scholarly journals On the complexity of determining tolerances for ε-optimal solutions to min-max combinatorial optimization problems

2003 ◽  
Vol 30 (3) ◽  
pp. 305-313
Author(s):  
Diptesh Ghosh ◽  
Gerard Sierksma
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Optimal Solutions ◽  
Combinatorial Optimization Problems

Space Contraction and Partition Algorithm for Combinatorial Optimization

2011 ◽  
Vol 421 ◽  
pp. 559-563
Author(s):  
Yong Chao Gao ◽  
Li Mei Liu ◽  
Heng Qian ◽  
Ding Wang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Solution Space ◽  
Search Space ◽  
Small Scale ◽  
Optimal Solutions ◽  
Solution Quality ◽  
Intelligent Algorithms ◽  
Combinatorial Optimization Problems

The scale and complexity of search space are important factors deciding the solving difficulty of an optimization problem. The information of solution space may lead searching to optimal solutions. Based on this, an algorithm for combinatorial optimization is proposed. This algorithm makes use of the good solutions found by intelligent algorithms, contracts the search space and partitions it into one or several optimal regions by backbones of combinatorial optimization solutions. And optimization of small-scale problems is carried out in optimal regions. Statistical analysis is not necessary before or through the solving process in this algorithm, and solution information is used to estimate the landscape of search space, which enhances the speed of solving and solution quality. The algorithm breaks a new path for solving combinatorial optimization problems, and the results of experiments also testify its efficiency.

An Improved Immune Algorithm for Solving TSP Problem

2012 ◽  
Vol 468-471 ◽  
pp. 678-682
Author(s):  
Hong Quan Xue ◽  
Sheng Min Wei ◽  
Lin Yang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Immune Algorithm ◽  
Optimal Solutions ◽  
Typical Application ◽  
Immune Optimization ◽  
Quantum Bit ◽  
Combinatorial Optimization Problems ◽  
Biological Immune System ◽  
Computational Systems

Immune algorithm is a set of computational systems inspired by the defense process of the biological immune system, and is widespread used in the combinatorial optimization problems. This paper describes an improved immune algorithm to solve the combinatorial optimization problems. The TSP problem is a typical application of the combinatorial optimization problems. The improved immune algorithm which based on the quantum principles is proposed for finding the optimal solutions to solve the TSP problem. In process of solving TSP problem, the quantum concept is used in initializing a population of quantum bit chromosomes. In the antibody’s updating, the general quantum rotation gate strategy and the dynamic adjusting angle mechanism are applied to accelerate convergence.According to the analysis of the experiment, the algorithm is not only feasible but also effective to solve TSP problem. It effectively relieves some disadvantages of the quantum and immune optimization.

scholarly journals High-performance combinatorial optimization based on classical mechanics

2021 ◽  
Vol 7 (6) ◽  
pp. eabe7953
Author(s):  
Hayato Goto ◽  
Kotaro Endo ◽  
Masaru Suzuki ◽  
Yoshisato Sakai ◽  
Taro Kanao ◽  
...  
Keyword(s):  
Combinatorial Optimization ◽  
High Speed ◽  
High Performance ◽  
Optimization Problems ◽  
Classical Mechanics ◽  
Massively Parallel ◽  
Optimal Solutions ◽  
Combinatorial Optimization Problems ◽  
Superconducting Circuit ◽  
Solution Accuracy

Quickly obtaining optimal solutions of combinatorial optimization problems has tremendous value but is extremely difficult. Thus, various kinds of machines specially designed for combinatorial optimization have recently been proposed and developed. Toward the realization of higher-performance machines, here, we propose an algorithm based on classical mechanics, which is obtained by modifying a previously proposed algorithm called simulated bifurcation. Our proposed algorithm allows us to achieve not only high speed by parallel computing but also high solution accuracy for problems with up to one million binary variables. Benchmarking shows that our machine based on the algorithm achieves high performance compared to recently developed machines, including a quantum annealer using a superconducting circuit, a coherent Ising machine using a laser, and digital processors based on various algorithms. Thus, high-performance combinatorial optimization is realized by massively parallel implementations of the proposed algorithm based on classical mechanics.

scholarly journals COST SHARING IN NETWORKS: SOME OPEN QUESTIONS

2013 ◽  
Vol 15 (02) ◽  
pp. 1340001 ◽  
Author(s):  
HERVÉ MOULIN
Keyword(s):  
Computational Complexity ◽  
Combinatorial Optimization ◽  
Cooperative Game ◽  
Cost Sharing ◽  
Optimization Problems ◽  
Fair Division ◽  
Optimal Solutions ◽  
Combinatorial Optimization Problems ◽  
Open Questions

The fertile application of cooperative game techniques to cost sharing problems on networks has so far concentrated on the Stand Alone core test of fairness and/or stability, and ignored many combinatorial optimization problems where this core can be empty. I submit there is much room for an axiomatic discussion of fair division in the latter problems, where Stand Alone objections are not implementable. But the computational complexity of optimal solutions is still a very severe obstacle to this approach.

scholarly journals A Sensitivity Analysis of Critical Genetic Algorithm Parameters

2016 ◽  
pp. 863-880
Author(s):  
Eungcheol Kim ◽  
Manoj K. Jha ◽  
Min-Wook Kang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Critical Parameters ◽  
Optimal Solutions ◽  
Genetic Operators ◽  
Solution Quality ◽  
Local Optima ◽  
3 Dimensional ◽  
Combinatorial Optimization Problems ◽  
Decision Variables

Genetic Algorithms (GAs) have been applied in many complex combinatorial optimization problems and have been proven to yield reasonably good solutions due to their ability of searching in continuous spaces and avoiding local optima. However, one issue in GA application that needs to be carefully explored is to examine sensitivity of critical parameters that may affect the quality of solutions. The key critical GA parameters affecting solution quality include the number of genetic operators, the number of encoded decision variables, the parameter for selective pressure, and the parameter for non-uniform mutation. The effect of these parameters on solution quality is particularly significant for complex problems of combinatorial nature. In this paper the authors test the sensitivity of critical GA parameters in optimizing 3-dimensional highway alignments which has been proven to be a complex combinatorial optimization problem for which an exact solution is not possible warranting the application of heuristics procedures, such as GAs. If GAs are applied properly, similar optimal solutions should be expected at each replication. The authors perform several example studies in order to arrive at a general set of conclusions regarding the sensitivity of critical GA parameters on solution quality. The first study shows that the optimal solutions obtained for a range of scenarios consisting of different combinations of the critical parameters are quite close. The second study shows that different optimal solutions are obtained when the number of encoded decision variables is changed.

A Sensitivity Analysis of Critical Genetic Algorithm Parameters

2015 ◽  
Vol 6 (1) ◽  
pp. 30-48 ◽  
Author(s):  
Eungcheol Kim ◽  
Manoj K. Jha ◽  
Min-Wook Kang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Critical Parameters ◽  
Optimal Solutions ◽  
Genetic Operators ◽  
Solution Quality ◽  
Local Optima ◽  
3 Dimensional ◽  
Combinatorial Optimization Problems ◽  
Decision Variables

Genetic Algorithms (GAs) have been applied in many complex combinatorial optimization problems and have been proven to yield reasonably good solutions due to their ability of searching in continuous spaces and avoiding local optima. However, one issue in GA application that needs to be carefully explored is to examine sensitivity of critical parameters that may affect the quality of solutions. The key critical GA parameters affecting solution quality include the number of genetic operators, the number of encoded decision variables, the parameter for selective pressure, and the parameter for non-uniform mutation. The effect of these parameters on solution quality is particularly significant for complex problems of combinatorial nature. In this paper the authors test the sensitivity of critical GA parameters in optimizing 3-dimensional highway alignments which has been proven to be a complex combinatorial optimization problem for which an exact solution is not possible warranting the application of heuristics procedures, such as GAs. If GAs are applied properly, similar optimal solutions should be expected at each replication. The authors perform several example studies in order to arrive at a general set of conclusions regarding the sensitivity of critical GA parameters on solution quality. The first study shows that the optimal solutions obtained for a range of scenarios consisting of different combinations of the critical parameters are quite close. The second study shows that different optimal solutions are obtained when the number of encoded decision variables is changed.

A Sensitivity Analysis of Critical Genetic Algorithm Parameters

2015 ◽  
pp. 1064-1081
Author(s):  
Eungcheol Kim ◽  
Manoj K. Jha ◽  
Min-Wook Kang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Critical Parameters ◽  
Optimal Solutions ◽  
Genetic Operators ◽  
Solution Quality ◽  
Local Optima ◽  
3 Dimensional ◽  
Combinatorial Optimization Problems ◽  
Decision Variables

Genetic Algorithms (GAs) have been applied in many complex combinatorial optimization problems and have been proven to yield reasonably good solutions due to their ability of searching in continuous spaces and avoiding local optima. However, one issue in GA application that needs to be carefully explored is to examine sensitivity of critical parameters that may affect the quality of solutions. The key critical GA parameters affecting solution quality include the number of genetic operators, the number of encoded decision variables, the parameter for selective pressure, and the parameter for non-uniform mutation. The effect of these parameters on solution quality is particularly significant for complex problems of combinatorial nature. In this paper the authors test the sensitivity of critical GA parameters in optimizing 3-dimensional highway alignments which has been proven to be a complex combinatorial optimization problem for which an exact solution is not possible warranting the application of heuristics procedures, such as GAs. If GAs are applied properly, similar optimal solutions should be expected at each replication. The authors perform several example studies in order to arrive at a general set of conclusions regarding the sensitivity of critical GA parameters on solution quality. The first study shows that the optimal solutions obtained for a range of scenarios consisting of different combinations of the critical parameters are quite close. The second study shows that different optimal solutions are obtained when the number of encoded decision variables is changed.

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