An Optimal Balanced Partitioning of a Set of 1D Intervals

2010 ◽  
Vol 1 (2) ◽  
pp. 72-79
Author(s):  
Chuan-Kai Yang
Keyword(s):  
Simulated Annealing ◽  
Load Balancing ◽  
Optimal Partitioning ◽  
Partition Number ◽  
Partitioning Problem

Given a set of 1D intervals and a desired partition number, in this paper, the author examines how to make an optimal partitioning of these intervals, such that the number of intervals between the largest partition and smallest partition is minimal among all possible partitioning schemes. This problem has its difficulty due to the fact that an interval “striding” multiple partitions should be counted multiple times. Previously the author proposed an approximated solution to this problem by employing a simulated annealing approach (Yang & Chiueh, 2006), which could give satisfactory results in most cases; however, there is no theoretical guarantee on its optimality. This paper proposes a method that could both optimally and deterministically partition a given set of 1D intervals into a given number of partitions. The author shows that some load balancing problems could also be formulated as a balanced interval partitioning problem.

Hull mixed-model assembly line balancing using a multi-objective genetic algorithm simulated annealing optimization approach

2016 ◽  
Vol 25 (1) ◽  
pp. 30-40 ◽  
Author(s):  
Yu-guang Zhong
Keyword(s):  
Genetic Algorithm ◽  
Simulated Annealing ◽  
Load Balancing ◽  
Assembly Line ◽  
Assembly Line Balancing ◽  
Line Balancing ◽  
Optimization Approach ◽  
Multi Objective ◽  
Mutation Operators ◽  
Mixed Model Assembly Line

Hull assembly line balancing has significant impact on performance of shipbuilding system and is usually a multi-objective optimization problem. In this article, the primary objectives of the hull assembly line balancing are to minimize the number of workstations, to minimize the static load balancing index, to minimize the dynamic load balancing index between workstations, and to minimize the multi-station-associated complexity. Because this problem comes under combinatorial optimization category and is non-deterministic polynomial-time hard, an improved genetic algorithm simulated annealing is presented. In genetic algorithm simulated annealing, the task sequence numbers are used as chromosomes, and selection, crossover, and mutation operators only deal with the elements of task set instead of the ones of the problem space. In order to prevent the algorithm appearing early convergence or getting local optimal result, the simulated annealing algorithm is used to deal with the individuals. Meanwhile, the algorithm is embedded with the hierarchical scheduling tactics in order to solve the selection problem on optimal solution in the Pareto-optimal set. A number of benchmark problems are solved to prove the superior efficiency of the proposed algorithm. Finally, a case study of the optimization of a hull assembly line was given to illustrate the feasibility and effectiveness of the method.

Solving Load Phase Balancing Problem in LV Distribution Networks by Chaotic Simulated Annealing

2012 ◽  
Vol 463-464 ◽  
pp. 689-693 ◽  
Author(s):  
Chun Guo Fei
Keyword(s):  
Simulated Annealing ◽  
Load Balancing ◽  
Objective Function ◽  
Heuristic Algorithm ◽  
Energy Function ◽  
Current Flow ◽  
Low Voltage ◽  
Distribution Networks ◽  
Maximum Difference ◽  
Chaotic Simulated Annealing

Phase balancing problem is to make a feeder system balanced in terms of phases in low voltage (LV) distribution networks. In this paper, we investigate the use of chaotic simulated annealing (CSA) for realize phase balancing in the low voltage circuit of the distribution network. The network energy function of the CSA is constructed for objective function that defined the load balancing problem. The CSA is applied to solve the problem when load is represented in terms of current flow at the connection points. The results obtained using CSA are compared with those from a heuristic algorithm. Simulations results show that the CSA is very effective and outperforms the heuristic algorithm in terms of the maximum difference of the phase currents

Application of the “descent with mutations” metaheuristic to a clique partitioning problem

2019 ◽  
Vol 53 (3) ◽  
pp. 1083-1095 ◽  
Author(s):  
Olivier Hudry
Keyword(s):  
Cluster Analysis ◽  
Simulated Annealing ◽  
Weighted Graph ◽  
Local Transformation ◽  
Clique Partitioning ◽  
Clique Partitioning Problem ◽  
Partitioning Problem ◽  
And Cluster Analysis ◽  
Symmetric Relations ◽  
Annealing Method

We study here the application of the “descent with mutations” metaheuristic to a problem arising from the field of classification and cluster analysis (dealing more precisely with the aggregation of symmetric relations) and which can be represented as a clique partitioning of a weighted graph. In this problem, we deai with a complete undirected graphe G; the edges of G have weights which can be positive, negative or equal to 0; the aim is to partition the vertices of G into disjoint cliques (whose number depends on G in order to minimize the sum of the weights of the edges with their two extremities in a same clique; this problem is NP-hard. The “descent with mutations” is a local search metaheuristic, of which the design is very simple and is based on local transformation. It consists in randomly performing random elementary transformations, irrespective improvement or worsening with respect to the objective function. We compare it with another very efficient metaheuristic, which is a simulated annealing method improved by the addition of some ingredients coming from the noising methods. Experiments show that the descent with mutations is at least as efficient for the studied problem as this improved simulated annealing, usually a little better, while it is much easier to design and to tune.

A GRAPH BASED DAVIDSON ALGORITHM FOR THE GRAPH PARTITIONING PROBLEM

1999 ◽  
Vol 10 (02) ◽  
pp. 225-246 ◽  
Author(s):  
MICHAEL HOLZRICHTER ◽  
SUELY OLIVEIRA
Keyword(s):  
Graph Theory ◽  
Load Balancing ◽  
Graph Partitioning ◽  
Graph Laplacian ◽  
Matrix Factorizations ◽  
Graph Partitioning Problem ◽  
Spectral Graph ◽  
Partitioning Problem ◽  
Davidson Algorithm ◽  
Spectral Graph Partitioning

The problem of partitioning a graph such that the number of edges incident to vertices in different partitions is minimized, arises in many contexts. Some examples include its recursive application for minimizing fill-in in matrix factorizations and load-balancing for parallel algorithms. Spectral graph partitioning algorithms partition a graph using the eigenvector associated with the second smallest eigenvalue of a matrix called the graph Laplacian. The focus of this paper is the use graph theory to compute this eigenvector more quickly.

Sign in / Sign up

Export Citation Format

Share Document