Metaheuristic algorithms are general optimization techniques that demonstrate remarkable performance in solving different classes of optimization problems. However, equipping their stochastic search mechanisms with auxiliary logical strategies can still increase their search capability. Based on this fact, in the current study, the search performance of the Interactive Search Algorithm (ISA), as a metaheuristic search method, is improved by adding a new Bayesian regulator strategy to adjust its search behavior. In this regard, the search patterns of the ISA method are unified and classified according to the memory and learning concepts. Subsequently, during the optimization process, the developed Bayesian module dynamically regulates the ratio of the exploration and exploitation search behaviors by tuning the effect of memory concept. The recent technique is named Bayesian Interactive Search Algorithm (BISA), and its search performance tested on a suite of unconstraint mathematical functions and constrained engineering problems. Acquired outcomes indicate that the proposed BISA considerably speeds up the convergence rate, and improves the stability of the process as well as the accuracy of the solutions, for both engineering and mathematical problems.