© 2022 Informa UK Limited, trading as Taylor & Francis Group.The present work compares the performance of scientific law-inspired optimization algorithms for real-life constrained optimization applications. Ten such scientific law-inspired algorithms developed during the past decade are considered in this article. A constrained engineering application of the Stirling heat engine system is investigated with these algorithms. Four operating variables and two output constraints of the Stirling heat engine are considered for optimization. Comparative results are presented with statistical data to judge the performance of the algorithms and subsequently to identify the statistical significance and rank of each algorithm. The effects of various constraint handling methods on the performance of the algorithms are evaluated and presented. The behaviour of the constraint handling methods is analysed and presented. The effect of output constraints on the performance of the algorithms is also evaluated and presented. Finally, the convergence behaviour of the competitive algorithms is obtained and demonstrated.