Use of a self-adaptive penalty approach for engineering optimization problems

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An improved particle swarm optimizer for mechanical design optimization problems (2004, methodology): “This problem was dealt with by Coello Coello [34] using GA with a dominance-based tournament selection scheme (GADTS) to handle constraints.”
Lévy-Flight Moth-Flame Algorithm for Function Optimization and Engineering Design Problems (2016, background): “The objective is to evaluate the optimal fabrication cost of a welded beam as shown in Figure 39 [35].”
Prairie Dog Optimization Algorithm (2022, background): “Pc X ð Þ 1⁄4 4:013E ffiffiffiffiffiffi x(2) 3 x(6) 4 36 q L2 1 x3 2L ffiffiffi E p =4G The parameters for WBD are set as follows: rmax 1⁄4 3000psi; P 1⁄4 6000lb;L 1⁄4 14in; dmax 1⁄4 0:25in;E 1⁄4 3 10(6)psi; smax 1⁄4 13600psi; andG 1⁄4 12 10(6)psi [65].”
CONSTRAINT-HANDLING USING AN EVOLUTIONARY MULTIOBJECTIVE OPTIMIZATION TECHNIQUE (2000, result): “It should be noted that the solution reported here is not the global optimum, and we have found a better solution in previous work (f(~x) = 1:74830941 [11]).”
Sand Cat swarm optimization: a nature-inspired algorithm to solve global optimization problems (2022, background): “The objective of this problem to minimize the total cost of a cylinder-shaped pressure vessel including material, welding, and forming [58, 59].”