A Hopfield Neural Network Approach to the Dual Response Problem

Abstract

The application of neural networks to optimization problems has been an active research area since the early 1980s. Unconstrained optimization, constrained optimization and combinatorial optimization problems have been solved using neural networks. This study presents a new approach using Hopfield neural networks (HNNs) for solving the dual response system (DRS) problems. The major aim of the proposed method is to produce a string of solutions, rather than a 'one-shot' optimum solution, to make the trade-offs available between the mean and standard deviation responses. This gives more flexibility to the decision-maker in exploring alternative solutions. The proposed method has been tested on two examples. The HNN results are very close to those obtained by using the NIMBUS (Nondifferentiable Interactive Multiobjective Bundle-based Optimization System) algorithm. Choosing an appropriate solution method for a certain multi-objective optimization problem is not easy, as has been made abundantly clear. Unlike the NIMBUS method, the HNN approach does not set any specific assumptions on the behaviour or the preference structure of the decision maker. As a result, the proposed method will still work and generate alternative solutions whether or not the decision maker has enough time and capabilities for co-operation.

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