Improvement Analysis and Application of Real-Coded Genetic Algorithm for Solving Constrained Optimization Problems

Abstract

An improved real-coded genetic algorithm (IRCGA) is proposed to solve constrained optimization problems. First, a sorting grouping selection method is given with the advantage of easy realization and not needing to calculate the fitness value. Secondly, a heuristic normal distribution crossover (HNDX) operator is proposed. It can guarantee the cross-generated offsprings to locate closer to the better one among the two parents and the crossover direction to be very close to the optimal crossover direction or to be consistent with the optimal crossover direction. In this way, HNDX can ensure that there is a great chance of generating better offsprings. Thirdly, since the GA in the existing literature has many iterations, the same individuals are likely to appear in the population, thereby making the diversity of the population worse. In IRCGA, substitution operation is added after the crossover operation so that the population does not have the same individuals, and the diversity of the population is rich, thereby helping avoid premature convergence. Finally, aiming at the shortcoming of a single mutation operator which cannot simultaneously take into account local search and global search, this paper proposes a combinational mutation method, which makes the mutation operation take into account both local search and global search. The computational results with nine examples show that the IRCGA has fast convergence speed. As an example application, the optimization model of the steering mechanism of vehicles is formulated and the IRCGA is used to optimize the parameters of the steering trapezoidal mechanism of three vehicle types, with better results than the other methods used.

A review on genetic algorithm: past, present, and future

“…However, the search directions are limited. The heuristic normal distribution crossover operator was developed by Wang et al [ 207 ]. It generates the cross-generated offspring for better search operation.…”

An Improved Real-Coded Genetic Algorithm Using the Heuristical Normal Distribution and Direction-Based Crossover

“…Similarly, the offspring individual Y j ( j = n /2 + 1, n /2 + 2,…, n ) generated by crossover according to equation (7) is near the optimal individual X 1 ′ in the population. Because X 1 ′ is the best individual in the population, the offsprings generated by crossover with the HNDDBX operator are expected to be better than those of the crossover operator in [31, 37].…”

“…At this point, there are countless search directions, and Y k may be located at any point within X 1 ′ CFG . In addition, because X 1 ′ is better than X i ′, the offsprings Y k generated by the HNDDBX operator have a great possibility to be superior to those of the crossover operator in [31, 37]. Thus, Y k may be very close to the optimal solution X ∗ of the problem to be solved.…”

“…In summary, the offsprings generated by the HNDDBX crossover operator are better than those of the crossover operator in [31, 37]. Therefore, the HNDDBX operator can significantly improve the convergence speed of MOIRCGA.…”

“…Currently, the search direction is randomly generated, and the search direction is not instructive. In 2018, Wang et al [37] developed a heuristic normal distribution crossover (HNDX) operator. It can guarantee the cross-generated offspring to locate closer to the better one among the two parents and the search direction to be very close to the optimal search direction or to be consistent with the optimal searching direction.…”