This study introduces three new algorithms, MPW-WOA, MP-WOA, and MPL-WOA, designed to enhance the exploration capability of the well-regarded whale optimization algorithm (WOA), a meta-heuristic optimization technique. These improvements aim to strengthen the exploration capabilities of the algorithm and converge toward the global optimum solution. The focus of WOA on the leader individual may cause the positions of new individuals to get stuck in sub-solutions. To solve this problem, the proposed algorithms aim to obtain stronger and more consistent results by the effect of the best three whales in various ratios instead of a single leader. After the proposed methods are applied 30 times on 23 benchmark test functions, the mean and standard deviation data are examined. This evaluation is carried out by comparing the three proposed algorithms among themselves by applying the Wilcoxon test, and as a result, the best algorithm is determined as MPW-WOA. The proposed algorithms are compared with WOA and shown to be superior. The results of the best algorithm are compared with the methods in the literature, and it is superior in 16 out of 23 functions. This success is also confirmed by the Friedman test. Furthermore, the three proposed algorithms have been successfully applied to four real-world engineering problems, and especially MPW-WOA has produced the best or competitive results compared to its competitors. The overall evaluations have shown that this algorithm is an effective and promising alternative for many optimization problems.