The Artificial Orca Algorithm (AOA) is an existing swarm intelligence algorithm, empowered in this paper by two well-known mutation operators and opposition-based learning, yielding the novel methods Deep Self-Learning Artificial Orca Algorithm (DSLAOA), Opposition Deep Self-Learning Artificial Orca Algorithm (ODSLAOA), and Opposition Artificial Orca Learning Algorithm. The DSLAOA and ODSLAOA are based on the Cauchy and Gauss mutation operators. Their effectiveness is evaluated on both continuous and discrete problems. The suggested algorithms are tested and compared to seven recent state-of-the-art metaheuristics in the continuous context. The results demonstrate that, when compared to the other algorithms, DSLAOA based on the Cauchy operator is the most effective technique. After that, a specific real-world scenario involving emergency medical services in a dire situation is tackled. The Ambulance Dispatching and Emergency Calls Covering Problem is the addressed problem, and a mathematical formulation is made to model this issue. AOA, DSLAOAC, and DSLAOAG are tested and contrasted with a successful recent heuristic in this field. The experiments are run on real data, and the results show that the swarm approaches are effective and helpful in determining the resources required in this kind of emergency.