Nonlinear Goal Programs

Kuriger and Ravindran (2005) have developed three intelligent search methods to solve nonlinear GP problems by adapting and extending the simplex search, complex search, and pattern search methods to account for multiple criteria. These modifications were largely accomplished by using partitioning concepts of GP. The paper also includes computational results with several test problems. 

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Kuriger, G. and A. Ravindran. 2005. Intelligent search methods for nonlinear goal programs. Information Systems and Operational Research. 43 79-92. 

Saber, H. M. and A. Ravindran. 1996. A partitioning gradient based (PGB) algorithm for solving nonlinear goal programming problem. Computers and Operations Research. 23 141-152. 

This paper reports on the investigation that was carried out on the application of Nonlinear Goal Programming to an R-C circuit based Electrical Discharge Machining of ceramic composites. The model was developed from the EDM machining experimental data on ceramic composites. This process utilizes the modified Hookes and Jeeves search technique to obtain the optimal operating conditions. 

Mehrbod et al. (2012) considered a multi-product, multi-time period CLSC network with manufacturing plants, distributors, retailers, return product collection centers, and recycling centers. The authors developed a bi-criteria mixed integer nonlinear program for the problem to minimize supply chain costs, delivery time of new products, and collection time of returned products. An interactive fuzzy goal programming method was used to solve the problem. 

The best way to approach the retrofit synthesis of the heat-exchanger network is to model all five tasks simultaneously. A mixed-integer nonlinear programming model is usually formulated to accomplish this goal. 

A process-synthesis problem can be formulated as a combination of tasks whose goal is the optimization of an economic objective function subject to constraints. Two types of mathematical techniques are the most used mixed-integer linear programming (MILP), and mixed-integer nonlinear programming (MINLP). 

In this example, you have two iterations - one because of the circular reference due to the recycle streams and one because of the nonlinear Rachford-Rice equation. Some computer programs cannot handle both of these complications together. Neither Goal Seek nor Solver worked for this example, and you iterated the vapor fraction by hand. 

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