Quantum Teaching-Learning-Based Optimization algorithm for sizing optimization of skeletal structures with discrete variables

In terms of optimization algorithm improvement, researchers utilize some strategies to establish the right balance between local and global search phases to escape from a local minimum in some NP-hard problems. The approach of quantum-behaved particles, as a novel strategy, uses uncertainty law and a distinct formulation obtained from solving the time-independent Schrodinger differential equation in the delta-potential-well function to update the solution candidates' positions. New formulation defines the local attractors as probable solutions between the best solution and the others to explore all solution space domain. Also, mentioned formulation employs the difference between the average solution and other ones as a new step size. Both local attractors and new step sizes guarantee diversification besides the inherent intensification. In the present paper, the teacher phase of the Teaching-Learning-Based Optimization algorithm (TLBO), which has been introduced recently, is improved using the formulation obtained from solving the time-independent Schrodinger equation to predict the probable positions of optimal solutions. The results show that QTLBO, an acronym for the Quantum Teaching- Learning- Based Optimization, improves the stability and robustness of the TLBO by defining the quantum teacher phase. The two planner rigid frames and two trusses with strength and serviceability constraints are chosen to verify the quality and performance of QTLBO. Comparing the results obtained from the proposed algorithm with those of the standard version of the TLBO algorithm and other literature methods shows that QTLBO increases the chance of finding a better solution besides improving the statistical criteria compared to the current TLBO.

Automated summary

Researchers improve the optimization algorithms by using quantum-behaved particles method and a formulation obtained from solving the Schrodinger equation to escape from local minimum in NP-hard problems. The results show that QTLBO improves the stability and robustness of TLBO by defining the quantum teacher phase while ensuring diversification and inherent intensification.