the total value of selected items is maximized and their total weight  ...  Introduction The starting point for the knapsack problem (KP) is a set of multiple items and a knapsack with a given capacity. Each item is associated with a positive value and a weight.  ... 
doi:10.2139/ssrn.2997916 fatcat:bhk7tzckvfd3zlftlyftyxxlbi

Upper bounds for the 0-1 stochastic knapsack problem and a B&B algorithm

Stefanie Kosuch, Abdel Lisser
2009 Annals of Operations Research  
In this paper we study and solve two different variants of static knapsack problems with random weights: The stochastic knapsack problem with simple recourse as well as the stochastic knapsack problem  ...  with probabilistic constraint.  ...  ., 2004) the focus lies on the comparison of adaptive and non-adaptive policies for a stochastic knapsack problem where the size of each item is random but is revealed when the item is chosen.  ... 
doi:10.1007/s10479-009-0577-5 fatcat:bwh4tthcvbc2bpot4ansfzw64u

Specific Single- and Multi-Objective Evolutionary Algorithms for the Chance-Constrained Knapsack Problem [article]

Yue Xie, Aneta Neumann, Frank Neumann
2020 arXiv   pre-print
The chance-constrained knapsack problem is a variant of the classical knapsack problem where each item has a weight distribution instead of a deterministic weight.  ...  We examine the use of heavy-tail mutations and introduce a problem-specific crossover operator to deal with the chance-constrained knapsack problem.  ...  [1] studied the dynamic chance-constrained knapsack problem and proposed another objective function to deal with the dynamic capacity of the knapsack.  ... 
arXiv:2004.03205v2 fatcat:c6nlrbisebgj3nzyrnyyrknsom

A Branch-and-Price Algorithm for the Multiperiod Single-Sourcing Problem

Richard Freling, H. Edwin Romeijn, Dolores Romero Morales, Albert P. M. Wagelmans
2003 Operations Research  
We reformulate the MPSSP as a Generalized Assignment Problem (GAP) with a convex objective function. We then extend a branch-and-price algorithm that was developed for the GAP to this problem.  ...  Integer programming: branch-and-price algorithm and penalized knapsack problem.  ...  The work of the third author was supported in part by the Netherlands Organization for Scientific Research (NWO) and the National Science Foundation under grant no. DMI-0085682.  ... 
doi:10.1287/opre.51.6.922.24914 fatcat:srnyj42td5azzox4f76crn6o2a

Evolutionary Bi-objective Optimization for the Dynamic Chance-Constrained Knapsack Problem Based on Tail Bound Objectives [article]

Hirad Assimi, Oscar Harper, Yue Xie, Aneta Neumann, Frank Neumann
2020 arXiv   pre-print
In this paper, we consider the dynamic chance-constrained knapsack problem where the weight of each item is stochastic, the capacity constraint changes dynamically over time, and the objective is to maximize  ...  Real-world combinatorial optimization problems are often stochastic and dynamic. Therefore, it is essential to make optimal and reliable decisions with a holistic approach.  ...  ACKNOWLEDGEMENTS This work has been supported by the Australian Research Council through grant DP160102401 and by the South Australian Government through the Research Consortium "Unlocking Complex Resources  ... 
arXiv:2002.06766v1 fatcat:wrgxgr4lxjhjphqnf6xqijstwu

Page 1585 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
Just like in the knapsack problem, there is a constraint on the total weight of the selected items, and, moreover, for each class, there is a bound on the multiplicity of the selected items.  ...  A, 125-136. The bounded multiple-class binary knapsack problem is a variant of the knapsack problem. Items are classified and in each class the item weights are multiples of the class weight.  ... 

Absolute semi-deviation risk measure for ordering problem with transportation cost in Supply Chain [article]

Saravanan Venkatachalam, Lewis Ntaimo
2016 arXiv   pre-print
We perform computational study on a supply chain replenishment problem and standard knapsack instances.  ...  The proposed decomposition algorithm uses another risk-measure 'expected excess', and provides tighter bounds for ASD stochastic models.  ...  This is the most general class of dynamic lot sizing problem, involving multiple items, capacity restrictions and a common replenishment cost structure with stochastic demand.  ... 
arXiv:1605.08391v1 fatcat:joq6ojuevvh37ghosgb7tx6vjq

Towards Stochastic Constraint Programming: A Study of Onine Multi-Choice Knapsack with Deadlines [chapter]

Thierry Benoist, Eric Bourreau, Yves Caseau, Benoît Rottembourg
2001 Lecture Notes in Computer Science  
This benchmark is used to test a framework with four different dynamic strategies that utilize a different combination of the stochastic and combinatorial aspects of the problem.  ...  Constraint Programming (CP) is a very general programming paradigm that proved its efficiency on solving complex industrial problems.  ...  different topics that must be investigated before we may develop a generic method for solving stochastic combinatorial optimization problems with constraints: 1.  ... 
doi:10.1007/3-540-45578-7_5 fatcat:jg4dra4vojedfaideao3uuhx3y

Approximation Algorithms for Stochastic Combinatorial Optimization Problems

Jian Li, Yu Liu
2016 Journal of the Operations Research Society of China  
Our purpose is to provide the readers a quick glimpse to the models, problems and techniques in this area, and hopefully inspire new contributions.  ...  for designing approximation algorithms for stochastic combinatorial optimization problems, including the linear programming relaxation approach, boosted sampling, content resolution schemes, Poisson approximation  ...  We apologize in advance for the omission of any important results. We would like to thank Xiaodong Hu for inviting us to write the survey.  ... 
doi:10.1007/s40305-015-0116-9 fatcat:wewxh47vgjgazg3thpbnonreaq

An Incremental Model for Combinatorial Maximization Problems [chapter]

Jeff Hartline, Alexa Sharp
2006 Lecture Notes in Computer Science  
We introduce a general model for such problems, and define incremental versions of maximum flow, bipartite matching, and knapsack.  ...  With this in mind, we give general yet simple techniques to adapt algorithms for optimization problems to their respective incremental versions, and discuss tightness of these adaptations with respect  ...  Maximum Flow The Knapsack The knapsack problem is defined by a knapsack capacity B and a set of items U , item u ∈ U with size |u| and value vu; the elements are the items we could place in our knapsack  ... 
doi:10.1007/11764298_4 fatcat:usppqcoxvnasnhua7mqzla2bja

An agent-based stochastic ruler approach for a stochastic knapsack problem with sequential competition

Matthew R. Gibson, Jeffrey W. Ohlmann, Michael J. Fry
2010 Computers & Operations Research  
Utilizing a multi-period bounded multiple-choice knapsack framework, we introduce a general discrete stochastic optimization model that allows a nonlinear objective function, cardinality constraints, and  ...  Utilizing a set of greedy selection rules and agent-based modeling to simulate the competitors' actions, we solve the problem with a stochastic ruler approach that incorporates beam search to determine  ...  An agent-based stochastic ruler approach for a stochastic knapsack problem with sequential competition.  ... 
doi:10.1016/j.cor.2009.02.028 fatcat:xv5wppc72raa3c3fsytmmiyk54
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