Interactive multiple objective programming using Tchebycheff programs and artificial neural networks

Abstract

A new interactive multiple objective programming procedure is developed that combines the strengths of the interactive weighted Tchebycheff procedure (Steuer and Choo. Mathematical Programming 1983;26(1):326–44.) and the interactive FFANN procedure (Sun, Stam and Steuer. Management Science 1996;42(6):835–49.). In this new procedure, nondominated solutions are generated by solving augmented weighted Tchebycheff programs (Steuer. Multiple criteria optimization: theory, computation and application. New York: Wiley, 1986.). The decision maker indicates preference information by assigning “values” to or by making pairwise comparisons among these solutions. The revealed preference information is then used to train a feed-forward artificial neural network. The trained feed-forward artificial neural network is used to screen new solutions for presentation to the decision maker on the next iteration. The computational experiments, comparing the current procedure with the interactive weighted Tchebycheff procedure and the interactive FFANN procedure, produced encouraging results. Scope and purpose Artificial neural networks have been shown to possess an ability to learn and represent complex mappings, and have been applied to pattern recognition problems. The authors of the current paper believe that a decision maker's preference structure may be viewed as a pattern, and thus should be amenable to artificial neural networks. In a previous work (Sun, Stam and Steuer. Mangement Science 1996;42(6):835–49.), the authors developed a neural-network-based interactive solution method for multiple objective programming problems. The current paper extends that earlier work, combining elements of traditional interactive method with neural networks. In the computational experiments, the new method produced better results for most problems than both the traditional interactive method and the earlier neural-network-based method, thus providing an attractive alternative to existing interactive multiple objective programming procedures.