## 1 Introduction
In addition to the initialization of solution and fitness evaluation, ML applications to guide metaheuristics during the search process have been reported in the literature. The Q-learning-based selection of perturbation mechanism for a greedy metaheuristics algorithm to solve the scheduling problem was proposed in [31]. The purpose operator selection derived from the fact that individual operators may be particularly effective at certain stages of the search process, but perform poorly at others [32]. Some recent research using ML for operator selection in metaheuristics was published in [33; 34; 35]. Another variant of the use of ML is metaheuristics learnable evolution models (LEM), in which the lessons learned from previous generations are used to guide metaheuristics [36]. In these approaches, a machine learning algorithm seeks to extract information from the search space to either guide the metaheuristics to a more promising region (exploitation) or help the algorithm scape local optima (exploration). The LEM model for a general discrete optimization problem was developed in [37]. Its application in specific areas, such as the vehicle routing problem in [38], pickup and delivery optimization in [39; 40], finned-tube evaporator in [41], and water-distribution system in [42], were illustrated. Readers interested in a comprehensive review of the various techniques used to integrate machine learning to assist metaheuristics are referred to [32]. In this paper, we developed a technique for clustering and discriminating ordered permutations with potential applications in the development of a neural-network-guided genetic algorithm to solve permutation-based optimization problems. This class of problems includes traveling salesman, linear ordering, quadratic assignment, and flow shop scheduling. In this effort, we developed two techniques to convert ordered permutations to binary vectors and considered Adaptive Resonance Theory (ART) neural networks for clustering the resulting binary vectors. The proposed binary conversion techniques and two neural networks (ART-1 and Improved ART-1) were examined under various performance indicators. Three performance indicators (misclassification, cluster homogeneity, and average distance) were introduced to empirically examine the proposed binary conversion methods. Numerical examples show that one of the binary conversion methods provides better results than the other, and Improved ART-1 is superior to ART-1. Later, a framework for a neural-network-guided GA was developed to solve permutation-based optimization problems by employing the proposed permutation-to-binary conversion method and ART-based neural network. Finally, a case study was conducted to solve a flexible flow shop scheduling problem. The results indicate that the Improved-ART-1 NN-guided GA with binary conversion method-1 performs better than pure GA. The work presented in this paper is an expansion of a conference proceeding by [PERSON] and [PERSON] [43]. The remainder of this paper is organized as follows: Section 2 presents the basic concept of the ART neural network; Section 3 shows the proposed binary conversion methods; Section 4 illustrates the clustering ordered permutations under experimental data generation, performance criteria, and empirical analysis; a case study based on flow shop scheduling is investigated in Section 6; lastly, Section 7 presents the conclusions and future work.