Adaptive Linear Programming Algorithm With Parameter Learning for Managing Engineering-Design Problems

Abstract

Abstract The adaptive linear programming (ALP) algorithm is an extension of the sequential linear programming algorithm where nonlinear formulations are iteratively approximated as linear formulations linearized about an iteration starting point. In the ALP algorithm, heuristics are used to determine the value of a critical parameter, namely, the reduced move coefficient (RMC). The RMC defines how far to move towards the solution of iteration “n” from the starting point for iteration “n” in specifying the starting point for iteration “n+1”. The RMC choice affects the efficacy of the approximation; however, there is no mechanism of evaluating the algorithm performance with respect to the RMC value so as to improve the design efficiency and effectiveness. This limitation is addressed in this paper. In this paper, we enhance the ALP algorithm with parameter learning (ALPPL) and generalize to make the knowledge gained reusable. We propose a three-step procedure of rule-based parameter learning leading to robust solutions. An industry-inspired problem, the integrated design of a hot rolling process chain for the production of a steel rod, is used to demonstrate the implementation. The three-step procedure could be used to improve other critical parameter determinations, especially when there is a lack of mechanisms for algorithm-performance evaluation, evaluation criteria vary with problems, or heuristics are over-used.