Some faces of Smarandache semigroups' concept in transformation semigroups' approach

In the following text, the main aim is to distinguish some relations between Smarad- che semigroups and (topological) transformation semigroups areas. We will see that a transformation group is not distal if and only if its enveloping semigroup is a Smarandache semigroup. Moreover we will find a classifying of minimal right ideals of the enveloping semigroup of a transformation semigroup

Transparency effect in the emergence of monopolies in social networks

Power law degree distribution was shown in many complex networks. However, in most real systems, deviation from power-law behavior is observed in social and economical networks and emergence of giant hubs is obvious in real network structures far from the tail of power law. We propose a model based on the information transparency (transparency means how much the information is obvious to others). This model can explain power structure in societies with non-transparency in information delivery. The emergence of ultra powerful nodes is explained as a direct result of censorship. Based on these assumptions, we define four distinct transparency regions: perfect non-transparent, low transparent, perfect transparent and exaggerated regions. We observe the emergence of some ultra powerful (very high degree) nodes in low transparent networks, in accordance with the economical and social systems. We show that the low transparent networks are more vulnerable to attacks and the controllability of low transparent networks is harder than the others. Also, the ultra powerful nodes in the low transparent networks have a smaller mean length and higher clustering coefficients than the other regions.Comment: 14 Pages, 3 figure

Adaptive Estimation of Distribution Algorithms for Low-Thrust Trajectory Optimization

A direct adaptive scheme is presented as an alternative approach for minimum-fuel low-thrust trajectory design in non-coplanar orbit transfers, utilizing fitness landscape analysis (FLA). Spacecraft dynamics is modeled with respect to modified equinoctial elements, considering $J_2$ orbital perturbations. Taking into account the timings of thrust arcs, the discretization nodes for thrust profile, and the solution of multi-impulse orbit transfer, a constrained continuous optimization problem is formed for low-thrust orbital maneuver. An adaptive method within the framework of Estimation of Distribution Algorithms (EDAs) is proposed, which aims at conserving feasibility of the solutions within the search process. Several problem identifiers for low-thrust trajectory optimization are introduced, and the complexity of the solution domain is analyzed by evaluating the landscape feature of the search space via FLA. Two adaptive operators are proposed, which control the search process based on the need for exploration and exploitation of the search domain to achieve optimal transfers. The adaptive operators are implemented in the presented EDA and several perturbed and non-perturbed orbit transfer problems are solved. Results confirm the effectiveness and reliability of the proposed approach in finding optimal low-thrust transfer trajectories.BEAZ Bizkaia, 3/12/DP/2021/00150; SPRI Group, Ekintzaile Program EK-00112-202

Multi-objective Optimization of Orbit Transfer Trajectory Using Imperialist Competitive Algorithm

This paper proposes a systematic direct approach to carry out effective multi-objective optimization of space orbit transfer with high-level thrust acceleration. The objective is to provide a transfer trajectory with acceptable accuracy in all orbital parameters while minimizing spacecraft fuel consumption. With direct control parameterization, in which the steering angles of thrust vector are interpolated through a finite number of nodes, the optimal control problem is converted into the parameter optimization problem to be solved by nonlinear programming. Besides the thrust vector direction angles, the thrust magnitude is also considered as variable and unknown along with initial conditions. Since the deviation of thrust vector in spacecraft is limited in reality, mathematical modeling of thrust vector direction is carried out in order to satisfy constraints in maximum deviation of thrust vector direction angles. In this modeling, the polynomial function of each steering angle is defined by interpolation of a curve based on finite number of points in a specific range with a nominal center point with uniform distribution. This kind of definition involves additional parameters to the optimization problem which results the capability of search method in satisfying constraint on the variation of thrust direction angles. Thrust profile is also modeled based on polynomial functions of time with respect to solid and liquid propellant rockets. Imperialist competitive algorithm is used in order to find optimal coefficients of polynomial for thrust vector and the optimal initial states within the transfer. Results are mainly affected by the degree of polynomials involved in mathematical modeling of steering angles and thrust profile which results different optimal initial states where the transfer begins. It is shown that the proposed method is fairly beneficial in the viewpoint of optimality and convergence. The optimality of the technique is shown by comparing the finite thrust optimization with the impulsive analysis. Comparison shows that the accuracy is acceptable with respect to fair precision in orbital elements and minimum fuel mass. Also, the convergence of the optimization algorithm is investigated by comparing the solution of the problem with other optimization techniques such as Genetic Algorithm. Results confirms the practicality of Imperialist Competitive Algorithm in finding optimum variation of thrust vector which results best transfer accuracy along with minimizing fuel consumption

Robust Estimation of Distribution Algorithms via Fitness Landscape Analysis for Optimal Low-Thrust Orbital Maneuvers

One particular kind of evolutionary algorithms known as Estimation of Distribution Algorithms (EDAs) has gained the attention of the aerospace industry for its ability to solve nonlinear and complicated problems, particularly in the optimization of space trajectories during on-orbit operations of satellites. This article describes an effective method for optimizing the trajectory of a spacecraft using an evolutionary approach based on EDAs, incorporated with fitness landscape analysis (FLA). The approach utilizes flexible operators that are paired with seeding and selection mechanisms of EDAs. Initially, the orbit transfer problem is mathematically modeled and the objectives and constraints are identified. The landscape feature of the search space is analyzed via the dispersion metric to measure the modality and ruggedness of the search domain. The obtained information are used as feedback in developing adaptive operators for truncation factor and constraints separation threshold of the employed EDA. A framework for spacecraft trajectory optimization has been presented where the dispersion value for a space mission is estimated using a k-nearest neighbors (k-NN) algorithm. The suggested method is used to solve several problems related to low-thrust orbit transfer of satellites in Earth’s orbit. Results demonstrate that the suggested framework for trajectory design and optimization of space transfers is effective enough to offer fuel-efficient and energy-efficient maneuvers for different thrust levels of the propulsion system. Moreover, the performance of the proposed approach is evaluated against non-adaptive EDA and other advanced evolutionary algorithms. The obtained results certify that the proposed adaptive evolutionary approach is superior in identifying feasible minimum-fuel and minimum-energy transfer trajectories.BEAZ Bizkaia, 3/12/DP/2021/00150; SPRI Group, Ekintzaile Program EK-00112-202

Analysis of a hybrid Genetic Simulated Annealing strategy applied in multi-objective optimization of orbital maneuvers

Optimization of orbital maneuvers is one of the main issues in conceptual and preliminary design of spacecraft in different space missions. The main issue in optimization of high-thrust orbit transfers is that the common optimization algorithms such as Genetic Algorithm and Simulated Annealing are not effectual in finding optimal transfer when they are purely used in optimization. In such problems, modified algorithms are required to find the optimal transfer. Such modifications involve consecutive search and dynamic boundary delimitation. This paper presents a direct approach to optimize high-thrust orbit transfers using a hybrid algorithm based on Simulated Annealing and Genetic Algorithm. This multi-objective optimization method considers optimum fuel transfers while minimizing the error of orbital elements at the end of orbital maneuver. Trajectory optimization is conducted based on converting the orbit transfer problem into a parameter optimization one by assigning proper mathematical functions to the variation of thrust vector direction. Optimization problem is solved using intelligent boundary delimitation in a general optimization method. Taking advantage of nonlinear simulation, a technique is proposed to acquire good quantity for optimization variables, which results in enlarged convergence domain. Numerical example of a three dimensional optimal orbit transfer is analyzed and the accuracy of proposed algorithm is presented. Optimality and convergence of the proposed algorithm is discussed by comparing the results obtained by different approaches. Results confirm the efficiency of the proposed hybrid algorithm in comparison to Simulated Annealing and Genetic Algorithm

Efficient meta-heuristics for spacecraft trajectory optimization

Meta-heuristics has a long tradition in computer science. During the past few years, different types of meta-heuristics, specially evolutionary algorithms got noticeable attention in dealing with real-world optimization problems. Recent advances in this field along with rapid development of high processing computers, make it possible to tackle various engineering optimization problems with relative ease, omitting the barrier of unknown global optimal solutions due to the complexity of the problems. Following this rapid advancements, scientific communities shifted their attention towards the development of novel algorithms and techniques to satisfy their need in optimization. Among different research areas, astrodynamics and space engineering witnessed many trends in evolutionary algorithms for various types of problems. By having a look at the amount of publications regarding the development of meta-heuristics in aerospace sciences, it can be seen that a high amount of efforts are dedicated to develop novel stochastic techniques and more specifically, innovative evolutionary algorithms on a variety of subjects. In the past decade, one of the challenging problems in space engineering, which is tackled mainly by novel evolutionary algorithms by the researchers in the aerospace community is spacecraft trajectory optimization. Spacecraft trajectory optimization problem can be simply described as the discovery of a space trajectory for satellites and space vehicles that satisfies some criteria. While a space vehicle travels in space to reach a destination, either around the Earth or any other celestial body, it is crucial to maintain or change its flight path precisely to reach the desired final destination. Such travels between space orbits, called orbital maneuvers, need to be accomplished, while minimizing some objectives such as fuel consumption or the transfer time. In the engineering point of view, spacecraft trajectory optimization can be described as a black-box optimization problem, which can be constrained or unconstrained, depending on the formulation of the problem. In order to clarify the main motivation of the research in this thesis, first, it is necessary to discuss the status of the current trends in the development of evolutionary algorithms and tackling spacecraft trajectory optimization problems. Over the past decade, numerous research are dedicated to these subjects, mainly from two groups of scientific communities. The first group is the space engineering community. Having an overall look into the publications confirms that the focus in the developed methods in this group is mainly regarding the mathematical modeling and numerical approaches in dealing with spacecraft trajectory optimization problems. The majority of the strategies interact with mixed concepts of semi-analytical methods, discretization, interpolation and approximation techniques. When it comes to optimization, usually traditional algorithms are utilized and less attention is paid to the algorithm development. In some cases, researchers tried to tune the algorithms and make them more efficient. However, their efforts are mainly based on try-and-error and repetitions rather than analyzing the landscape of the optimization problem. The second group is the computer science community. Unlike the first group, the majority of the efforts in the research from this group has been dedicated to algorithm development, rather than developing novel techniques and approaches in trajectory optimization such as interpolation and approximation techniques. Research in this group generally ends in very efficient and robust optimization algorithms with high performance. However, they failed to put their algorithms in challenge with complex real-world optimization problems, with novel ideas as their model and approach. Instead, usually the standard optimization benchmark problems are selected to verify the algorithm performance. In particular, when it comes to solve a spacecraft trajectory optimization problem, this group mainly treats the problem as a black-box with not much concentration on the mathematical model or the approximation techniques. Taking into account the two aforementioned research perspectives, it can be seen that there is a missing link between these two schemes in dealing with spacecraft trajectory optimization problems. On one hand, we can see noticeable advances in mathematical models and approximation techniques on this subject, but with no efforts on the optimization algorithms. On the other hand, we have newly developed evolutionary algorithms for black-box optimization problems, which do not take advantage of novel approaches to increase the efficiency of the optimization process. In other words, there seems to be a missing connection between the characteristics of the problem in spacecraft trajectory optimization, which controls the shape of the solution domain, and the algorithm components, which controls the efficiency of the optimization process. This missing connection motivated us in developing efficient meta-heuristics for solving spacecraft trajectory optimization problems. By having the knowledge about the type of space mission, the features of the orbital maneuver, the mathematical modeling of the system dynamics, and the features of the employed approximation techniques, it is possible to adapt the performance of the algorithms. Knowing these features of the spacecraft trajectory optimization problem, the shape of the solution domain can be realized. In other words, it is possible to see how sensitive the problem is relative to each of its feature. This information can be used to develop efficient optimization algorithms with adaptive mechanisms, which take advantage of the features of the problem to conduct the optimization process toward better solutions. Such flexible adaptiveness, makes the algorithm robust to any changes of the space mission features. Therefore, within the perspective of space system design, the developed algorithms will be useful tools for obtaining optimal or near-optimal transfer trajectories within the conceptual and preliminary design of a spacecraft for a space mission. Having this motivation, the main goal in this research was the development of efficient meta-heuristics for spacecraft trajectory optimization. Regarding the type of the problem, we focused on space rendezvous problems, which covers the majority of orbital maneuvers, including long-range and short-range space rendezvous. Also, regarding the meta-heuristics, we concentrated mainly on evolutionary algorithms based on probabilistic modeling and hybridization. Following the research, two algorithms have been developed. First, a hybrid self adaptive evolutionary algorithm has been developed for multi-impulse long-range space rendezvous problems. The algorithm is a hybrid method, combined with auto-tuning techniques and an individual refinement procedure based on probabilistic distribution. Then, for the short-range space rendezvous trajectory optimization problems, an estimation of distribution algorithm with feasibility conserving mechanisms for constrained continuous optimization is developed. The proposed mechanisms implement seeding, learning and mapping methods within the optimization process. They include mixtures of probabilistic models, outlier detection algorithms and some heuristic techniques within the mapping process. Parallel to the development of algorithms, a simulation software is also developed as a complementary application. This tool is designed for visualization of the obtained results from the experiments in this research. It has been used mainly to obtain high-quality illustrations while simulating the trajectory of the spacecraft within the orbital maneuvers.La Caixa TIN2016-78365R PID2019-1064536A-I00 Basque Government consolidated groups 2019-2021 IT1244-1

Minimum-Fuel Low-Thrust Trajectory Optimization Via a Direct Adaptive Evolutionary Approach

Space missions with low-thrust propulsion systems are of appreciable interest to space agencies because of their practicality due to higher specific impulses. This research proposes a technique to the solution of minimum-fuel non-coplanar orbit transfer problem. A direct adaptive method via Fitness Landscape Analysis (FLA) is coupled with a constrained evolutionary technique to explore the solution space for designing low-thrust orbit transfer trajectories. Taking advantage of the solution for multi-impulse orbit transfer problem, and parameterization of thrust vector, the orbital maneuver is transformed into a constrained continuous optimization problem. A constrained Estimation of Distribution Algorithms (EDA) is utilized to discover optimal transfer trajectories, while maintaining feasibility of the solutions. The low-thrust trajectory optimization problem is characterized via three parameters, referred to as problem identifiers, and the dispersion metric is utilized for analyzing the complexity of the solution domain. Two adaptive operators including the kernel density and outlier detection distance threshold within the framework of the employed EDA are developed, which work based on the landscape feature of the orbit transfer problem. Simulations are proposed to validate the efficacy of the proposed methodology in comparison to the non-adaptive approach. Results indicate that the adaptive approach possesses more feasibility ratio and higher optimality of the obtained solutions.BEAZ Bizkaia, 3/12/DP/2021/00150; SPRI Group, Ekintzaile Program EK-00112-202

A comparative study on the functional response of Wolbachia-infected and uninfected forms of the parasitoid wasp Trichogramma brassicae

Trichogramma species (Hymenoptera: Trichogrammatidae) are haplo-diploid egg parasitoids that are frequently used as biological control agents against lepidopteran pests. These wasps display two reproductive modes, including arrhenotoky (bisexuality) and thelytoky (unisexuality). Thelytokous forms are often associated with the presence of endosymbiotic Wolbachia bacteria. The use of thelytokous wasps has long been considered as a way to enhance the efficacy of biological control. The present study investigates the potential of a thelytokous Wolbachiainfected and an arrhenotokous uninfected Trichogramma brassicae Bezdenko strain as inundative biocontrol agents by evaluating their functional response towards different egg densities of the factitious host, the Angoumois grain moth, Sitotroga cerealella (Olivier) (Lepidoptera: Gelechiidae). The results revealed a type II functional response for both strains in which parasitism efficiency decreases with host egg density because of an increasing host handling time. A model with an indicator variable was used to compare the parameters of Holling’s disc equation in different data sets. It was demonstrated that the two strains did not differ in host attack rate. However, the Wolbachia-infected strain did have an increased host handling time when compared to the bisexual strain. Some applied aspects of the findings are discusse

A Reactive and Efficient Walking Pattern Generator for Robust Bipedal Locomotion

Available possibilities to prevent a biped robot from falling down in the presence of severe disturbances are mainly Center of Pressure (CoP) modulation, step location and timing adjustment, and angular momentum regulation. In this paper, we aim at designing a walking pattern generator which employs an optimal combination of these tools to generate robust gaits. In this approach, first, the next step location and timing are decided consistent with the commanded walking velocity and based on the Divergent Component of Motion (DCM) measurement. This stage which is done by a very small-size Quadratic Program (QP) uses the Linear Inverted Pendulum Model (LIPM) dynamics to adapt the switching contact location and time. Then, consistent with the first stage, the LIPM with flywheel dynamics is used to regenerate the DCM and angular momentum trajectories at each control cycle. This is done by modulating the CoP and Centroidal Momentum Pivot (CMP) to realize a desired DCM at the end of current step. Simulation results show the merit of this reactive approach in generating robust and dynamically consistent walking patterns