An Efficient Binary Hybrid Equilibrium Algorithm for Binary Optimization Problems: Analysis, Validation, and Case Studies

Abstract

Binary optimization problems belong to the NP-hard class because their solutions are hard to find in a known time. The traditional techniques could not be applied to tackle those problems because the computational cost required by them increases exponentially with increasing the dimensions of the optimization problems. Therefore, over the last few years, researchers have paid attention to the metaheuristic algorithms for tackling those problems in an acceptable time. But unfortunately, those algorithms still suffer from not being able to avert local minima, a lack of population diversity, and low convergence speed. As a result, this paper presents a new binary optimization technique based on integrating the equilibrium optimizer (EO) with a new local search operator, which effectively integrates the single crossover, uniform crossover, mutation operator, flipping operator, and swapping operator to improve its exploration and exploitation operators. In a more general sense, this local search operator is based on two folds: the first fold borrows the single-point crossover and uniform crossover to accelerate the convergence speed, in addition to avoiding falling into local minima using the mutation strategy; the second fold is based on applying two different mutation operators on the best-so-far solution in the hope of finding a better solution: the first operator is the flip mutation operator to flip a bit selected randomly from the given solution, and the second operator is the swap mutation operator to swap two unique positions selected randomly from the given solution. This variant is called a binary hybrid equilibrium optimizer (BHEO) and is applied to three common binary optimization problems: 0–1 knapsack, feature selection, and the Merkle–Hellman knapsack cryptosystem (MHKC) to investigate its effectiveness. The experimental findings of BHEO are compared with those of the classical algorithm and six other well-established evolutionary and swarm-based optimization algorithms. From those findings, it is concluded that BHEO is a strong alternative to tackle binary optimization problems. Quantatively, BHEO could reach an average fitness of 0.090737884 for the feature section problem and an average difference from the optimal profits for some used Knapsack problems of 2.482.