A Hybrid Approach for Constraint Handling in MINLP Optimization Using Stochastic Algorithms

DURAND GUILLERMO A.; BLANCO ANÍBAL M.; SANCHEZ MABEL C.; BANDONI J. ALBERTO

Stochastic Global Optimization: Techniques and Applications in Chemical Engineering

World Scientific Publishing Co Pte Ltd

Lugar: Singapore; Año: 2009;

Global optimization deals with the calculation and characterization of global extrema of functions. Due to its outstanding importance in applied mathematics to science, an overwhelming amount of theoretical and computational contributions, categorized into deterministic and stochastic approaches, has been produced in the last decades. Stochastic strategies such as evolutionary algorithms, simulated annealing and taboo search, showed to be successful in non-convex optimization due to their inherent parallel nature, which allows the simultaneous exploration of the whole search space, reducing the possibility of premature convergence to local extrema. In essence, evolutionary algorithms are unconstrained optimization procedures. As real world optimization problems involve constraints of certain kind, the issue of constraint handling in evolutionary optimization has received considerable attention in the last decade. A critical analysis of the reviewed methodologies indicates that each one presents advantages and disadvantages. To explicitly avoid the constraint handling issue in optimization, in this work a novel methodology is proposed which combines the strengths of the deterministic optimality theory together with the ability of stochastic techniques as unconstrained model optimizers. The proposed methodology consists in an adequate reformulation of the constrained model, in order to pose an equivalent unconstraint version, which can be efficiently solved by stochastic optimization algorithms. The rationale is to formulate the Karush-Kuhn-Tucker system of the problem, meaning its optimality conditions, whose stationary points are also the solutions. An iterative scheme is adopted then to find, one by one, the solutions of the resulting system.