Constrained Multiobjective Optimization Algorithm Based On Biological Immune System And Its Application

Various control and engineering models can be constructed constrained multiobjective optimization problems(CMOPs).Since the classical mathematical optimization methods are very sensitive to the characteristics of CMOPs to be optimized,it is challenge to solve the CMOPs with complex(nonconvex,discontinuous,dynamic,and so on)Pareto-optimal fronts(PFs)by using the mathematical approaches.However,immune algorithm(IA)based on the biological immune system possesses many distinctive properties,such as parallel,adaptive,and antibody's diversity.Therefore,IA is more suitable to address CMOPs when compared to other intelligent algorithms.In this paper,several constrained multiobjective optimization algorithms(CMOAs)are proposed to solve static CMOPs(SCMOPs)and dynamic CMOPs(DCMOPs)by exploiting advanced intelligent optimization techniques.Moreover,several applications on the control and engineering sciences are investigated by using the proposed algorithms.The concrete contributions are as follows:1)An multi-layer response immune algorithm(CMIGA),based on the multi-layer response model of biological immune system,is proposed to solve SCMOPs with multi-modal,high-dimensional,and complex PFs.In CMIGA,the feasible population and infeasible population are evolved independently in evolution process.And then,the information communication between the two subpopulation is occur to find the global optimal solution.To accelerate the exploitation of the constrained boundaries to be optimized problems,a transformation technique is applied to the individuals with low affinity by using the excellent genes of memory cells as transformation genes.In numerical experiments,eighteen benchmark SCMOPs are considered to evaluate the performance of the proposed algorithm and it is also compared to six state-of-art algorithms.The results indicate that the new method achieves superior constraint-handling ability and the best ranking than other algorithms do on most of the benchmark suite.2)In order to overcome the disadvantage of discard infeasible individuals,such that algorithms are easy to trap into local search in addressing SCMOPs.In this paper,a parallel constrained multiobjective immune algorithm(PCMIOA)by merging objectives and constraints,based on the interactive operation of innate immune and adaptive immune in the immune system,is proposed to solve SCMOPs.The proposed evaluation approach assembled objectives and constraints accelerates the exploration to the constrained boundaries.In addition,a transformation mechanism that occurs in the recombination process of DNA segment is presented to improve the population diversity.An improved domination scope metric is developed in order to overcome the disadvantages of the existing ones.PCMIOA is applied to solve a set of twelve two-objective SCMOPs and four unconstrained three-objective test problems.The experimental results indicate that PCMIOA is able to achieve a superior performance.The PFs obtained by PCMIOA can approximate the true PFs very well and exhibit a well-spread compared to other algorithms.3)Due to the lack of DCMOPs,a set of DCMOPs is developed based on the benchmark SCMOPs.A dynamic constrained multiobjective immune algorithm(DCMOIA)is proposed based on the flowchart of CMIGA with neighbor search strategy.The exploitation and exploitation ability is enhanced by using the proposed neighbor search method.In addition,a gauss immigrations approach is used to response the environmental change to track the moving PFs.In numerical experiments,DCMOIA is applied to solve the proposed DCMOPs,and compared with the other two peer DCMOAs for validating the effectiveness of the proposed algorithm and functions.Simulation results indicate that the proposed DCMOPs are challenge for DCMOIA.However,DCMOIA can obtain spread-well changing PFs when compared with other algorithms.4)Since clonal selection algorithm(CSA)on high-dimensional knapsack problems(KPs)can only obtain a low feasible rate,and it's easy to fall into local search,an improved clonal selection algorithm(CSA-ER),based on a receptor editing mechanism and a repeat repair strategy,is proposed to solve high-dimensional KPs.CSA-ER is compared with CSA's several variants(CSA-M,CSA-E,CSA-MR)and two other intelligent algorithms on KPs in simulation experiments.The results show that CSA-ER has strong capability to handle high-dimensional KPs.Meanwhile,the sensitivity of selection rate ?,editing rate T r,and basic gene segment length ? are analyzed,and the appropriate parameter settings are suggested in the last.5)A novel immune algorithm(MERIA),based on an improving memory update method without replacement and an adaptive environment reaction schemes,has been proposed to solve constrained optimization problems in dynamic environments(DOPs).To maintain the diversity of memory individuals in the memory set,the memory update scheme is used to update the memory pool at every generation.That is,when the memory is greater than or equal to the maximum number of memory level,the elite that differs from any one of memories in terms of fitness is used to replace the worst memory in memory set.Otherwise,the elite that is different with any one of the individual in memory set.In addition,an adaptive environment reaction operation based on an proposed environment detection method is used to determine when to retrieve and how to use the memories in the memory set.Namely,when the environmental change is small,a random immigration strategy is adapted to response the change.Otherwise,the memories mutated immigration scheme is used to response the change.The above strategies can improve the ability of tracking the dynamic optimal solutions of MERIA.Experimental results on DKPs and DUFs indicate that MERIA can faster track the changing environments with different environment change rate,when compared with peer dynamic genetic algorithms.MERIA achieves superior performance of tracking environments and finding optimal solutions.6)To overcome large total harmonic distortion(THD),high compute complex,and low real-time application of the PWM switching sequences obtained by the existing algorithms in inverter control,we propose a simplified clonal selection algorithm(SCSA)to adapt for optimizing the PWM switching sequence of inverters in this paper.SCSA is applied to the single-phase full-bridge inverter for obtaining the optimal PWM switching sequence,and compared with GA,improved immune algorithm(IIA),and clonal selection algorithm(CSA)in numerical experiments.The results demonstrate that the PWM switching sequence obtained by SCSA can generate higher quality power than those gained by other algorithms.The total THD is decreased to 2.19%,moreover,many odd-order harmonics are eliminated.