Hybrid genetic algorithm for solving the computable general equilibrium model

摘要

It is a part of the main contents for mathematical economics to solve the equilibrium point of computable general equilibrium (CGE) models. Scarfs algorithm is the fundamental approach to this task. But, it depends on the number of subsimplices in unit simplex. The number is proportional to Zn-1. Therefore, the time complexity of Scarfs algorithm is G(Zn-1). To solve this problem, the hybrid genetic algorithm (HGA) is put forward. HGA has the mechanism combining the global optimization with the local optimization. HGA takes CGE as the problem of optimization and its solvent is the search for fixed point in unit complex. The time complexity of HGA does not depend on any subsimplex in unit simplex. The simulation example with n=3 shows that the time complexity of HGA is O(n) and the error is 0.01 resulted from HGA. However, under the same error of 0.01, the time complexity of Scarfs algorithm is O (1002). So HGA is efficient.