Describing the grasshopper optimization algorithm to solve multi-objective optimization problems, the key idea in this paper is to simulate the swarm behavior of grasshoppers to find an optimal or near-optimal solution to a problem in which up to four objectives are pursued. (Optimization problems with more than four objectives are called many-objective problems, but that is beyond the scope of this study.) The end result of a solution should have the objectives in the problem reach a balanced state following the Pareto optimality.
The algorithm sets the position of the ith grasshopper as the result of the combined forces of social interaction (Si), gravity (Gi), and wind advection (Ai), that is, Xi = Si + Gi + Ai.
Si is determined by a function of the distances from the ith grasshopper to the rest of the grasshoppers. Gi and Ai are all exponential functions of some adjustable parameters. When converging, the algorithm generates a stable state that is optimal or near optimal for the given problem.
To assess the performance of the proposed algorithm, the authors compare it with a few other recent optimization algorithms using some standard test functions in the literature. The performance metrics include the inverse generational distance (IGD), which measures how close the obtained Pareto optimal solution is to the true Pareto optimal solution; the spacing (SP), which measures the average distance between different obtained optimal Pareto solutions; and the maximum spread (MS), which is a measure of the maximum distance among all solutions. Extensive tests show the proposed algorithm is equal to or faster than other state-of-the-art algorithms.
The proposed algorithm is very interesting in obtaining an optimal or near-optimal solution to the multi-objective problem by simulating the swarm behavior of grasshoppers. The proposed algorithm belongs to the category of genetic algorithms (GAs). This should be of interest to all who are interested in GAs. The paper itself is self-contained and well written.
