Algorithms for clustering data
Algorithms for clustering data
A simulated annealing algorithm for the clustering problem
Pattern Recognition
Adaptation in natural and artificial systems
Adaptation in natural and artificial systems
A near-optimal initial seed value selection in K-means algorithm using a genetic algorithm
Pattern Recognition Letters
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators
Artificial Intelligence Review
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth annual ACM symposium on Theory of computing
Proceedings of the 42nd annual Design Automation Conference
Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art
Evolutionary Computation
A Graph-Theoretic Approach to Nonparametric Cluster Analysis
IEEE Transactions on Computers
A Branch and Bound Clustering Algorithm
IEEE Transactions on Computers
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
An Evolutionary Approach to Multiobjective Clustering
IEEE Transactions on Evolutionary Computation
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Multiobjective GAs, quantitative indices, and pattern classification
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
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The classical problem of partitioning a given set of points, has applications in several areas such as facility location, scattered network, and in hierarchical design of VLSI circuits. While equipartitioning is traditionally associated with the single objective of minimum cutcost, the above application areas appear to demand more. In this paper, we introduce the problem of multiobjective k-way equipartitioning of a point set. Brief discussions on the above applications are followed by their generic formulation as a multiobjective k-way equipartitioning problem of a given point set. The non-commensurate multiobjective criteria addressed include (i) minimizing overall areas of the partitions, (ii) maximizing area of the individual partitions, (iii) minimizing the total compactness of the partitions, and (iv) minimizing the total geometric diversity of the obtained partitions. Since this optimization problem is computationally expensive in time and space, a technique based on genetic algorithm is proposed in order to obtain high quality results. Crossover and mutation operators specific to the k-way equipartitioning problem, have been designed and a new greedy operator named compaction is proposed to accelerate convergence. To illustrate the utility of the proposed formulation and the algorithm, a problem in VLSI layout design is considered. Results on synthetic data sets as well as those extracted from layouts of benchmark circuits demonstrate the effectiveness of the proposed multiobjective approach.