A flexible platform for mixed-integer non-linear programming problems - Ostermark, Ralf (Kybernetes, 2007)
Purpose - To propose a new algorithmic platform (minlp_machine) for complex mixed-integer non-linear programming (MINLP) problems.Design methodology approach - The platform combines features from classical non-linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around non-integer discrete-valued variables of local solutions, which reduces the search process significantly. In complicated problems fast feasibility restoration is achieved through concentrated Hessians. The system is programmed in strict ANSI C and can be run either stand alone or as a support library for other programs. File I O is designed to recognize possible usage in both single and parallel processor environments.Findings - The system has been tested on Alpha and Sun mainframes and - as a support library for a Genetic Hybrid Algorithm (GHA()) - in Linux and IBM parallel supercomputer environments. The constrained problem can, for example, be solved through a sequence of first order Taylor approximations of the non-linear constraints and occasional feasibility restoration through Hessian information of the Lagrangian of the MINLP problem, or by invoking a nonlinear solver like SQP directly in the branch and bound tree. The system has been successfully tested on a small sample of representative continuous-valued non-linear programming problems.Originality value - It is demonstrated that - through zone-constrained search - minlp_machine() outperforms some recent competing approaches with respect to the number of nodes in the branch and bound tree.