Gradient-based deterministic optimization methods can ensure the convergence toward the optima of nonlinear problems. However, they need a descent search direction computed using the gradient of the objective function, which becomes expensive in many cases. This drawback motivated the development of various population-based metaheuristics without requiring gradient information, which could successfully approximate the global optima even of many challenging problems. However, they suffer from convergence proof toward the optima due to their inability to ensure a descent search direction, thus causing excessive function evaluation or even to get stuck at some local optima. Accordingly, this work proposes a new global optimizer, namely UniPop, by combining the unidirectional search used in gradient-based deterministic methods and population of solutions used in metaheuristics, in which descent search directions are first obtained by pair-wise connecting the solutions from the population without requiring any gradient information, and then unidirectional search is performed for determining the optimum points along those descent directions. The potentiality of UniPop is demonstrated here through its successful application to a large set of real-valued unconstrained benchmark functions of different nature.

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UniPop: A Unidirectional Search Based Global Optimizer Assisted by a Population of Solutions

  • Dilip Datta

摘要

Gradient-based deterministic optimization methods can ensure the convergence toward the optima of nonlinear problems. However, they need a descent search direction computed using the gradient of the objective function, which becomes expensive in many cases. This drawback motivated the development of various population-based metaheuristics without requiring gradient information, which could successfully approximate the global optima even of many challenging problems. However, they suffer from convergence proof toward the optima due to their inability to ensure a descent search direction, thus causing excessive function evaluation or even to get stuck at some local optima. Accordingly, this work proposes a new global optimizer, namely UniPop, by combining the unidirectional search used in gradient-based deterministic methods and population of solutions used in metaheuristics, in which descent search directions are first obtained by pair-wise connecting the solutions from the population without requiring any gradient information, and then unidirectional search is performed for determining the optimum points along those descent directions. The potentiality of UniPop is demonstrated here through its successful application to a large set of real-valued unconstrained benchmark functions of different nature.