Optimization method for linear constraint problems

There are various optimization problems that involve different constraints. In this study, we propose an optimization method, called the error feedback method (EFM), for linear constraint problems. This method is used to calculate the errors that violate the constraints and then allocates the errors in proportion to each parameter, such that the new offspring satisfies the constraints. EFM has the advantages of saving computing resources and converging faster than the penalty function method. To verify the performance of the EFM, we use a typical benchmark function and three engineering models as examples. The models include a complex linear inequality constraint, a Markov prediction model with linear equality constraints, and two mathematical planar four-bar linkage models with inequality constraints. To optimize each model, we select three popular algorithms, namely, particle swarm optimization, teaching-learning-based optimization, and differential evolution algorithm. We compare the EFM with the penalty function method and other methods for handling linear constraint problems. The experimental results show that the EFM has significantly better stability and faster convergence than the compared methods.