<p>The multi-row facility layout problem is an important component of the facility layout problem. Typically, in this problem, no restrictions are imposed on the location and order of facility placement. However, practical problems in the real world require the addition of various constraints on the facilities. To address these shortcomings in the scientific literature, this paper focuses on the constrained multi-row facility layout problem, incorporating both specified-row positioning and ordering constraints. A mixed-integer programming model is developed to accurately represent the problem with the objective of minimising material handling costs, serving as a foundation for exact optimisation and performance evaluation. Recognising the computational complexity of solving the constrained multi-row facility layout problem, we propose a novel genetic-based hyper-heuristic algorithm with a reward mechanism to efficiently explore the solution space. A problem-specific heuristic rule is developed in the algorithm to generate high-quality initial solutions. The proposed algorithm employs a genetic algorithm on a high-level algorithm, manipulates low-level heuristic operators to act on the problem domain, and designs nine simple and efficient low-level heuristics. An extensive series of experiments on the benchmark instances have been conducted to evaluate the proposed algorithm. The results illustrate that the proposed algorithm outperforms the comparative methods in 13 out of 17 sets of instances in terms of solution results, and 20 sets of instances in terms of solution time, which demonstrates that the proposed algorithm outperforms the other methods in terms of solution quality, stability, and efficiency.</p>