Parallel Adaptive Kriging Method with Constraint Aggregation for Expensive Black-Box Optimization Problems

Mode Pursuing Sampling (MPS) was developed as a global optimization algorithm for optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for problems of low dimensionality, i.e., the number of design variables is less than ten. A previous conference publication integrated the concept of trust regions into the MPS framework to create a new algorithm, TRMPS, which dramatically improved performance and efficiency for high dimensional problems. However, although TRMPS performed better than MPS, it was unproven against other established algorithms such as GA. This paper introduces an improved algorithm, TRMPS2, which incorporates guided sampling and low function value criterion to further improve algorithm performance for high dimensional problems. TRMPS2 is benchmarked against MPS and GA using a suite of test problems. The results show that TRMPS2 performs better than MPS and GA on average for high dimensional, expensive, and black box (HEB) problems.

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Fresa: A Plant Propagation Algorithm for Black-Box Single and Multiple Objective Optimization

International Journal on Engineering Technologies and Informatics ◽

10.51626/ijeti.2021.02.00022 ◽

2021 ◽

Vol 2 (4) ◽

Keyword(s):

Mathematical Programming ◽

Objective Function ◽

Optimization Problems ◽

Population Based ◽

Black Box ◽

Multiple Objective ◽

Multiple Objective Optimization ◽

Plant Propagation ◽

Propagation Algorithm ◽

Multiple Dispatch

Fresa implements a nature inspired plant propagation algorithm for the solution of single and multiple objective optimization problems. The method is population based and evolutionary. Treating the objective function as a black box, the implementation is able to solve problems exhibiting behaviour that is challenging for mathematical programming methods. Fresa is easily adapted to new problems which may benefit from bespoke representations of solutions by taking advantage of the dynamic typing and multiple dispatch capabilities of the Julia language. Further, the support for threads in Julia enables an efficient implementation on multi-core computers.

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Surrogate Optimization of Computationally Expensive Black-Box Problems with Hidden Constraints

INFORMS Journal on Computing ◽

10.1287/ijoc.2018.0864 ◽

2019 ◽

Vol 31 (4) ◽

pp. 689-702 ◽

Cited By ~ 4

Author(s):

Juliane Müller ◽

Marcus Day

Keyword(s):

Objective Function ◽

Optimization Problems ◽

Black Box ◽

Direct Search ◽

Test Problems ◽

Large Set ◽

Mesh Adaptive Direct Search ◽

Surrogate Optimization ◽

Computationally Expensive ◽

Hidden Constraints

We introduce the algorithm SHEBO (surrogate optimization of problems with hidden constraints and expensive black-box objectives), an efficient optimization algorithm that employs surrogate models to solve computationally expensive black-box simulation optimization problems that have hidden constraints. Hidden constraints are encountered when the objective function evaluation does not return a value for a parameter vector. These constraints are often encountered in optimization problems in which the objective function is computed by a black-box simulation code. SHEBO uses a combination of local and global search strategies together with an evaluability prediction function and a dynamically adjusted evaluability threshold to iteratively select new sample points. We compare the performance of our algorithm with that of the mesh-based algorithms mesh adaptive direct search (MADS, NOMAD [nonlinear optimization by mesh adaptive direct search] implementation) and implicit filtering and SNOBFIT (stable noisy optimization by branch and fit), which assigns artificial function values to points that violate the hidden constraints. Our numerical experiments for a large set of test problems with 2–30 dimensions and a 31-dimensional real-world application problem arising in combustion simulation show that SHEBO is an efficient solver that outperforms the other methods for many test problems.

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Black-box combinatorial optimization using models with integer-valued minima

Annals of Mathematics and Artificial Intelligence ◽

10.1007/s10472-020-09712-4 ◽

2020 ◽

Author(s):

Laurens Bliek ◽

Sicco Verwer ◽

Mathijs de Weerdt

Keyword(s):

Optimization Algorithm ◽

Surrogate Model ◽

Optimization Problems ◽

Random Search ◽

Continuous Optimization ◽

Optimal Solution ◽

Black Box ◽

Combinatorial Problems ◽

Bayesian Optimization ◽

Bayesian Optimization Algorithm

Abstract When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation make use of surrogate models. These models are usually continuous and smooth, which is beneficial for continuous optimization problems, but not necessarily for combinatorial problems. However, by choosing the basis functions of the surrogate model in a certain way, we show that it can be guaranteed that the optimal solution of the surrogate model is integer. This approach outperforms random search, simulated annealing and a Bayesian optimization algorithm on the problem of finding robust routes for a noise-perturbed traveling salesman benchmark problem, with similar performance as another Bayesian optimization algorithm, and outperforms all compared algorithms on a convex binary optimization problem with a large number of variables.

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