Abstract
Multiobjective evolutionary algorithm based on decomposition (MOEA/D) is the seminal framework of multiobjective evolutionary algorithms (MOEAs). To alleviate the nonuniformly distributed solutions generated by a fixed set of evenly distributed weight vectors in the presence of nonconvex and disconnected problems, an adaptive vector generation mechanism is proposed. A coevolution strategy and a vector generator are synergistically cooperated to remedy the weight vectors. Optimal weight vectors are generated to replace the useless weight vectors to assure that optimal solutions are distributed evenly. Experiment results indicate that this mechanism is efficient in improving the diversity of MOEA/D.
Highlights
Multiobjective optimization problems (MOPs), different from the single-objective optimization problems (SOPs), have more than one objective function, and the objective functions conflict with each other
Draw the Median Attainment Surface that approximates the Pareto optimal frontal surface obtained after running all the comparison algorithms 31 times, as shown in Figures 2 and 3. e statistical results of the values with respect to HV, Inverted Generational Distance (IGD), Generational Distance (GD), and Pure Diversity (PD) metrics are listed in Tables 2 to 5
Since all algorithms are essentially random search methods, it is difficult to determine whether an algorithm is good or bad based on the results of a single operation. erefore, the average statistics of the results of 31 independent operations are compared with respect to different performance metrics. e best performing algorithms in each of these problems are given in bold in Tables 2 to 5
Summary
Multiobjective optimization problems (MOPs), different from the single-objective optimization problems (SOPs), have more than one objective function, and the objective functions conflict with each other. Conventional analytical algorithms aggregate multiple objective functions into one, which can be solved by the analytical method These algorithms can only obtain one optimized solution at each iteration. By running multiple times and setting different single “composite” objective functions can we obtain enough Pareto optimal solutions. Since the optimization process of each iteration is independent of each other, the information in the iteration process cannot be shared, requiring complex computations [12]. E iconic research on employing EA to solve MOPs refers to Goldberg, by which the notion of nondominated sorting and niching technique are introduced [13]. Because the portion of nondominated solutions in the whole population increase
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