Effective multi-Agent algorithm with roulette inversion operator for approximating linear systems

The irrationality of the inversion operator designed by John Holland is analyzed and revealed; and a new roulette inversion operator is proposed to cope with this problem. A new multi-agent evolutionary algorithm (RAER) is then developed by integrating the roulette inversion operator. Theoretical analysis shows that RAER converges to the global optimum. Four benchmark functions are used to test the performance of RAER, the results show that RAER achieves a better performance than other algorithms. RAER can be successfully used to solve linear system approximation problems in fixed search areas and dynamically expanded search areas. Especially, in the stable linear system approximation in several enlarged search areas, RAER can find the typical and optimal solutions in one specified area. This demonstrates the efficacy of RAER in practical applications.