Scatter search for chemical and bio-process optimization

Abstract

Scatter search is a population-based method that has recently been shown to yield promising outcomes for solving combinatorial and nonlinear optimization problems. Based on formulations originally proposed in the 1960s for combining decision rules and problem constraints such as the surrogate constraint method, scatter search uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we develop a general purpose heuristic for a class of nonlinear optimization problems. The procedure is based on the scatter search methodology and treats the objective function evaluation as a black box, making the search algorithm context-independent.Most optimization problems in the chemical and bio-chemical industries are highly nonlinear in either the objective function or the constraints. Moreover, they usually present differential-algebraic systems of constraints. In this type of problem, the evaluation of a solution or even the feasibility test of a set of values for the decision variables is a time-consuming operation. In this context, the solution method is limited to a reduced number of solution examinations. We have implemented a scatter search procedure in Matlab for this special class of difficult optimization problems. Our development goes beyond a simple exercise of applying scatter search to this class of problem, but presents innovative mechanisms to obtain a good balance between intensification and diversification in a short-term search horizon. Computational comparisons with other recent methods over a set of benchmark problems favor the proposed procedure.

Optimal design and operation of activated sludge processes: State-of-the-art

“…[9]), pattern search (e.g. [10]), simulated annealing [11], ant colony [12], scatter search [13], tabu search [14], etc.…”

“…Therefore, some authors, e.g. [13], have opted for simpler models, which are however probably less accurate than ASMs. Nonetheless, the use of simple models may be necessary when computation time is an issue, i.e.…”

“…Some authors [12][13][14] have even considered such challenging problems with the aim of testing the effectiveness of the optimization algorithms that they developed. However, to be of industrial relevance, several aspects relative to the problem formulation should be considered, so as to achieve an optimal solution that is applicable to the real-scale ASP.…”

“…Some studies [8,13,14] compared the efficiency of stochastic/hybrid and global-deterministic algorithms. Their results revealed that stochastic techniques generally outperform global-deterministic solvers in terms of both objective function value and computation time requirement.…”

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

“…Pattern search methods have been combined with genetic algorithms, and the resulting hybrid methodology has significantly better performance when compared to pure evolutionary algorithms (Egea et al, 2007a(Egea et al, ,b, 2010. Griffin and Kolda (2010) integrate the DIRECT algorithm with a stochastic generating set search approach to solve box-constrained problems, while Hemker and Werner (2011) combine DIRECT with surrogate-based local search for general constrained CDFO problems.…”