NSGA-II: A Non-dominated Sorting Genetic Algorithm for Multi-objective Optimization

In the following section, I will provide a detailed explanation of the NSGA-II optimization algorithm. NSGA-II is a multi-objective optimization algorithm capable of simultaneously optimizing two or more objective functions. The algorithm is based on genetic algorithms and employs a technique called "non-dominated sorting" to rank individuals in the population. Each individual is assigned a numerical value known as its "rank" and is further evaluated based on its crowding distance from other individuals. In this approach, individuals can possess multiple attributes - for example, a solution might exhibit low cost and high performance simultaneously. The algorithm's primary objective is to identify optimal solutions across all possible attribute combinations, commonly referred to as the "Pareto front." Key implementation aspects include tournament selection for parent selection, simulated binary crossover (SBX) for recombination, and polynomial mutation for maintaining diversity. NSGA-II finds extensive applications in engineering design, finance, and various other domains requiring multi-objective optimization solutions. The algorithm terminates when either the maximum number of generations is reached or convergence criteria are satisfied, typically measured by stabilization of the Pareto front.