Application of Genetic Algorithm in Multi-Objective Optimization of an Indeterminate Structure with Discontinuous Space for Support Locations

PURPOSE: Genetic Algorithms (GA) have gained popularity in structural design optimization due to their proficiency to search global optimal solution. The purpose of this work was to apply GA to solve support locations of an indeterminate structure, study the effect of various penalty functions and the size of discontinuous solution space on GA’s performance and develop an algorithm to eliminate penalty functions for similar constrained problems. TEST CASE: A rectangular shaped indeterminate homogeneous plate overhung with three supports was developed. METHOD: It was mathematically formulated with “Normalized” multi-objective function and solved using a novel approach, “Discretized Method” (DM), where the solution space was divided in smaller strips having specific index numbers and GA performed on those index numbers instead of real solution space, and compared with Continuous Simple GA (CSGA). With discontinuities applied, three penalty functions (flat, linear and non-linear) were developed and size of discontinuous space was increased by 25% and 50%. An algorithm was developed where smaller strips were generated using Finite Element Model. Paired t-test (α=5%) was used and sample size was 30. RESULTS: Statistically significant difference was observed between DM and CSGA. No significant difference was observed among penalty functions and the effect of the size of discontinuous spaces was not momentous. The developed algorithm successfully eliminated the complex procedure of applying penalty function. CONCLUSION: It is concluded that DM provided better results compared to CSGA and the proposed algorithm made GA more robust and effective for a class of constrained problems by eliminating penalty functions.