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.

存在涉及不同约束的各种优化问题。在这项研究中，我们针对线性约束问题提出了一种称为误差反馈法（EFM）的优化方法。此方法用于计算违反约束的错误，然后按每个参数按比例分配错误，以使新的后代满足约束。与惩罚函数方法相比，EFM具有节省计算资源和收敛速度更快的优点。为了验证EFM的性能，我们以典型的基准测试功能和三个工程模型为例。这些模型包括一个复杂的线性不等式约束，一个具有线性等式约束的Markov预测模型以及两个具有不等式约束的数学平面四杆连杆模型。要优化每个模型，我们选择了三种流行的算法，即粒子群优化，基于教学的优化和差分进化算法。我们将EFM与惩罚函数方法和其他用于处理线性约束问题的方法进行比较。实验结果表明，与比较方法相比，EFM具有更好的稳定性和更快的收敛性。