Bernard K.-S. Cheung

Analysis of Global k-Means, an Incremental Heuristic for Minimum Sum-of-Squares Clustering

The global k-means heuristic is a recently proposed (Likas, Vlassis and Verbeek, 2003) incremental approach for minimum sum-of-squares clustering of a set X of N points of R d into M clusters. For k = 2,3,.... M - 1 it considers the best-known set of k - 1 centroids previously obtained, adds a new cluster center at each point of X in turn and applies k-means to each set of k centroids so-obtained, keeping the best k-partition found. We show that global k-means cannot be guaranteed to find the optimum partition for any M ≥ 2 and d > 1; moreover, the same holds for all M > 3 if the new cluster center is chosen anywhere in R d instead of belonging to X. The empirical performance of global k-means is also evaluated by comparing the values it obtains with those obtained for three data sets with N < 150 which are solved optimally, as well as with values obtained by the recent j-means heuristic and extensions thereof for three larger data sets with N ≤ 3038.

Solving the multi-buyer joint replenishment problem with a modified genetic algorithm

The joint replenishment problem (JRP) is a multi-item inventory problem. The objective is to develop inventory policies that minimize the total costs (comprised of holding cost and setup cost) over the planning horizon. In this paper, we look at the multi-buyer, multi-item version of the JRP. We propose a new modified genetic algorithm which is very efficient. Tests are conducted on problems from a leading bank in Hong Kong and from the literature.

High performing evolutionary techniques for solving complex location problems in industrial system design

We propose an overall reconstruction of the traditional genetic algorithm method so that its inherent weaknesses such as slow convergence can be overcome. We explore a number of variations of crossover operators and of the genetic search scheme. The algorithm is also implemented as a partially parallel algorithm on a multi-processors workstation and is capable of handling a large class of real-life location problems. Hub location problems from airline networks and location-allocation problems from the oil industry have been solved successfully.

Composition of module stock for final assembly using an enhanced genetic algorithm

The paper focuses on modelling and solving a design problem, namely the selection of a set of modules to be manufactured at one or more distant sites and shipped to a proximity site for final assembly subject to time constraints. The problem is modelled as a mathematical one, and solved by an appropriately designed genetic algorithm enhanced with a modified crossover operation, a uniform mutation with adaptive rate and a partial reshuffling procedure. The actual design problem is solved with 17 components. Larger problems may be solved without modifying the modelling steps, although they may require variation in terms of processing time, depending on the constraints that exist between the components.

Virtual Distribution Systems: an integrated model with research initiatives

In this article, we attempt to give a comprehensive review of how classical supply chain models have evolved with advances in information technology and its related branches of knowledge. To illustrate a possible solution to meet the challenges of the present day, we propose a model of a Virtual Distribution System for a supplier (or a group of suppliers) to use in planning and operating the distribution of goods and merchandise to customers over the entire region. These customers often demand that the products they have ordered be delivered to their preferred destinations in a highly efficient way. The modular structure of this system enables it to be more flexible and responsive to dynamic changes in the market. Illustrative example of the solution obtained by the main distribution model is given in the paper.

SELECTION OF A MODULES STOCK COMPOSITION USING GENETIC ALGORITHM

Abstract The paper focuses on modelling and solving a design problem. The problem consists in selecting a set of modules that will be manufactured in distant sites and shipped in a nearby location site for a final assembly operation under time limits. The problem is modelled as a mathematical problem and solved by a genetic algorithm with a modified crossover operation, a uniform mutation with adaptive rate and a partial reshuffling procedure.