Several Modified Decomposition-Based Multi-objective Evolutionary Algorithms And Their Applications

As population-based heuristic search methods, evolutionary algorithms are verypromising to solve the multi-objective optimization problems (MOPs). The research ofevolutionary multi-objective optimization has become a hot research topic. As acombination of mathematical programming methods and evolutionary algorithms,MOEA/D proposed in1997, is a novel decomposition-based algorithm. Compared withother state-of-the-art multi-objective algorithms, MOEA/D has certain advantages whensolving complicated multi-objective optimization problems. However, all thepopulation-based optimization algorithms suffer from heavy computational burden ingeneral, not excepting MOEA/D, and the results obtained by MOEA/D are not goodenough for many-objective problems and more complicated multi-objective problems.Therefore, researchs on improving MOEA/D and modified decomposition-basedmulti-objective evolutionary algorithms are of great theoretical significance andpotential practical value.The aim of this dissertation is to explore the theories and mechanisms of MOEA/D,to design modified decomposition-based multi-objective evolutionary algorithms, and todo the corresponding numerical experimental analyses. The main research works in thisdissertation consist of the following aspects:1. For well dealing with many-objective problems, uniform design method isadopted to set the aggregation coefficient vectors of the subproblems. Uniform designmulti-objective evolutionary algorithm based on decomposition (UMOEA/D) isproposed. Compared with MOEA/D using the simplex-lattice design method,distribution of the coefficient vectors in UMOEA/D is more uniform over the designspace, and the population size neither increases nonlinearly with the number ofobjectives nor considers a formulaic setting, which extends MOEA/D’s use inoptimizing problems with many objectives. Three sets of experiments with3-5objectives problems are carried out. The experimental results indicate that UMOEA/Doutperforms MOEA/D and NSGA-II on almost all these many-objective problems,especially on problems with more objectives and complicated Pareto set shapes.Experimental results also show that UMOEA/D runs faster than NSGA-II.2. For accelerating the convergence speed of MOEA/D, a simplified quadraticapproximation (SQA) as a local search operator is integrated into MOEA/D. Amulti-objective memetic algorithm based on decomposition, i.e. a hybrid of MOEA/Dwith SQA (MOEA/D-SQA) is proposed. SQA is a three-point quadratic approximation,it is convenient to compute and easy to use. Simplified quadratic approximation needsno gradient computation, and it tries to make good use of the values of the objectivefunction already evaluated. MOEA/D-SQA has been tested on thirteen unconstrainedCEC2009test problems. Experimental results indicate that the proposed approachperforms better than MOEA/D. In addition, the results obtained are very competitive when comparing MOEA/D-SQA with other state-of-the-art techniques.3. Uniform design multi-objective differential algorithm based on decomposition(UMODE/D) is presented. The algorithm is a modification to the new version ofMOEA/D based on differential evolution (DE), i.e., MOEA/D-DE. Its distinguishingfeatures include:(1) The uniform design method is applied to generate the aggregationcoefficient vectors so that the decomposed single objective optimization subproblemsare uniformly distributed, and therefore the algorithm could explore uniformly theregion of interest from the initial iteration;(2) The SQA is employed to improve thelocal search ability and the accuracy of the minimum scalar aggregation function value.UMODE/D is compared with the original MOEA/D-DE and NSGA-II by solving ninemulti-objective problems with complicated Pareto set shapes. Experimental resultsindicate that UMODE/D significantly outperforms MOEA/D-DE and NSGA-II on thesetest problems. Two sets of experiments are carried out to illustrate the efficiency of theuniform design method and the SQA separately. In addition, UMODE/D is tested onCEC2009problems. Experimental results show that the proposed algorithm performsbetter than the other algorithms for almost all the CEC2009problems.4. UMOEA/D is employed to solve multi-objective0-1knapsack problems.0-1knapsack problem is a typical0-1linear integer programming problem withnonnegative coefficients, it belongs to the category of discrete optimization problems.Compared with the continuous multi-objective optimization problems, the discretemulti-objective optimization problems are more difficult to handle. UMOEA/D isemployed to solve knapsack problems with2-4objectives. Experimental results indicatethat the final solutions obtained by UMOEA/D have better spread and convergence thanthose obtained by NSGA-II, SPEA2and PESA. Which demonstrates UMOEA/D iseffective for solving this type of discrete multi-objective optimization problems.5. UMODE/D is applied to optimization designs of a linear array antenna forphase-only based pattern reconfigurable. UMODE/D considers the optimization designsof pattern reconfigurable antenna as multi-objective problems, and realizes them inparallel. In practical applications, considering the weight preferences of the patterns,decision markers can select the Pareto solution (i.e., optimized design of reconfigurableantenna) corresponding to the weight preference they want. UMODE/D is used tosynthesize the desired double-pattern and triple-pattern. Simulation results show that theoptimized patterns are in good agreement with the desired ones. Which demonstratesUMODE/D is an effective technique to design pattern reconfigurable antenna.