A Study On Quantum Differential Multi-objective Evolutionary Algorithm Based On Decomposition

As swarm intelligence search algorithms, evolutionary algorithms are based onthe theory of evolution, and have incomparable advantages in solving themulti-objective optimization problems (MOPs).The research has been a hot topic.With mathematical programming methods, MOEA/D (Multi-ObjectiveEvolutionary Algorithm based on Decomposition) is a fast and efficient MOEA(Multi-Objective Evolutionary Algorithm). Compared with other algorithms, MOEA/Dhas faster speed and better distribution when solving the MOPs. However the quality ofPareto solutions obtained by the algorithm are not good enough to solve non-convexPareto Front functions. There are theoretical and engineering values to improve theperformance of MOEA/D in non-convex functions.As a combination of MOEA/D and QEA, QD-MOEA/D(Quantum DifferentialMulti-objective Evolutionary Algorithm Based on Decomposition) is put forward toenhance the performance of MOEA/D in solving the non-convex MOPs, and thealgorithm is used to do the corresponding numerical simulation experimental analysesand solve the credit decision bank portfolio problems. The main contents are followed:1.A brief introduction to basic definitions of MOPs is given, and the currentresearches on multi-objective evolutionary algorithms (MOEAs) are reviewed. At thesame time, a detailed description of the characteristics and the algorithm flow ofMOEA/D and the commonly used test functions and performance metrics ofmulti-objective evolutionary algorithms are descried, finally the relevant concepts andprocess of QEAare briefly introduced.2. In view of the excellent properties of quantum evolutionary algorithm in themulti-peak functions, MOEA/D is combined with QEA and quantum differentialmulti-objective evolutionary algorithm based on decomposition (QD-MOEA/D) isproposed. The quantum chromosome of QD-MOEA/D adopts real number encoding,saves memory space and accelerates arithmetic speed. In order to accelerate theconvergence speed and improve the detection of the algorithm, quantum chromosomeadopts differential evolution and its way of mutation is quantum non-gate. Theexperimental results of several standard test functions shows that the algorithmimproves the convergence and the distribution of MOEA/D in non-convex functions.3.QD-MOEA/D is applied to optimization problems of the bank loan portfolio. First of all, bank loan portfolio optimization problems are abstracted as amulti-objective optimization problem, and then QD-MOEA/D is used to solve theproblem, by this way, a range of different preferences decision support are provided todecision makers, and further demonstrate the effectiveness of the proposed algorithm.