Issue No 7: November 2003 |
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The goal of finding
an efficient way to transport goods from an origin node to a destination
node has received help from mathematicians at The Hong Kong Polytechnic
University.
Oriented from the Wardrops single criterion user-optimal equilibrium conditions in 1952, which suggests road users travel on a path with minimum time delay, the study of traffic equilibrium has been the subject of research for more than half a century. In real life, many road users are concerned not only with minimum time delay, but also with monetary cost and how pleasant it is to drive on a particular path, said Dr Yang. Thus, traffic flow along a path joining origin and destination nodes in a road network is greater than zero only if the resulting multiple criteria objective is efficient among all the paths that join the pair of nodes. Dr Yang and his researchers devised the mathematical model using a new approach to the problem, namely vector variational inequality. The integral nature of the decision variables / fixed charge results in non-convexity in the mathematical formulation, where the classical linear Lagrangian technique cannot be applied. Motivated by these observations, the researchers studied a general non-convex multiple criteria optimisation problem and used a nonlinear Lagrangian technique which, he said, allowed better duality representation of the multiple criteria optimisation problems involved. Advancement in non-convex multiple criteria optimisation, said Dr Yang, will have a significant impact on improving the current practice of design, operation, and management in many fields of business and engineering. Principal Investigator |