This study addresses the issue of minimizing computational resources spent on solving the multi-robot path planning (MRPP) problem. We propose a novel algorithm inspired by Lamarckian evolution principles integrated into the traditional Darwin evolutionary algorithm. The proposed Lamarckian Evolution-Based (LEB) algorithm aims to enhance both the convergence rate and the accuracy of the MRPP problem solution, thereby reducing overall computational effort. Through extensive simulations, the LEB algorithm demonstrated superior performance compared to standard approaches such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). Despite requiring additional computational resources per iteration due to added local optimization stages, the LEB algorithm achieves significant reductions in total resource expenditure and improves solution quality within a specified computational budget. Our findings highlight the potential of Lamarckian-inspired strategies for efficient multirobot navigation tasks. Moreover, the research emphasizes the importance of balancing convergence speed with accuracy under strict resource constraints, especially in scenarios with limited onboard energy. The proposed framework can be further generalized to other classes of combinatorial optimization problems where the trade-off between local refinement and global exploration is critical. Overall, the LEB algorithm contributes a promising direction for resource-aware multi-robot coordination in dynamic and uncertain environments.