A supervisor of a discrete-event system can prohibit controllable events to ensure the safety and liveness specifications of the system. However， the supervisor does not actively select the controllable events that are allowed to occur， so it is possible that several controllable events occur simultaneously. In practice， such as traffic scheduling and robot path planning， the system is required to allow at most one controllable event to occur in each state. In response to the above problem， an optimal mechanism was introduced to quantify control cost， and an optimal supervisory control algorithm of discrete-event systems was proposed， which not only can guarantee the safety and liveness of the system， but also can minimize the cumulative cost of event execution. Firstly， the automata model of controlled system and behavioral constraints was given， and a nonblocking supervisor with maximum allowable behaviors was solved on the basis of the supervisory control theory of Ramadge and Wonham. Secondly， a cost function was defined to assign the corresponding cost to the execution of each event in the supervisor. Finally， an optimal directed supervisor was calculated iteratively based on dynamic programming to achieve the goals of at most one controllable event occurring in each state and minimizing the cumulative cost of event execution. To verify the effectiveness and correctness of the proposed algorithm， a one-way train guideway example and a multi-track train control example were used. For the above two examples， the cumulative cost of the event execution required for the directed supervisor solved by the proposed algorithm to reach the target state is 26.0 and 14.0 respectively， which is lower than the 27.5 and 16.0 of greedy algorithm and the 26.5 and 14.0 of Q-learning.

To study the performance and application prospects of novel intelligent optimization algorithms， six bionic intelligent optimization algorithms proposed in the past few years were analyzed， concluding Harris Hawks Optimization （HHO） algorithm， Equilibrium Optimizer （EO）， Marine Predators Algorithm （MPA）， Political Optimizer （PO）， Slime Mould Algorithm （SMA）， and Heap-Based Optimizer （HBO）. Their performance and applications in different constrained engineering optimization problems were compared and analyzed. Firstly， the basic principles of six optimization algorithms were introduced. Secondly， the optimization tests were performed on ten standard benchmark functions for six optimization algorithms. Thirdly， six optimization algorithms were applied to solve three engineering optimization problems with constraints. Experimental results show that the convergence accuracy of PO is the best for the optimization of unimodal and multimodal test functions and can reach the theoretical optimal value zero many times. The EO and MPA are better for solving constrained engineering problems with fast optimization speed， high stability and standard deviation of a small order of magnitude. Finally， the improvement methods and development potentials of six optimization algorithms were analyzed.