Empirical orthogonal constraint generation for Multidimensional 0/1 Knapsack Problems

2020 ◽  
Vol 282 (1) ◽  
pp. 58-70 ◽  
Author(s):  
Thomas Setzer ◽  
Sebastian M. Blanc
Keyword(s):  
Knapsack Problems ◽  
Constraint Generation

Modified adaptive genetic algorithms for solving 0/1 knapsack problems

2013 ◽  
Vol 32 (6) ◽  
pp. 1682-1684
Author(s):  
Na WANG ◽  
Feng-hong XIANG ◽  
Jian-lin MAO
Keyword(s):  
Genetic Algorithms ◽  
Knapsack Problems ◽  
Adaptive Genetic Algorithms

scholarly journals Solving knapsack problems using a binary gaining sharing knowledge-based optimization algorithm

2021 ◽  
Author(s):  
Prachi Agrawal ◽  
Talari Ganesh ◽  
Ali Wagdy Mohamed
Keyword(s):  
Life Span ◽  
Population Size ◽  
Linear Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Search Space ◽  
Knapsack Problems ◽  
Local Optima ◽  
Knowledge Based ◽  
Two Stages

AbstractThis article proposes a novel binary version of recently developed Gaining Sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. A binary version of GSK named novel binary Gaining Sharing knowledge-based optimization algorithm (NBGSK) depends on mainly two binary stages: binary junior gaining sharing stage and binary senior gaining sharing stage with knowledge factor 1. These two stages enable NBGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. Moreover, to enhance the performance of NBGSK and prevent the solutions from trapping into local optima, NBGSK with population size reduction (PR-NBGSK) is introduced. It decreases the population size gradually with a linear function. The proposed NBGSK and PR-NBGSK applied to set of knapsack instances with small and large dimensions, which shows that NBGSK and PR-NBGSK are more efficient and effective in terms of convergence, robustness, and accuracy.

scholarly journals A column-and-constraint generation algorithm for two-stage stochastic programming problems

Top ◽  
2021 ◽  
Author(s):  
Denise D. Tönissen ◽  
Joachim J. Arts ◽  
Zuo-Jun Max Shen
Keyword(s):  
Stochastic Programming ◽  
Benders Decomposition ◽  
Equivalent Model ◽  
Computational Time ◽  
Two Stage ◽  
Generation Algorithm ◽  
Constraint Generation ◽  
Deterministic Equivalent ◽  
Location Routing ◽  
Relative Tolerance

AbstractThis paper presents a column-and-constraint generation algorithm for two-stage stochastic programming problems. A distinctive feature of the algorithm is that it does not assume fixed recourse and as a consequence the values and dimensions of the recourse matrix can be uncertain. The proposed algorithm contains multi-cut (partial) Benders decomposition and the deterministic equivalent model as special cases and can be used to trade-off computational speed and memory requirements. The algorithm outperforms multi-cut (partial) Benders decomposition in computational time and the deterministic equivalent model in memory requirements for a maintenance location routing problem. In addition, for instances with a large number of scenarios, the algorithm outperforms the deterministic equivalent model in both computational time and memory requirements. Furthermore, we present an adaptive relative tolerance for instances for which the solution time of the master problem is the bottleneck and the slave problems can be solved relatively efficiently. The adaptive relative tolerance is large in early iterations and converges to zero for the final iteration(s) of the algorithm. The combination of this relative adaptive tolerance with the proposed algorithm decreases the computational time of our instances even further.

scholarly journals A Hybridization of Dragonfly Algorithm Optimization and Angle Modulation Mechanism for 0-1 Knapsack Problems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 598
Author(s):  
Lin Wang ◽  
Ronghua Shi ◽  
Jian Dong
Keyword(s):  
Vertical Displacement ◽  
Continuous Functions ◽  
Convergence Speed ◽  
Knapsack Problems ◽  
Stability And Convergence ◽  
Algorithm Optimization ◽  
Solution Quality ◽  
Dragonfly Algorithm ◽  
Algorithm Stability ◽  
Angle Modulation

The dragonfly algorithm (DA) is a new intelligent algorithm based on the theory of dragonfly foraging and evading predators. DA exhibits excellent performance in solving multimodal continuous functions and engineering problems. To make this algorithm work in the binary space, this paper introduces an angle modulation mechanism on DA (called AMDA) to generate bit strings, that is, to give alternative solutions to binary problems, and uses DA to optimize the coefficients of the trigonometric function. Further, to improve the algorithm stability and convergence speed, an improved AMDA, called IAMDA, is proposed by adding one more coefficient to adjust the vertical displacement of the cosine part of the original generating function. To test the performance of IAMDA and AMDA, 12 zero-one knapsack problems are considered along with 13 classic benchmark functions. Experimental results prove that IAMDA has a superior convergence speed and solution quality as compared to other algorithms.

scholarly journals Solving Billion-Scale Knapsack Problems

2020 ◽  
Author(s):  
Xingwen Zhang ◽  
Feng Qi ◽  
Zhigang Hua ◽  
Shuang Yang
Keyword(s):  
Knapsack Problems
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