Biogeography Based Optimization (BBO) Approach for Sensor Selection in Aircraft Engine

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1 Biogeography Based Optimization (BBO) Approach for Sensor Selection in Aircraft Engine V.Hymavathi, B.Abdul Rahim, Fahimuddin.Shaik P.G Scholar, (M.Tech), Department of Electronics and Communication Engineering, Annamacharya institute of Technology and Sciences, Rajampet, Andhra Pradesh, India Department of Electronics and Communication Engineering, Annamacharya institute of Technology and Sciences, Rajampet, Andhra Pradesh, India, Department of Electronics and Communication Engineering, Annamacharya institute of Technology and Sciences, Rajampet, Andhra Pradesh, India, ABSTRACT: Nowadays many optimization techniques have come into implementation for various applications and this made to look for a better optimization mechanism to achieve good results. Heuristic optimization has become popular because of flexibility and has been inspired by very simple concepts. This work proposes a heuristic optimization algorithm known as biogeography based optimization (BBO). Actually biogeography based optimization (BBO) has been inspired by biogeography. Biogeography refers to the study of organisms based on their locations. The main inspiration of BBO algorithm was from the evolution and balance of prays and predators of ecosystems. Hence BBO is considered as an Evolutionary algorithm. The main aim of this work is to find the optimized solution for sensor selection in an Aircraft Engine. The sensor selection is mainly based on Health estimation parameters of Aircraft engine. For this purpose the data provided by NASA for MAPSS (Modular aero propulsion system simulation.) is utilized and investigated using different Optimization algorithms. A comparative analysis showing the proposed BBO method is better than other algorithm in use.. KEYWORDS: Biogeography based optimization, differential evolution, and genetic algorithm I. INTRODUCTION Optimization is defined as an act, process, or methodology of making something (as a design, system, or decision) as fully perfect, functional, or effective as possible; specifically : the mathematical procedures (as finding the maximum of a function) involved in this. It is a field of applied mathematics whose principles and methods are used to solve quantitative problems in disciplines including physics, biology, engineering, and economics. Questions of maximizing or minimizing functions arising in the various disciplines can be solved using the same mathematical tools. In a typical optimization problem, the goal is to find the values of controllable factors determining the behavior of a system (e.g., a physical production process, an investment scheme) that maximize productivity or minimize waste. The simplest problems involve functions (systems) of a single variable (input factor) and may be solved with differential calculus. There are different types of optimization techniques like ACO, PSO, GA, DE, ES, BBO etc,. Optimization strategies have gained wide importance in solving complex problems in various fields. Many optimization algorithms such as genetic algorithm, ant colony optimization algorithm etc, are used widely in applications like image processing, bioinformatics etc, to solve problems with high complexity. Biogeography-based optimization (BBO) is an optimization technique introduced by Dan Simon in 2008[1]. This technique is based on the theory of biogeography. This optimization algorithm works on the basis of two concepts-migration and mutation. Biogeography can be traced to the work of nineteenth century naturalists such as Alfred Wallace and Charles Darwin. IJIRCCE 176

2 Until the 1960s, biogeography was mainly descriptive and historical. In the early 1960s, Robert MacArthur and Edward Wilson began working together on mathematical models of biogeography, their work culminating with the classic 1967 publication. Biogeography is the study of the geographical distribution of biological organisms. Mathematical equations that govern the distribution of organisms were first discovered and developed. Always the mindset of an engineer is that we can learn from nature. This motivates the application of biogeography to optimization problems [2]. Just as the mathematics of biological genetics inspired the development of genetic algorithms (GAs), and the mathematics of biological neurons inspired the development of artificial neural networks, this paper considers the mathematics of biogeography as the basis for the development of a new field: biogeography-based optimization (BBO). II.WORKING PROCEDURE BBO algorithm can be sequenced as follows: 1. Define the migration probability and mutation probability 2. Initialize the population. 3. Calculate the immigration rate and emigration rate of each candidate in the population. 4. Select the island to be modified based on the immigration rate. 5. Using roulette wheel selection on the emigration rate, select the island from which the SIV is to be emigrated. 6. Randomly select an SIV from the selected island to be emigrated. 7. Perform mutation based on the mutation probability of each island. 8. Calculate the fitness of each individual island. If the fitness criterion is not satisfied go to step3. ADVANTAGES: 1. Generation time is minimum when compared to the other optimization techniques. 2. Better performance than other techniques. 3. This approach is used in many applications. DISADVANTAGES: 1. BBO is poor in exploiting the solutions. 2. There is no provision for selecting the best members from each generation. 3. A habitat doesn t consider its resultant fitness while immigrating the features, as a result so many infeasible solutions are generated. OBSERVATIONS: 1. BBO is better than ACO because ACO generates a new set of solution with each iteration. But BBO maintains its set of solutions from one iteration to the next, relying on migration to probabilistically adopt those solution. 2. BBO has the most in common with Particle Swarm Optimization and DE. In these approaches, Solutions are maintained in one iteration to the next, but each solution is able to learn from its neighbors and adopt itself as the algorithm progresses. III.LITERATURE SURVEY There are many optimization techniques such as ant colony optimization (ACO), biogeography-based optimization (BBO), differential evolution (DE), evolutionary strategy (ES), genetic algorithm (GA), probability-based incremental learning (PBIL), particle swarm optimization (PSO). Each optimization technique has its own advantages and disadvantages. ANT COLONY OPTIMIZATION (ACO): ACO is a population-based meta-heuristic that can be used to find approximate solutions to difficult optimization problems. In ACO, a set of software agents called artificial ants search for good solutions to a given optimization problem. To apply ACO, the optimization problem is transformed into the problem of finding the best path on a weighted graph. The artificial ants (hereafter ants) incrementally build solutions by moving on the graph. The solution IJIRCCE 177

3 construction process is stochastic and is biased by a pheromone model, that is, a set of parameters associated with graph components (either nodes or edges) whose values are modified at runtime by the ants. BIOGEOGRAPHY-BASED OPTIMIZATION (BBO): BBO is a new biogeography inspired algorithm for global optimization. It is also a bio-inspired and population based optimization algorithm. DIFFERENTIAL EVOLUTION (DE): DE is a method that optimizes the problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. Such methods are commonly known as meta-heuristics as they make few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. However, meta-heuristics such as DE do not guarantee an optimal solution is ever found. DE is used for multi-dimensional real valued functions but does not use the gradient of the problem being optimized, which means DE does not require for the optimization problem to be differentiable as is required by classic optimization methods such as gradient descent and quasi-newton methods. DE can therefore also be used on optimization problems that are not even continuous, are noisy, change over time, etc. DE optimizes a problem by maintaining a population of candidate solutions and creating new candidate solutions by combining existing ones according to its simple formulae, and then keeping whichever candidate solution has the best score or fitness on the optimization problem at hand. In this way the optimization problem is treated as a black box that merely provides a measure of quality given a candidate solution and the gradient is therefore not needed. DE is originally due to Storn and Price. Books have been published on theoretical and practical aspects of using DE in parallel computing, multi-objective optimization, constrained optimization, and the books also contain surveys of application areas. EVOLUTION STRATEGY (ES) : It is an optimization technique based on ideas of adaptation and evolution. It belongs to the general class of evolutionary computation or artificial evolution methodologies. Evolution strategies use natural problem-dependent representations, and primarily mutation and selection, as search operators. In common with evolutionary algorithms, the operators are applied in a loop. An iteration of the loop is called a generation. The sequence of generations is continued until a termination criterion is met. As far as real-valued search spaces are concerned, mutation is normally performed by adding a normally distributed random value to each vector component. The step size or mutation strength (i.e. the standard deviation of the normal distribution) is often governed by self-adaptation (see evolution window). Individual step sizes for each coordinate or correlations between coordinates are either governed by self-adaptation or by covariance matrix adaptation (CMA-ES). The (environmental) selection in evolution strategies is deterministic and only based on the fitness rankings, not on the actual fitness values. The resulting algorithm is therefore invariant with respect to monotonic transformations of the objective function. The simplest evolution strategy operates on a population of size two: the current point (parent) and the result of its mutation. Only if the mutant's fitness is at least as good as the parent one, it becomes the parent of the next generation. Otherwise the mutant is disregarded. GENETIC ALGORITHM (GA): GA is a search heuristic that mimics the process of natural selection. This heuristic (also sometimes called a metaheuristic) is routinely used to generate useful solutions to optimization and search problems[1]. Genetic algorithms belong to the larger class of evolutionary algorithms (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover. Genetic algorithms find application in bioinformatics, phylogenetics, computational science, engineering, economics, chemistry, manufacturing, mathematics, physics, pharmacometrics and other fields. PARTICLE SWARM OPTIMIZATION (PSO): PSO is a computational method that optimizes a problem by iteratively trying to improve a candidate solution with regard to a given measure of quality. PSO optimizes a problem by having a population of candidate solutions, here dubbed particles, and moving these particles around in the search-space according to simple mathematical formulae over the particle's position and velocity. Each particle's movement is influenced by its local best known position but, is IJIRCCE 178

4 also guided toward the best known positions in the search-space, which are updated as better positions are found by other particles. This is expected to move the swarm toward the best solutions. PSO is originally attributed to Kennedy, Eberhart and Shi[1][2] and was first intended for simulating social behavior[3], as a stylized representation of the movement of organisms in a bird flock or fish school. The algorithm was simplified and it was observed to be performing optimization. The book by Kennedy and Eberhart[4] describes many philosophical aspects of PSO and swarm intelligence. An extensive survey of PSO applications is made by Poli[5][6]. PSO is a meta-heuristic as it makes few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. However, meta-heuristics such as PSO do not guarantee an optimal solution is ever found. More specifically, PSO is a pattern search method which does not use the gradient of the problem being optimized, which means PSO does not require that the optimization problem be differentiable as is required by classic optimization methods such as gradient descent and quasi-newton methods. PSO can therefore also be used on optimization problems that are partially irregular, noisy, change over time, etc. IV.RESULTS The simulation has been carried out on existing optimization techniques and the results are shown in a graphical form considering generation time on x axis and minimum cost function on y-axis. ANT COLONY OPTIMIZATION (ACO): DIFFERENTIAL EVALUTION (DE): IJIRCCE 179

5 PARTICLE SWARM OPTIMIZATION (PSO): EVOLUTIONARY STRATEGY (ES): GENETIC ALGORITHM (GA): IJIRCCE 180

6 PROBABILITY BASED INCREMENTAL LEARNING(PBIL): V.CONCLUSION The optimized solution for sensor selection in an Aircraft Engine is carried out using different algorithms. A comparative analysis showing the proposed BBO method is better than other algorithms is shown via graphical and tabular representation ALGORITHM MINIMUM COST GENERATION TIME ACO PSO BBO DE GA PBIL REFERENCES [1] Shahrzad Saremi and Seyedali Mirjalili, Integrating Chaos to Biogeography-Based Optimization Algorithm, International Journal of Computer and Communication Engineering, Vol. 2, No. 6, November [2] Dan Simon, Biogeography-Based Optimization, IEEE Transactions on Evolutionary Computation, VOL. 12, NO. 6, DECEMBER [3] Ammu P K, Sivakumar K C, Rejimoan R, Biogeography-Based Optimization - A Survey, International Journal of Electronics and Computer Science Engineering ISSN PP [4] H. Muhlenbein and D. Schlierkamp-Voosen, Predictive models for the breeder genetic algorithm: I. Continuous parameter optimization,, Evol. Comput., vol. 1, pp , [5] T. Back, Evolutionary Algorithms in Theory and Practice. Oxford, U.K.: Oxford Univ. Press, [6] K. Parker and K. Melcher, The modular aero-propulsion systems simulation (MAPSS) users guide, NASA, Tech. Memo , [7] D. Simon and D. L. Simon, Kalman filter constraint switching for turbofan engine health estimation, Eur. J. Control, vol. 12, pp ,May [8] D. Simon, Optimal State Estimation, New York: Wiley, [9] R. Mushini and D. Simon, On optimization of sensor selection for aircraft gas turbine engines, Proc. Int. Conf. Syst. Eng., Las Vegas, NV, Aug. 2005, pp [10] C. Chuan-Chong and K. Khee-Meng, Principles and Techniques in Combinatorics. Singapore: World Scientific, IJIRCCE 181

7 BIOGRAPHY V. Hymavathi received her B. Tech Degree from J.N.T University, Anantapur. She is currently working towards M.Tech in Embedded Systems from Annamacharya Institute of Technology & Sciences, Rajampet, A.P, India. She has research interests in optimization and sensor networks. B. Abdul Rahim received B.E degree in Electronics & Communication Engineering from Gulbarga University in 1990 and M.Tech (Digital Systems & Computer Electronics) from Jawaharlal Nehru Technological University in He is currently working towards Ph.D. degree from JNT University Anantapur. He has published papers in international journals and conferences. He is a member of professional bodies like IEEE, EIE, ISTE, IACSIT, IAENG etc. His research interests include Fault Tolerant Systems, Embedded Systems and parallel processing Fahimuddin Shaik did his B. Tech in Electronics & Communication Engineering and M.Tech in Digital Electronics & Communication Systems from JNT University, Hyderabad, India. He is currently working towards a PhD in biomedical image processing. He is with Annamacharya Institute of Technology & Sciences Rajampet, Andhra Pradesh. His research interests include signal processing, time series analysis, and biomedical image processing. He has presented many research papers at national and international conferences. He has authored a book MEDICAL IMAGING IN DIABETES, VOL 1- A Technical Approach, Cinnamonteal Publishing, December 2011 IJIRCCE 182