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The circle packing problem involves finding the best way to place non-overlapping circles within a given space, while the smog-free tower installation problem aims to minimize the exposure of residents to secondhand smog by identifying the optimal tower locations. This study proposes a Real Coded Genetic Algorithm (RCGA) that uses real-valued representations of circle positions to solve the smog-free tower installation problem. A new crossover operator is introduced, combining the information from two parent solutions to generate two new offspring solutions. The operator uses a random crossover point and two scaling factors to control the amount of information exchanged. The performance of the operator is evaluated on CEC-2017 benchmark problem set and compared to other commonly used operators, with results indicating that it produces high-quality solutions and outperforms other operators in terms of solution quality and convergence speed. This research contributes to developing effective optimization algorithms that can have important implications for improving public health and reducing the negative effects of secondhand smog.

Installation of Smog-Free Towers using novel Real Coded Genetic Algorithm