Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
A global optimization model for ship design
Computers in Industry
Computers and Operations Research
A framework for Response Surface Methodology for simulation optimization
Proceedings of the 32nd conference on Winter simulation
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
Response Surface Methodology: Process and Product in Optimization Using Designed Experiments
Global Optimization of Nonconvex Polynomial Programming Problems HavingRational Exponents
Journal of Global Optimization
Efficient Global Optimization of Expensive Black-Box Functions
Journal of Global Optimization
A Radial Basis Function Method for Global Optimization
Journal of Global Optimization
A Comparison of Global Optimization Methods for the Design of a High-speed Civil Transport
Journal of Global Optimization
A Taxonomy of Global Optimization Methods Based on Response Surfaces
Journal of Global Optimization
A Global Optimization RLT-based Approach for Solving the Fuzzy Clustering Problem
Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
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In this paper, we present a new class of pseudo-global optimization procedures for solving formidable optimization problems in which the objective and/or constraints might be analytically complex and expensive to evaluate, or available only as black-box functions. The proposed approach employs a sequence of polynomial programming approximations that are constructed using the Response Surface Methodology (RSM), and embeds these within a branch-and-bound framework in concert with a suitable global optimization technique. The lower bounds constructed in this process might only be heuristic in nature, and hence, this is called a pseudo-global optimization approach. We develop two such procedures, each employing two alternative branching techniques, and apply these methods to the problem of designing containerships. The model involves five design variables given by the design draft, the depth at side, the speed, the overall length, and the maximum beam. The constraints imposed enforce the balance between the weight and the displacement, a required acceptable length to depth ratio, a restriction on the metacentric height to ensure that the design satisfies the Coast Guard wind heel criterion, a minimum freeboard level as governed by the code of federal regulations (46 CFR 42), and a lower bound on the rolling period to ensure sea-worthiness. The objective function seeks to minimize the required freight rate that is induced by the design in order to recover capital and operating costs, expressed in dollars per metric ton per nautical mile. The model formulation also accommodates various practical issues in improving the representation of the foregoing considerations, and turns out to be highly nonlinear and nonconvex. A practical test case is solved using the proposed methodology, and the results obtained are compared with those derived using a contemporary commercialized design optimization tool. The prescribed solution yields an improved design that translates to an estimated increase in profits of about $18.45 million, and an estimated 27% increase in the return on investment, over the life of the ship.