Edmondo Minisci

An Inflationary Differential Evolution Algorithm for Space Trajectory Optimization

In this paper, we define a discrete dynamical system that governs the evolution of a population of agents. From the dynamical system, a variant of differential evolution (DE) is derived. It is then demonstrated that, under some assumptions on the differential mutation strategy and on the local structure of the objective function, the proposed dynamical system has fixed points toward which it converges with probability one for an infinite number of generations. This property is used to derive an algorithm that performs better than standard DE on some space trajectory optimization problems. The novel algorithm is then extended with a guided restart procedure that further increases the performance, reducing the probability of stagnation in deceptive local minima.

Analysis of Some Global Optimization Algorithms for Space Trajectory Design

In this paper, we analyze the performance of some global search algorithms on a number of space trajectory design problems. A rigorous testing procedure is introduced to measure the ability of an algorithm to identify the set of ²-optimal solutions. From the analysis of the test results, a novel algorithm is derived. The development of the novel algorithm starts from the redefinition of some evolutionary heuristics in the form of a discrete dynamical system. The convergence properties of this discrete dynamical system are used to derive a hybrid evolutionary algorithm that displays very good performance on the particular class of problems presented in this paper.

On testing global optimization algorithms for space trajectory design

In this paper we discuss the procedures to test a global search algorithm applied to a space trajectory design problem. Then, we present some performance indexes that can be used to evaluate the effectiveness of global optimization algorithms. The performance indexes are then compared highlighting the actual significance of each one of them. A number of global optimization algorithms are tested on four typical space trajectory design problems. From the results of the proposed testing procedure we infer for each pair algorithm-problem the relation between the heuristics implemented in the solution algorithm and the main characteristics of the problem under investigation. From this analysis we derive a novel interpretation of some evolutionary heuristics, based on dynamical system theory and we significantly improve the performance of one of the tested algorithms.

A dynamical system perspective on evolutionary heuristics applied to space trajectory optimization problems

In this paper we propose a generalized formulation of the evolutionary heuristic governing the movement of the individuals of Differential Evolution in the search space. The basic heuristic of Differential Evolution is casted in form of discrete dynamical system and extended to improve local convergence. It is demonstrated that under some assumptions on the local structure of the objective function, the proposed dynamical system, has fixed points towards which it converges asymptotically. This property is used to derive an algorithm that performs better than standard Differential Evolution on some space trajectory optimization problems. The novel algorithm is then extended with a guided restart procedure that further increases the performance reducing the probability of stagnation in deceptive local minima.

Aerodynamic performances of propellers with parametric considerations on the optimal design

Two numerical procedures are presented: the first algorithm allows for the determination of the geometric characteristics of the maximum efficiency propeller for a given operative condition and profile distribution along the blade; the output of this numerical procedure is the chord distribution and twist angle of the blade, together with its efficiency and its torque and thrust coefficients for the prescribed operative condition. The aerodynamic characteristics of the optimum propeller when operating in a condition different from the design one are obtained by a second algorithm that allows for the evaluation of the efficiency, the thrust and torque coefficients of a propeller of known geometry, when the blade pitch and operative condition are varied. The formulation used for deriving the geometry of the optimum propeller and determining its performances when operating off-design is described in detail

Approximated Computation of Belief Functions for Robust Design Optimization

This paper presents some ideas to reduce the computational cost of evidence-based robust design optimization. Evidence Theory crystallizes both the aleatory and epistemic uncertainties in the design parameters, providing two quantitative measures, Belief and Plausibility, of the credibility of the computed value of the design budgets. The paper proposes some techniques to compute an approximation of Belief and Plausibility at a cost that is a fraction of the one required for an accurate calculation of the two values. Some simple test cases will show how the proposed techniques scale with the dimension of the problem. Finally a simple example of spacecraft system design is presented.

Orbit transfer manoeuvres as a test benchmark for comparison metrics of evolutionary algorithms

In the present paper some metrics for evaluating the performance of evolutionary algorithms are considered. The capabilities of two different optimisation approaches are compared on three test cases, represented by the optimisation of orbital transfer trajectories. The complexity of the problem of ranking stochastic algorithms by means of quantitative indices is analyzed by means of a large sample of runs, so as to derive statistical properties of the indices in order to evaluate their usefulness in understanding the actual algorithm capabilities and their possible intrinsic limitations in providing reliable information.

Ascent trajectory optimisation for a single-stage-to-orbit vehicle with hybrid propulsion

This paper addresses the design of ascent trajectories for a hybrid-engine, high performance, unmanned, single-stage-to-orbit vehicle for payload deployment into low Earth orbit. A hybrid optimisation technique that couples a population-based, stochastic algorithm with a deterministic, gradient-based technique is used to maximize the nal vehicle mass in low Earth orbit after accounting for operational constraints on the dynamic pressure, Mach number and maximum axial and normal accelerations. The control search space is first explored by the population-based algorithm, which uses a single shooting method to evaluate the performance of candidate solutions. The resultant optimal control law and corresponding trajectory are then further refined by a direct collocation method based on finite elements in time. Two distinct operational phases, one using an air-breathing propulsion mode and the second using rocket propulsion, are considered. The presence of uncertainties in the atmospheric and vehicle aerodynamic models are considered in order to quantify their effect on the performance of the vehicle. Firstly, the deterministic optimal control law is re-integrated after introducing uncertainties into the models. The proximity of the final solutions to the target states are analysed statistically. A second analysis is then performed, aimed at determining the best performance of the vehicle when these uncertainties are included directly in the optimisation. The statistical analysis of the results obtained are summarized by an expectancy curve which represents the probable vehicle performance as a function of the uncertain system parameters. This analysis can be used during the preliminary phase of design to yield valuable insights into the robustness of the performance of the vehicle to uncertainties in the specification of its parameters.

Multi-objective evolutionary optimization of subsonic airfoils by meta-modelling and evolution control:

Abstract The current work concerns the application of multi-objective evolutionary optimization by approximation function to aerodynamic design. A new general technique, named evolution control (EC), is used in order to manage the on-line enriching of correct solutions database, which is the basis of the learning procedure for the approximators. Substantially, this approach provides that the database, initially quite small and enabling a very inaccurate approximation, should be integrated during the optimization. Such integration is done by means of some choice criteria, allowing deciding which individuals of the current population should be verified. The technique showed being efficacious and very efficient for the considered problem, whose dimensionality are 5. Even if general principle of EC is valid independently from the kind of adopted approximator, this last strongly affects the application. Obtained results are utilized to show how the adoption of artificial neural networks and kriging can differently influence the whole optimization process. Moreover, first results, achieved after reformulating the same problem with seven parameters, support the idea of the performance of the method scale well with dimensionality.

Multi-Population Inflationary Differential Evolution algorithm with Adaptive Local Restart

In this paper a Multi-Population Inflationary Differential Evolution algorithm with Adaptive Local Restart is presented and extensively tested over more than fifty test functions from the CEC 2005, CEC 2011 and CEC 2014 competitions. The algorithm combines a multi-population adaptive Differential Evolution with local search and local and global restart procedures. The proposed algorithm implements a simple but effective mechanism to avoid multiple detections of the same local minima. The novel mechanism allows the algorithm to decide whether to start or not a local search. The local restart of the population, which follows the local search, is, therefore, automatically adapted.