A preliminary study of a new multi-objective optimization algorithm

This paper presents a preliminary study which describes and evaluates a multi-objective (MO) version of a recently created single objective (SO) optimization algorithm called the "Alliance Algorithm" (AA). The algorithm is based on the metaphorical idea that several tribes, with certain skills and resource needs, try to conquer an environment for their survival and to ally together to improve the likelihood of conquest. The AA has given promising results in several fields to which has been applied, thus the development of a MO variant (MOAA) is a natural extension. Here the MOAA's performance is compared with two well-known MO algorithms: NSGA-II and SPEA-2. The performance measures chosen for this study are the convergence and diversity metrics. The benchmark functions chosen for the comparison are from the ZDT and OKA families and the main classical MO problems. The results show that the three algorithms have similar overall performance. Thus, it is not possible to identify a best algorithm for all the problems; the three algorithms show a certain complementarity because they offer superior performance for different classes of problems. © 2012 IEEE.

Multi-objective optimization for multiphase orbital rendezvous missions

A multi-objective optimization approach was proposed for multiphase orbital rendezvous missions and validated by application to a representative numerical problem. By comparing the Pareto fronts obtained using the proposed method, the relationships between the three objectives considered are revealed, and the influences of other mission parameters, such as the sensors' field of view, can also be analyzed effectively. For multiphase orbital rendezvous missions, the tradeoff relationships between the total velocity increment and the trajectory robustness index as well as between the total velocity increment and the time of flight are obvious and clear. However, the tradeoff relationship between the time of flight and the trajectory robustness index is weak, especially for the four- and five-phase missions examined. The proposed approach could be used to reorganize a stable rendezvous profile for an engineering rendezvous mission, when there is a failure that prevents the completion of the nominal mission.

Multi-objective optimization of a fluid structure interaction benchmarking

The integration and application of a new multi-objective tabu search optimization algorithm for Fluid Structure Interaction (FSI) problems are presented. The aim is to enhance the computational design process for real world applications and to achieve higher performance of the whole system for the four considered objectives. The described system combines the optimizer with a well established FSI solver which is based on the fully implicit, monolithic formuFlation of the problem in the Arbitrary Lagrangian-Eulerian FEM approach. The proposed solver resolves the proposed uid-structure interaction benchmark which describes the self-induced elastic deformation of a beam attached to a cylinder in laminar channel ow. The optimized ow characteristics of the aforementioned geometrical arrangement illustrate the performance of the system in two dimensions. Special emphasis is given to the analysis of the simulation package, which is of high accuracy and is the core of application. The design process identifies the best combination of ow features for optimal system behavior and the most important objectives. In addition, the presented methodology has the potential to run in parallel, which will significantly speed-up the elapsed time. Finite Element Method (FEM), Fluid-Structure Interaction (FSI), Multi-Ojective Tabu search (MOTS2). Copyright © 2013 Tech Science Press.

An investigation of higher-order multi-objective optimisation for 3D aerodynamic shape design

We investigate the performance of different variants of a suitably tailored Tabu Search optimisation algorithm on a higher-order design problem. We consider four objective func- tions to describe the performance of a compressor stator row, subject to a number of equality and inequality constraints. The same design problem has been previously in- vestigated through single-, bi- and three-objective optimisation studies. However, in this study we explore the capabilities of enhanced variants of our Multi-objective Tabu Search (MOTS) optimisation algorithm in the context of detailed 3D aerodynamic shape design. It is shown that with these enhancements to the local search of the MOTS algorithm we can achieve a rapid exploration of complicated design spaces, but there is a trade-off be- tween speed and the quality of the trade-off surface found. Rapidly explored design spaces reveal the extremes of the objective functions, but the compromise optimum areas are not very well explored. However, there are ways to adapt the behaviour of the optimiser and maintain both a very efficient rate of progress towards the global optimum Pareto front and a healthy number of design configurations lying on the trade-off surface and exploring the compromise optimum regions. These compromise solutions almost always represent the best qualitative balance between the objectives under consideration. Such enhancements to the effectiveness of design space exploration make engineering design optimisation with multiple objectives and robustness criteria ever more practicable and attractive for modern advanced engineering design. Finally, new research questions are addressed that highlight the trade-offs between intelligence in optimisation algorithms and acquisition of qualita- tive information through computational engineering design processes that reveal patterns and relations between design parameters and objective functions, but also speed versus optimum quality. © 2012 AIAA.

Interactive multi-objective particle swarm optimisation using decision space interaction

The most common approach to decision making in multi-objective optimisation with metaheuristics is a posteriori preference articulation. Increased model complexity and a gradual increase of optimisation problems with three or more objectives have revived an interest in progressively interactive decision making, where a human decision maker interacts with the algorithm at regular intervals. This paper presents an interactive approach to multi-objective particle swarm optimisation (MOPSO) using a novel technique to preference articulation based on decision space interaction and visual preference articulation. The approach is tested on a 2D aerofoil design case study and comparisons are drawn to non-interactive MOPSO. © 2013 IEEE.

Application of the multi-objective Alliance algorithm to a benchmark aerodynamic optimization problem

This paper introduces a new version of the multiobjective Alliance Algorithm (MOAA) applied to the optimization of the NACA 0012 airfoil section, for minimization of drag and maximization of lift coefficients, based on eight section shape parameters. Two software packages are used: XFoil which evaluates each new candidate airfoil section in terms of its aerodynamic efficiency, and a Free-Form Deformation tool to manage the section geometry modifications. Two versions of the problem are formulated with different design variable bounds. The performance of this approach is compared, using two indicators and a statistical test, with that obtained using NSGA-II and multi-objective Tabu Search (MOTS) to guide the optimization. The results show that the MOAA outperforms MOTS and obtains comparable results with NSGA-II on the first problem, while in the other case NSGA-II is not able to find feasible solutions and the MOAA is able to outperform MOTS. © 2013 IEEE.

Multi-objective shape optimisation for horizontal-axis wind turbine blades

We are developing a wind turbine blade optimisation package CoBOLDT (COmputa- tional Blade Optimisation and Load De ation Tool) for the optimisation of large horizontal- axis wind turbines. The core consists of the Multi-Objective Tabu Search (MOTS), which controls a spline parameterisation module, a fast geometry generation and a stationary Blade Element Momentum (BEM) code to optimise an initial wind turbine blade design. The objective functions we investigate are the Annual Energy Production (AEP) and the fl apwise blade root bending moment (MY0) for a stationary wind speed of 50 m/s. For this task we use nine parameters which define the blade chord, the blade twist (4 parameters each) and the blade radius. Throughout the optimisation a number of binary constraints are defined to limit the noise emission, to allow for transportation on land and to control the aerodynamic conditions during all phases of turbine operation. The test case shows that MOTS is capable to find enhanced designs very fast and eficiently and will provide a rich and well explored Pareto front for the designer to chose from. The optimised blade de- sign could improve the AEP of the initial blade by 5% with the same flapwise root bending moment or reduce MY0 by 7.5% with the original energy yield. Due to the fast runtime of order 10 seconds per design, a huge number of optimisation iterations is possible without the need for a large computing cluster. This also allows for increased design flexibility through the introduction of more parameters per blade function or parameterisation of the airfoils in future. © 2012 by Nordex Energy GmbH.

Multi-objective shape optimisation for horizontal-axis wind turbine blades

We are developing a wind turbine blade optimisation package CoBOLDT (COmputa- tional Blade Optimisation and Load Deation Tool) for the optimisation of large horizontal- axis wind turbines. The core consists of the Multi-Objective Tabu Search (MOTS), which controls a spline parameterisation module, a fast geometry generation and a stationary Blade Element Momentum (BEM) code to optimise an initial wind turbine blade design. The objective functions we investigate are the Annual Energy Production (AEP) and the apwise blade root bending moment (MY0) for a stationary wind speed of 50 m/s. For this task we use nine parameters which define the blade chord, the blade twist (4 parameters each) and the blade radius. Throughout the optimisation a number of binary constraints are defined to limit the noise emission, to allow for transportation on land and to control the aerodynamic conditions during all phases of turbine operation. The test case shows that MOTS is capable to find enhanced designs very fast and efficiently and will provide a rich and well explored Pareto front for the designer to chose from. The optimised blade de- sign could improve the AEP of the initial blade by 5% with the same apwise root bending moment or reduce MY0 by 7.5% with the original energy yield. Due to the fast runtime of order 10 seconds per design, a huge number of optimisation iterations is possible without the need for a large computing cluster. This also allows for increased design flexibility through the introduction of more parameters per blade function or parameterisation of the airfoils in future. © 2012 AIAA.

Testing of the multi-objective alliance algorithm on benchmark functions

A new version of the Multi-objective Alliance Algorithm (MOAA) is described. The MOAA's performance is compared with that of NSGA-II using the epsilon and hypervolume indicators to evaluate the results. The benchmark functions chosen for the comparison are from the ZDT and DTLZ families and the main classical multi-objective (MO) problems. The results show that the new MOAA version is able to outperform NSGA-II on almost all the problems.