Speeding-up Evolutionary Algorithms to solve Black-Box Optimization Problems

TL;DR

This work addresses the high computational cost of evaluating expensive black-box objective functions in population-based evolutionary algorithms. It introduces OPTECOT, an adaptive method that selects the evaluation cost by employing a set of cost-indexed approximate functions and preserving the population ranking via a threshold on ranking accuracy $A_c(P)$. OPTECOT uses a bisection procedure to identify the minimal cost $c^*$ ensuring $A_{c}(P) > \alpha$, estimates $A_c(P)$ through sampling, and monitors population score variance to trigger readjustments, with overhead bounded by 25% of runtime. Empirical results on four diverse problems (Symbolic Regressor, WindFLO, Swimmer, Turbines) show that OPTECOT can reach the same objective values in less than half the time in some cases, demonstrating practical improvements under constrained budgets; the authors provide open-source code for reproduction.

Abstract

Population-based evolutionary algorithms are often considered when approaching computationally expensive black-box optimization problems. They employ a selection mechanism to choose the best solutions from a given population after comparing their objective values, which are then used to generate the next population. This iterative process explores the solution space efficiently, leading to improved solutions over time. However, these algorithms require a large number of evaluations to provide a quality solution, which might be computationally expensive when the evaluation cost is high. In some cases, it is possible to replace the original objective function with a less accurate approximation of lower cost. This introduces a trade-off between the evaluation cost and its accuracy. In this paper, we propose a technique capable of choosing an appropriate approximate function cost during the execution of the optimization algorithm. The proposal finds the minimum evaluation cost at which the solutions are still properly ranked, and consequently, more evaluations can be computed in the same amount of time with minimal accuracy loss. An experimental section on four very different problems reveals that the proposed approach can reach the same objective value in less than half of the time in certain cases.

Figures (9)

• Figure 1: Hierarchical diagram associated with related work.
• Figure 2: The box on the left (named Original problem) defines the problem. The central box (named Optimization algorithm) illustrates the original functioning of the RBEA (column Original) with its limitations (cell Original disadvantages) and compares it with the proposed procedure (column Cost adjustment) indicating its advantages (cell Adjustment advantages). The box on the right (named Compute $c^*$) illustrates the definition of the optimal evaluation cost (defined in Equation \ref{['EQUATION_OptimalEvaluationCost']}).
• Figure 3: In the first row, the mean evaluation times using different cost values and the proportion of extra solutions that can be evaluated when the cost is decreased. The units of time in each problem are given in Table \ref{['TABLE_TrainTerms']}. In the second row, normalized absolute distances between the positions of the approximate rankings and the original.
• Figure 4: The quality evolution of the best solution found at each runtime for different cost values of the approximate function. The quality is measured in terms of the original objective function and the units of time in each problem are given in Table \ref{['TABLE_TrainTerms']}.
• Figure 5: The quality evolution of the best solution found at each runtime by applying OPTECOT and using the original objective function to solve problems. The quality is measured in terms of the original objective function and the units of time in each problem are given in Table \ref{['TABLE_TrainTerms']}.