Solving Multiple Objective Programming Problems Using Feed-Forward Artificial Neural Networks: The Interactive FFANN Procedure

In this paper, we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANNs), the method is called the Interactive FFANN Procedure. In the procedure, the decision maker articulates preference information over representative samples from the nondominated set either by assigning preference "values" to the sample solutions or by making pairwise comparisons in a fashion similar to that in the Analytic Hierarchy Process. With this information, a FFANN is trained to represent the decision maker's preference structure. Then, using the FFANN, an optimization problem is solved to search for improved solutions. An example is given to illustrate the Interactive FFANN Procedure. Also, the procedure is compared computationally with the Tchebycheff Method (Steuer and Choo 1983). From the computational results, the Interactive FFANN Procedure produces good results and is robust with regard to the neural network architecture

Interactive Multiple Objective Programming Using Tchebycheff Programs and Artificial Neural Networks

A new interactive multiple objective programming procedure is developed that combines the strengths of the Interactive Weighted Tchebycheff Procedure (Steuer and Choo 1983) and the Interactive FFANN Procedure (Sun, Stam and Steuer 1993). In this new procedure, nondominated trial solutions are generated by solving Augmented Weighted Tchebycheff Programs (Steuer 1986), based on which the decision maker articulates his/her preference information by assigning "values" to these solutions or by making pairwise comparisons. The elicited preference information is used to train a feed-forward artificial neural network, which in turn is used to screen new trial solutions for presentation to decision maker in the next iteration. Computational results are reported, comparing the current procedure with the Interactive Weighted Tchebycheff Procedure and the Interactive FFANN Procedure. The results show that this new procedure yields good quality solutions

Solving Multiple Objective Programming Problems Using Feed-forward Artificial Neural Networks: The Interactive FFANN Procedure of Innovation

In this paper we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANN), the method is called the Interactive FFANN Procedure. In the procedure, the decision maker articulates preference information over representative samples from the non-dominated set either by assigning preference "values" to the sample solutions or by making pairwise comparisons in a fashion similar to that in the Analytic Hierarchy Process. With this information, a FFANN is trained to represent the decision maker's preference structure. Then, using the FFANN, an optimization problem is solved to search for improved solutions. An example is given to illustrate the Interactive FFANN Procedure. Also, the procedure is compared computationally with the Tchebycheff Method (Steuer and Cho 1983). The computational results indicate that the Interactive FFANN Procedure produces good solutions and is robust with regard to the neural network architecture

Approximating the Pareto Front of Multi-criteria Optimization Problems

Abstract. We propose a general methodology for approximating the Pareto front of multi-criteria optimization problems. Our search-based methodology consists of submitting queries to a constraint solver. Hence, in addition to a set of solutions, we can guarantee bounds on the distance to the actual Pareto front and use this distance to guide the search. Our implementation, which computes and updates the distance efficiently, has been tested on numerous examples.

Overviewing the transition of Markowitz bi-criterion portfolio selection to tri-criterion portfolio selection

Over sixty years ago, Markowitz introduced the mean-variance efficient frontier to finance. While mean-variance is still the predominant model in portfolio selection, it has endured many criticisms. One serious one is that it does not allow for additional criteria. The difficulty is that the efficient frontier becomes a surface. With it now possible to compute such a surface, we provide an overview on how Markowitz's risk-return (bi-criterion) portfolio selection can be extended to tri-criterion portfolio selection. With a focus on the geometry of the extension, many graphs are used to illustrate

Solving multiple objective programming problems using feed-forward artificial neural networks: The interactive FFANN approach

In this paper, we propose a new interactive procedure for solving multiple objective programming problems. Based upon feed-forward artificial neural networks (FFANNs), the method is called the Interactive FFANN Procedure. In the procedure. In the procedure, the decision maker articulates preference information over representative samples from the nondominated set either by assigning preference "values" to the sample solutions or by making pairwise comparisons in a fashion similar to that in the Analytic Hierarchy Process. With this information, a FFANN is trained to represent the decision maker's preference structure. Then, using the FFANN, an optimization problem is solved to search for improved solutions. An example is given to illustrate the Interactive FFANN Procedure. Also, the procedure is compared computationally with the Tchebycheff Method (Steuer and Choo 1983). The computational results indicate that the Interactive FFANN Procedure procedures good solutions and is robust with regard to the neural network architecture

Interactive multiple objective programming using Tchebycheff programs and artificial neural networks

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