Multiple Lagrange multiplier method for constrained evolutionary optimization

One of the well-known problems in evolutionary search for solving optimization problem is the premature convergence. The general constrained optimization techniques such as hybrid evolutionary programming, two-phase evolutionary programming, and Evolian algorithms are not safe from the same problem in the first phase. To overcome this problem, we apply the sharing function to the Evolian algorithm and propose to use the multiple Lagrange multiplier method for the subsequent phases of Evolian. The method develops Lagrange multipliers in each subpopulation region independently and finds multiple global optima in parallel. The simulation results demonstrates the usefulness of the proposed sharing technique and the multiple Lagrange multiplier method.