Invited Session Fri.1.H 3003A

Friday, 10:30 - 12:00 h, Room: H 3003A

Cluster 6: Derivative-free & simulation-based optimization [...]

MINLP and constrained optimization without derivatives


Chair: Stefan Wild and Luís Nunes Vicente



Friday, 10:30 - 10:55 h, Room: H 3003A, Talk 1

Francisco N. C. Sobral
Constrained derivative-free optimization on thin domains

Coauthor: José Mario Martínez


Many derivative-free methods for constrained problems are not efficient for minimizing functions on "thin'' domains. Other algorithms, like those based on Augmented Lagrangians, deal with thin constraints using penalty-like strategies. When the constraints are computationally inexpensive but highly nonlinear, these methods spend many potentially expensive objective function evaluations motivated by the difficulties in improving feasibility. An algorithm that handles this case efficiently is proposed in this paper. The main iteration is split into two steps: restoration and minimization. In the restoration step, the aim is to decrease infeasibility without evaluating the objective function. In the minimization step, the objective function f is minimized on a relaxed feasible set. A global minimization result will be proved and computational experiments showing the advantages of this approach will be presented.



Friday, 11:00 - 11:25 h, Room: H 3003A, Talk 2

Juliane Müller
A surrogate model algorithm for computationally expensive mixed-integer black-box global optimization problems

Coauthors: Robert Piché, Christine Ann Shoemaker


We present a surrogate model algorithm for computationally expensive mixed-integer black-box global optimization problems that may have computationally expensive constraints. The goal is to find accurate solutions with relatively few function evaluations. A radial basis function surrogate model is used to select candidates for integer and continuous decision variable points at which the computationally expensive objective and constraint functions are to be evaluated. In every iteration multiple new points are selected based on different methods, and the objective and constraint functions are evaluated in parallel. The algorithm converges to the global optimum almost surely. The performance of this new algorithm (SO-MI) is compared to a branch and bound algorithm for nonlinear problems, a genetic algorithm, and the NOMAD (Nonsmooth Optimization by Mesh Adaptive Direct Search) algorithm for mixed-integer problems on test problems from the literature, and application problems arising from structural optimization. The numerical results show that SO-MI reaches significantly better results than the other algorithms.



Friday, 11:30 - 11:55 h, Room: H 3003A, Talk 3

Joshua Griffin
A parallel hybrid derivative-free SAS procedure for MINLP

Coauthor: Steven Gardner


We present a new parallel derivative-free SAS procedure for mixed-integer nonlinear black-box optimization. The solver is motivated by recent work on the EAGLS (Evolutionary Algorithms Guiding Local Search) algorithm developed for simulation-based groundwater optimization problems. The SAS procedure makes minimal assumptions on the structure of the nonlinear objective/constraint functions; they may be discontinuous, noisy, and expensive to evaluate. Integer variables are handled by running multiple genetic algorithms concurrently. In addition to crossover and mutation, a "growth step'' permits selected members of the population (based on fitness and diversity) to benefit from local optimization over the real variables. For local search algorithms normally limited to real variables, this provides a simple framework for supporting integer variables that fits naturally in a parallel context. Load imbalance is exploited by both global and local algorithms sharing evaluation threads running across multiple processors. Unique evaluations are cached. Linear constraints are handled explicitly using tangent search directions and the SAS/OR OPTLP procedure.


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