OQGRG: a multi-start algorithm for global solution of nonlinear and mixed integer programs

Economical, managerial, engineering, and natural systems are often represented by nonlinear equations and inequalities, using discrete and continuous variables. Global Optimization provides methodologies to find the global solutions for the prescriptive models that attempt to describe, predict, and optimize their behavior. OQGRG, the algorithm presented in this dissertation, was developed to solve problems in this large target class of mixed integer, nonlinear, constrained optimization models that often have multiple local optima. OQGRG is a multi-start, 2-stage, global optimization algorithm that combines the efficiency of the Scatter Search meta-heuristic and the power of a reduced gradient nonlinear solver. It uses OptQuest as the implementation of Scatter Search and Lsgrg2 as a nonlinear local solver. OQGRG is written in standard ANSI C, and a GAMS interface provides access to many test problems available in the literature. The effectiveness of the algorithm is demonstrated by solving 155 of 159 test problems within 1% of their best known solutions.