Influence of ensemble surrogate models and sampling strategy on the solution quality of algorithms for computationally expensive black-box global optimization problems

2014 ◽  
Vol 60 (2) ◽  
pp. 123-144 ◽  
Author(s):  
Juliane Müller ◽  
Christine A. Shoemaker
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Sampling Strategy ◽  
Surrogate Models ◽  
Black Box ◽  
Solution Quality ◽  
Computationally Expensive

A new Kriging–Bat Algorithm for solving computationally expensive black-box global optimization problems

2018 ◽  
Vol 51 (2) ◽  
pp. 265-285 ◽  
Author(s):  
Abdulbaset Saad ◽  
Zuomin Dong ◽  
Brad Buckham ◽  
Curran Crawford ◽  
Adel Younis ◽  
...  
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Bat Algorithm ◽  
Black Box ◽  
Computationally Expensive

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

2019 ◽  
Vol 31 (4) ◽  
pp. 689-702 ◽  
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.

A New Global Optimization Method for Simultaneous Computation on Expensive Black-Box Functions

2003 ◽  
Author(s):  
Liqun Wang ◽  
Songqing Shan ◽  
G. Gary Wang
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Search Space ◽  
Optimization Method ◽  
Global Optimum ◽  
Black Box ◽  
Efficient Global Optimization ◽  
Global Optimization Method ◽  
Global Optimization Methods

The presence of black-box functions in engineering design, which are usually computation-intensive, demands efficient global optimization methods. This work proposes a new global optimization method for black-box functions. The global optimization method is based on a novel mode-pursuing sampling (MPS) method which systematically generates more sample points in the neighborhood of the function mode while statistically covers the entire search space. Quadratic regression is performed to detect the region containing the global optimum. The sampling and detection process iterates until the global optimum is obtained. Through intensive testing, this method is found to be effective, efficient, robust, and applicable to both continuous and discontinuous functions. It supports simultaneous computation and applies to both unconstrained and constrained optimization problems. Because it does not call any existing global optimization tool, it can be used as a standalone global optimization method for inexpensive problems as well. Limitation of the method is also identified and discussed.

scholarly journals A Brief Look at Multi-Criteria Problems: Multi-Threshold Optimization versus Pareto-Optimization

2020 ◽  
Author(s):  
Nodari Vakhania ◽  
Frank Werner
Keyword(s):  
Optimization Problems ◽  
Optimality Criteria ◽  
General Notion ◽  
Objective Functions ◽  
Objective Criterion ◽  
Solution Quality ◽  
Pareto Optimal Set ◽  
Threshold Optimization ◽  
Feasible Solutions

Multi-objective optimization problems are important as they arise in many practical circumstances. In such problems, there is no general notion of optimality, as there are different objective criteria which can be contradictory. In practice, often there is no unique optimality criterion for measuring the solution quality. The latter is rather determined by the value of the solution for each objective criterion. In fact, a practitioner seeks for a solution that has an acceptable value of each of the objective functions and, in practice, there may be different tolerances to the quality of the delivered solution for different objective functions: for some objective criteria, solutions that are far away from an optimal one can be acceptable. Traditional Pareto-optimality approach aims to create all non-dominated feasible solutions in respect to all the optimality criteria. This often requires an inadmissible time. Besides, it is not evident how to choose an appropriate solution from the Pareto-optimal set of feasible solutions, which can be very large. Here we propose a new approach and call it multi-threshold optimization setting that takes into account different requirements for different objective criteria and so is more flexible and can often be solved in a more efficient way.

scholarly journals A time-predefined approach to course timetabling

2003 ◽  
Vol 13 (2) ◽  
pp. 139-151 ◽  
Author(s):  
Edmund Burke ◽  
Yuri Bykov ◽  
James Newall ◽  
Sanja Petrovic
Keyword(s):  
Local Search ◽  
Optimization Problems ◽  
Search Time ◽  
Test Problems ◽  
Solution Quality ◽  
Course Timetabling ◽  
Combinatorial Optimization Problems ◽  
University Course Timetabling ◽  
High Level

A common weakness of local search metaheuristics, such as Simulated Annealing, in solving combinatorial optimization problems, is the necessity of setting a certain number of parameters. This tends to generate a significant increase in the total amount of time required to solve the problem and often requires a high level of experience from the user. This paper is motivated by the goal of overcoming this drawback by employing "parameter-free" techniques in the context of automatically solving course timetabling problems. We employ local search techniques with "straightforward" parameters, i.e. ones that an inexperienced user can easily understand. In particular, we present an extended variant of the "Great Deluge" algorithm, which requires only two parameters (which can be interpreted as search time and an estimation of the required level of solution quality). These parameters affect the performance of the algorithm so that a longer search provides a better result - as long as we can intelligently stop the approach from converging too early. Hence, a user can choose a balance between processing time and the quality of the solution. The proposed method has been tested on a range of university course timetabling problems and the results were evaluated within an International Timetabling Competition. The effectiveness of the proposed technique has been confirmed by a high level of quality of results. These results represented the third overall average rating among 21 participants and the best solutions on 8 of the 23 test problems. .

Trust Region Based Mode Pursuing Sampling Method for Global Optimization of High Dimensional Design Problems

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
George H. Cheng ◽  
Adel Younis ◽  
Kambiz Haji Hajikolaei ◽  
G. Gary Wang
Keyword(s):  
Global Optimization ◽  
Optimization Problems ◽  
Trust Region ◽  
Standard Test ◽  
Black Box ◽  
High Dimensional ◽  
Efficient Global Optimization ◽  
Test Problems ◽  
Design Problems ◽  
Design Variables

Mode pursuing sampling (MPS) was developed as a global optimization algorithm for design optimization problems involving expensive black box functions. MPS has been found to be effective and efficient for design problems of low dimensionality, i.e., the number of design variables is less than 10. This work integrates the concept of trust regions into the MPS framework to create a new algorithm, trust region based mode pursuing sampling (TRMPS2), with the aim of dramatically improving performance and efficiency for high dimensional problems. TRMPS2 is benchmarked against genetic algorithm (GA), dividing rectangles (DIRECT), efficient global optimization (EGO), and MPS using a suite of standard test problems and an engineering design problem. The results show that TRMPS2 performs better on average than GA, DIRECT, EGO, and MPS for high dimensional, expensive, and black box (HEB) problems.

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