Path planning is a challenging navigation problem that can be handled using multi-objective methods. This paper, present a thre

     Path planning is a challenging navigation problem that can be handled using multi-objective methods. This paper presents a three-stage multi-objective path-planning method. The first stage is to locate the best or near-best solution path and avoid detected obstacles using a hybrid of the red fox–gray wolf optimizer (RFO–GWO), which finds a route from the start position to the target position. In the second step, a mutation operation using an evolutionary algorithm is utilized to enhance the length, integrity, and smoothness of the route generated by the RFO–GWO algorithm. The final step of the suggested method is refined further using a multiphase technique. By integrating the real sizes of the mobile robots and the size of the barriers and phrasing the issue as a traveling object in the available area, the suggested path-planning method resembles the actual world. The simulation results indicate that this strategy creates the most viable path even in complicated surroundings, overcoming the disadvantages of traditional approaches. Furthermore, when compared to prior path-planning methods, the simulation’s outcomes indicate that the suggested RFO–GWO method is effective in terms of the route, and the strategy is extremely competitive. The results showed a significant improvement, where the total percentage convergence time (in seconds) for RFO–GWO for the three maps was 15%, 12%, and 10%, respectively, whereas it was 35%, 41%, and 43% seconds in GWO and 34%, 35%, and 37% seconds in RFO. There was also a significant improvement in the number of nodes for RFO-GWO (2%, 3%, and 2%) compared to GWO nodes (64%, 65%, and 62%), and RFO nodes (32%, 30%, and 35%)  for the same three maps. Subsequently, the smoothness of the path formed by the recommended approach was enhanced using the evolutionary algorithm (EA), where the total percentage length of the path in the worst scenario for GWO was 28% and for RFO was 26% in units, but after improvement with the RFO-GWO with EA, it became 22% in units.

stages multi-objective path planning method: The first stage is to locate the best or near-best solution path and avoid the detected obstacles using a hybrid of the Red Fox-Grey Wolf optimizer (RFO-GWO) method, which finds a rout from the start position to the target position. In the second step, a mutation operation by evolutionary, are utilized to enhance the length, integrity, and smooth of the rout generated by the RFO-GWO method. the final step the suggested method is refined further by using the multiphase technique. By integrating both the real sizes of the mobile robots and the size of the barriers and phrasing the issue as a traveling object in the available area, the suggested path planning method resembles the actual world. The simulation results indicate that this strategy creates the best viable path even in complicated surroundings, overcoming the disadvantages of traditional approaches. Furthermore, when contrasted with prior path-planning methods, simulation outcomes indicate that the suggested RFO-GWO in terms of route effectivity, the strategy is extremely competitive.