Comparative study on the application of evolutionary optimization techniques to orbit transfer maneuvers

Orbit transfer maneuvers are here considered as benchmark cases for comparing performance of different optimization techniques in the framework of direct methods. Two different classes of evolutionary algorithms, a conventional genetic algorithm and an estimation of distribution method, are compared in terms of performance indices statistically evaluated over a prescribed number of runs. At the same time, two different types of problem representations are considered, a first one based on orbit propagation and a second one based on the solution of Lambert’s problem for direct transfers. In this way it is possible to highlight how problem representation affects the capabilities of the considered numerical approaches

Evolutionary design of a full-envelope full-authority flight control system for an unstable high-performance aircraft

The use of an evolutionary algorithm in the framework of H1 control theory is being considered as a means for synthesizing controller gains that minimize a weighted combination of the infinite norm of the sensitivity function (for disturbance attenuation requirements) and complementary sensitivity function (for robust stability requirements) at the same time. The case study deals with a complete full-authority longitudinal control system for an unstable high-performance jet aircraft featuring (i) a stability and control augmentation system and (ii) autopilot functions (speed and altitude hold). Constraints on closed-loop response are enforced, that representing typical requirements on airplane handling qualities, that makes the control law synthesis process more demanding. Gain scheduling is required, in order to obtain satisfactory performance over the whole flight envelope, so that the synthesis is performed at different reference trim conditions, for several values of the dynamic pressure, used as the scheduling parameter. Nonetheless, the dynamic behaviour of the aircraft may exhibit significant variations when flying at different altitudes, even for the same value of the dynamic pressure, so that a trade-off is required between different feasible controllers synthesized at different altitudes for a given equivalent airspeed. A multiobjective search is thus considered for the determination of the best suited solution to be introduced in the scheduling of the control law. The obtained results are then tested on a longitudinal non-linear model of the aircraft

Evolutionary design of a full–envelope flight control system for an unstable fighter aircraft

The use of an evolutionary algorithm in the framework of H∞ control theory is being considered as a means for synthesizing controller gains that minimize a weighted combination of the infinite-norm of the sensitivity function (for disturbance attenuation requirements) and complementary sensitivity function (for robust stability requirements) at the same time. The case study deals with the stability and control augmentation of an unstable high-performance jet aircraft. Constraints on closed-loop response are also enforced, that represent typical requirements on airplane handling qualities, that makes the control law synthesis process more demanding. Gain scheduling is required, in order to obtain satisfactory performance over the whole flight envelope, so that the synthesis is performed at different reference trim conditions, for several values of the dynamic pressure, Q, used as the scheduling parameter. Nonetheless, the dynamic behaviour of the aircraft may exhibit significant variations when flying at different altitudes h, even for the same value of the dynamic pressure, so that a trade-off is required between different feasible controllers synthesized for a given value of Q, but different h. A multi-objective search is thus considered for the determination of the best suited solution to be introduced in the scheduling of the control law. The obtained results are then tested on a longitudinal nonlinear model of the aircraft

A test problem for visual investigation of high-dimensional multi-objective search

An inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions

Using numerical plant models and phenotypic correlation space to design achievable ideotypes

Numerical plant models can predict the outcome of plant traits modifications resulting from genetic variations, on plant performance, by simulating physiological processes and their interaction with the environment. Optimization methods complement those models to design ideotypes, i.e. ideal values of a set of plant traits resulting in optimal adaptation for given combinations of environment and management, mainly through the maximization of a performance criteria (e.g. yield, light interception). As use of simulation models gains momentum in plant breeding, numerical experiments must be carefully engineered to provide accurate and attainable results, rooting them in biological reality. Here, we propose a multi-objective optimization formulation that includes a metric of performance, returned by the numerical model, and a metric of feasibility, accounting for correlations between traits based on field observations. We applied this approach to two contrasting models: a process-based crop model of sunflower and a functional-structural plant model of apple trees. In both cases, the method successfully characterized key plant traits and identified a continuum of optimal solutions, ranging from the most feasible to the most efficient. The present study thus provides successful proof of concept for this enhanced modeling approach, which identified paths for desirable trait modification, including direction and intensity.Comment: 25 pages, 5 figures, 2017, Plant, Cell and Environmen

Shift-based density estimation for pareto-based algorithms in many-objective optimization

It is commonly accepted that Pareto-based evolutionary multiobjective optimization (EMO) algorithms encounter difficulties in dealing with many-objective problems. In these algorithms, the ineffectiveness of the Pareto dominance relation for a high-dimensional space leads diversity maintenance mechanisms to play the leading role during the evolutionary process, while the preference of diversity maintenance mechanisms for individuals in sparse regions results in the final solutions distributed widely over the objective space but distant from the desired Pareto front. Intuitively, there are two ways to address this problem: 1) modifying the Pareto dominance relation and 2) modifying the diversity maintenance mechanism in the algorithm. In this paper, we focus on the latter and propose a shift-based density estimation (SDE) strategy. The aim of our study is to develop a general modification of density estimation in order to make Pareto-based algorithms suitable for many-objective optimization. In contrast to traditional density estimation that only involves the distribution of individuals in the population, SDE covers both the distribution and convergence information of individuals. The application of SDE in three popular Pareto-based algorithms demonstrates its usefulness in handling many-objective problems. Moreover, an extensive comparison with five state-of-the-art EMO algorithms reveals its competitiveness in balancing convergence and diversity of solutions. These findings not only show that SDE is a good alternative to tackle many-objective problems, but also present a general extension of Pareto-based algorithms in many-objective optimization. © 2013 IEEE