Space trajectories optimization using variable-chromosome-length genetic algorithms

The problem of optimal design of a multi-gravity-assist space trajectories, with free number of deep space maneuvers (MGADSM) poses multi-modal cost functions. In the general form of the problem, the number of design variables is solution dependent. To handle global optimization problems where the number of design variables varies from one solution to another, two novel genetic-based techniques are introduced: hidden genes genetic algorithm (HGGA) and dynamic-size multiple population genetic algorithm (DSMPGA). In HGGA, a fixed length for the design variables is assigned for all solutions. Independent variables of each solution are divided into effective and ineffective (hidden) genes. Hidden genes are excluded in cost function evaluations. Full-length solutions undergo standard genetic operations. In DSMPGA, sub-populations of fixed size design spaces are randomly initialized. Standard genetic operations are carried out for a stage of generations. A new population is then created by reproduction from all members based on their relative fitness. The resulting sub-populations have different sizes from their initial sizes. The process repeats, leading to increasing the size of sub-populations of more fit solutions. Both techniques are applied to several MGADSM problems. They have the capability to determine the number of swing-bys, the planets to swing by, launch and arrival dates, and the number of deep space maneuvers as well as their locations, magnitudes, and directions in an optimal sense. The results show that solutions obtained using the developed tools match known solutions for complex case studies. The HGGA is also used to obtain the asteroids sequence and the mission structure in the global trajectory optimization competition (GTOC) problem. As an application of GA optimization to Earth orbits, the problem of visiting a set of ground sites within a constrained time frame is solved. The J2 perturbation and zonal coverage are considered to design repeated Sun-synchronous orbits. Finally, a new set of orbits, the repeated shadow track orbits (RSTO), is introduced. The orbit parameters are optimized such that the shadow of a spacecraft on the Earth visits the same locations periodically every desired number of days.

MODULARITY BASED FUZZY COMMUNITY DETECTION IN SOCIAL NETWORKS

Fuzzy community detection is to identify fuzzy communities in a network, which are groups of vertices in the network such that the membership of a vertex in one community is in [0,1] and that the sum of memberships of vertices in all communities equals to 1. Fuzzy communities are pervasive in social networks, but only a few works have been done for fuzzy community detection. Recently, a one-step forward extension of Newman’s Modularity, the most popular quality function for disjoint community detection, results into the Generalized Modularity (GM) that demonstrates good performance in finding well-known fuzzy communities. Thus, GMis chosen as the quality function in our research. We first propose a generalized fuzzy t-norm modularity to investigate the effect of different fuzzy intersection operators on fuzzy community detection, since the introduction of a fuzzy intersection operation is made feasible by GM. The experimental results show that the Yager operator with a proper parameter value performs better than the product operator in revealing community structure. Then, we focus on how to find optimal fuzzy communities in a network by directly maximizing GM, which we call it Fuzzy Modularity Maximization (FMM) problem. The effort on FMM problem results into the major contribution of this thesis, an efficient and effective GM-based fuzzy community detection method that could automatically discover a fuzzy partition of a network when it is appropriate, which is much better than fuzzy partitions found by existing fuzzy community detection methods, and a crisp partition of a network when appropriate, which is competitive with partitions resulted from the best disjoint community detections up to now. We address FMM problem by iteratively solving a sub-problem called One-Step Modularity Maximization (OSMM). We present two approaches for solving this iterative procedure: a tree-based global optimizer called Find Best Leaf Node (FBLN) and a heuristic-based local optimizer. The OSMM problem is based on a simplified quadratic knapsack problem that can be solved in linear time; thus, a solution of OSMM can be found in linear time. Since the OSMM algorithm is called within FBLN recursively and the structure of the search tree is non-deterministic, we can see that the FMM/FBLN algorithm runs in a time complexity of at least O (n2). So, we also propose several highly efficient and very effective heuristic algorithms namely FMM/H algorithms. We compared our proposed FMM/H algorithms with two state-of-the-art community detection methods, modified MULTICUT Spectral Fuzzy c-Means (MSFCM) and Genetic Algorithm with a Local Search strategy (GALS), on 10 real-world data sets. The experimental results suggest that the H2 variant of FMM/H is the best performing version. The H2 algorithm is very competitive with GALS in producing maximum modularity partitions and performs much better than MSFCM. On all the 10 data sets, H2 is also 2-3 orders of magnitude faster than GALS. Furthermore, by adopting a simply modified version of the H2 algorithm as a mutation operator, we designed a genetic algorithm for fuzzy community detection, namely GAFCD, where elite selection and early termination are applied. The crossover operator is designed to make GAFCD converge fast and to enhance GAFCD’s ability of jumping out of local minimums. Experimental results on all the data sets show that GAFCD uncovers better community structure than GALS.

SCALABLE APPROXIMATION OF KERNEL FUZZY C-MEANS

Virtually every sector of business and industry that uses computing, including financial analysis, search engines, and electronic commerce, incorporate Big Data analysis into their business model. Sophisticated clustering algorithms are popular for deducing the nature of data by assigning labels to unlabeled data. We address two main challenges in Big Data. First, by definition, the volume of Big Data is too large to be loaded into a computer’s memory (this volume changes based on the computer used or available, but there is always a data set that is too large for any computer). Second, in real-time applications, the velocity of new incoming data prevents historical data from being stored and future data from being accessed. Therefore, we propose our Streaming Kernel Fuzzy c-Means (stKFCM) algorithm, which reduces both computational complexity and space complexity significantly. The proposed stKFCM only requires O(n2) memory where n is the (predetermined) size of a data subset (or data chunk) at each time step, which makes this algorithm truly scalable (as n can be chosen based on the available memory). Furthermore, only 2n2 elements of the full N × N (where N >> n) kernel matrix need to be calculated at each time-step, thus reducing both the computation time in producing the kernel elements and also the complexity of the FCM algorithm. Empirical results show that stKFCM, even with relatively very small n, can provide clustering performance as accurately as kernel fuzzy c-means run on the entire data set while achieving a significant speedup.

REAL TIME FUZZY CONTROLLER FOR QUADROTOR STABILITY CONTROL

In this report, we develop an intelligent adaptive neuro-fuzzy controller by using adaptive neuro fuzzy inference system (ANFIS) techniques. We begin by starting with a standard proportional-derivative (PD) controller and use the PD controller data to train the ANFIS system to develop a fuzzy controller. We then propose and validate a method to implement this control strategy on commercial off-the-shelf (COTS) hardware. An analysis is made into the choice of filters for attitude estimation. These choices are limited by the complexity of the filter and the computing ability and memory constraints of the micro-controller. Simplified Kalman filters are found to be good at estimation of attitude given the above constraints. Using model based design techniques, the models are implemented on an embedded system. This enables the deployment of fuzzy controllers on enthusiast-grade controllers. We evaluate the feasibility of the proposed control strategy in a model-in-the-loop simulation. We then propose a rapid prototyping strategy, allowing us to deploy these control algorithms on a system consisting of a combination of an ARM-based microcontroller and two Arduino-based controllers. We then use a combination of the code generation capabilities within MATLAB/Simulink in combination with multiple open-source projects in order to deploy code to an ARM CortexM4 based controller board. We also evaluate this strategy on an ARM-A8 based board, and a much less powerful Arduino based flight controller. We conclude by proving the feasibility of fuzzy controllers on Commercial-off the shelf (COTS) hardware, we also point out the limitations in the current hardware and make suggestions for hardware that we think would be better suited for memory heavy controllers.