On Grid Aware Refinement of the Unit Hypercube and Simplex: Focus on the Complete Tree Size
Branch and bound (BnB) Global Optimization algorithms can be used to find the global optimum (minimum) of a multiextremal function over the unit hypercube and unit simplex with a guaranteed accuracy. Subdivision strategies can take the information of the evaluated points into account leading to irregular shaped subsets. This study focuses on the passive generation of spatial subdivisions aiming at evaluating points on a predefined grid. The efficiency measure is in terms of the complete tree size, or worst case BnB scenario, with a termination criterion on the subset size. Longest edge bisection is used as a benchmark. It is shown that taking the grid for a given termination tolerance into account, other general partitions exist that improve the BnB upper bound on the number of evaluated points and subsets.
KeywordsBranch and bound Division Covering Unit hypercube Unit simplex
This work has been funded by grants from the Spanish Ministry (TIN2015-66680), in part financed by the European Regional Development Fund (ERDF). J.M.G. Salmerón is a fellow of the Spanish FPU program.
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