Dimensional Multi-objective Optimization Research Articles

Incorporating aggregation trees in two-archive algorithm 2 for solving high dimensional multi-objective electromagnetic optimization

The optimization designs of modern electromagnetic devices are often modeled as high dimensional multi-objective problems due to their high-quality demands in multiple functions and systemization. To identify and remove the redundant objectives, an interactive aggregation trees method embedded into the two-archive algorithm 2 is proposed to solve the high dimensional multi-objective optimizations. To balance the speed and the accuracy in finding the redundant objectives, conflict degree, conflict list and conflict flag are developed in an interactive aggregation trees frame. The two-archive algorithm 2 is modified to adjust the updated model obtained from the objective-reduction frame. Mathematical test functions and TEAM Workshop Problem 22 are used to test the performance of the proposed method. Numerical results demonstrate that the proposed method can remove the redundant objectives effectively and provide qualified solutions for the electromagnetic optimization designs.

Aerodynamic optimization to tandem stators by using sweep and dihedral

In the modern aerodynamic design of turbomachinery blades, the geometries of blades often need to be reshaped to achieve better aerodynamic performance by introducing extra parametric design variables. A higher variable dimension will lead to a larger sampling range as well as a sparser sample distribution, which challenges the effectiveness and stability of optimization schemes based on surrogate model by making the model prediction quality even poorer. In this paper, a multi-objective optimization based on Gaussian process model was carried out for a high dimensional design space. Based on the previous two-dimensional optimization, tandem stators of a modern compressor were optimized by the design of sweep and dihedral. The purpose of the study is to improve the aerodynamic performance of the compressor tandem stators as well as to provide an effective optimization scheme for high dimensional multi-objective optimization problems. The design of sweep and dihedral for reshaping the tandem stators consists of a total of 18 design variables. An improvement in total pressure recovery coefficient of at least 0.7% at positive incidence and at least 0.3% at negative incidence was obtained, much larger than that in the previous two-dimensional optimization. The optimization process shows that, by using Gaussian process as the surrogate model and a special sampling strategy, this optimization scheme is effective and efficient to handle this high dimensional space. The aerodynamic influences of design parameters of tandem blades were analyzed in detail and the superiority of sweep and dihedral in reducing aerodynamic loss was confirmed.

Gender approaches to evolutionary multi-objective optimization using pre-selection of criteria

ABSTRACTA novel idea to perform evolutionary computations (ECs) for solving highly dimensional multi-objective optimization (MOO) problems is proposed. Following the general idea of evolution, it is proposed that information about gender is used to distinguish between various groups of objectives and identify the (aggregate) nature of optimality of individuals (solutions). This identification is drawn out of the fitness of individuals and applied during parental crossover in the processes of evolutionary multi-objective optimization (EMOO). The article introduces the principles of the genetic-gender approach (GGA) and virtual gender approach (VGA), which are not just evolutionary techniques, but constitute a completely new rule (philosophy) for use in solving MOO tasks. The proposed approaches are validated against principal representatives of the EMOO algorithms of the state of the art in solving benchmark problems in the light of recognized EC performance criteria. The research shows the superiority of the gender approach in terms of effectiveness, reliability, transparency, intelligibility and MOO problem simplification, resulting in the great usefulness and practicability of GGA and VGA. Moreover, an important feature of GGA and VGA is that they alleviate the ‘curse’ of dimensionality typical of many engineering designs.

A Multiobjective Evolutionary Algorithm Using Gaussian Process-Based Inverse Modeling

To approximate the Pareto front, most existing multiobjective evolutionary algorithms store the nondominated solutions found so far in the population or in an external archive during the search. Such algorithms often require a high degree of diversity of the stored solutions and only a limited number of solutions can be achieved. By contrast, model-based algorithms can alleviate the requirement on solution diversity and in principle, as many solutions as needed can be generated. This paper proposes a new model-based method for representing and searching nondominated solutions. The main idea is to construct Gaussian process-based inverse models that map all found nondominated solutions from the objective space to the decision space. These inverse models are then used to create offspring by sampling the objective space. To facilitate inverse modeling, the multivariate inverse function is decomposed into a group of univariate functions, where the number of inverse models is reduced using a random grouping technique. Extensive empirical simulations demonstrate that the proposed algorithm exhibits robust search performance on a variety of medium to high dimensional multiobjective optimization test problems. Additional nondominated solutions are generated a posteriori using the constructed models to increase the density of solutions in the preferred regions at a low computational cost.

Multi-Objective Reactive Power Optimization Based On The Fuzzy Adaptive Particle Swarm Algorithm

To research the problem on the multi-objective reactive power optimization, to utilize the theory of multiobjective fuzzy optimization to change the multi-objective optimization into the single-objective optimization, and to adopt the fuzzy adaptive particle swarm algorithm to carry out solutions. Comprehensively considering the security and economical efficiency of the system, as well as the condition of the operation constraints, to propose a comprehensive and practical multi-objective reactive power optimization model. To consider the multi-objective reactive power optimization model of the voltage stability index can optimize the economic benefit and safety benefit of the system. Applying the theory of multi-objective fuzzy optimization combined with the adaptive particle swarm optimization algorithm to the problem of the multi-objective reactive power optimization could solve the problem of the different dimensional multi-objective optimization in a better way. After adopting the fuzzy adaptive particle swarm algorithm, the superiorities, such as achieving the global optimal solution, reducing the computational complexity, and improving the computational efficiency,are displayed.