Changtong Luo

Low Dimensional Simplex Evolution--A Hybrid Heuristic for Global Optimization

In this paper, a new real-coded evolutionary algorithm - low dimensional simplex evolution (LDSE) for global optimization is proposed. It is a hybridization of two well known heuristics, the differential evolution (DE) and the Nelder-Mead method. LDSE takes the idea of DE to randomly select parents from the population and perform some operations with them to generate new individuals. Instead of using the evolutionary operators of DE such as mutation and cross-over, we introduce operators based on the simplex method, which makes the algorithm more systematic and parameter-free. The proposed algorithm is very easy to implement, and its efficiency has been studied on an extensive testbed of 50 test problems from M.M. Ali et al. Numerical results show that the new algorithm outperforms DE in terms of number of function evaluations (nfe) and percentage of success (ps).With the development of Internet, p2p is increasingly receiving attention in research. Recently, a class of p2p applications with time constraints appear. These applications require a short time to locate the resource and(or) a low transit delay between the resource user and the resource holder, such as Skype, MSN. In this paper we propose a scalable p2p overlay for applications with time constraints. Our system provides supports for just two operations for uplayered p2p applications: (1) Given a resource key and the nodes IP who holds the resource, it registers the resource information to the associated node in at most two overlay hops; and (2) Given a resource key and a time constraint(0 for no constraint), it returns if possible a path(one or two overlay hops) to the resource holder, and the transit delay of the path is lower than the time constraint. Results from theoretical analysis and simulations show that our system is viable and scalable.

Low dimensional simplex evolution: a new heuristic for global optimization

This paper presents a new heuristic for global optimization named low dimensional simplex evolution (LDSE). It is a hybrid evolutionary algorithm. It generates new individuals following the Nelder-Mead algorithm and the individuals survive by the rule of natural selection. However, the simplices therein are real-time constructed and low dimensional. The simplex operators are applied selectively and conditionally. Every individual is updated in a framework of try-try-test. The proposed algorithm is very easy to use. Its efficiency has been studied with an extensive testbed of 50 test problems from the reference (J Glob Optim 31:635–672, 2005). Numerical results show that LDSE outperforms an improved version of differential evolution (DE) considerably with respect to the convergence speed and reliability.

Parse-matrix evolution for symbolic regression

Data-driven model is highly desirable for industrial data analysis in case the experimental model structure is unknown or wrong, or the concerned system has changed. Symbolic regression is a useful method to construct the data-driven model (regression equation). Existing algorithms for symbolic regression such as genetic programming and grammatical evolution are difficult to use due to their special target programming language (i.e., LISP) or additional function parsing process. In this paper, a new evolutionary algorithm, parse-matrix evolution (PME), for symbolic regression is proposed. A chromosome in PME is a parse-matrix with integer entries. The mapping process from the chromosome to the regression equation is based on a mapping table. PME can easily be implemented in any programming language and free to control. Furthermore, it does not need any additional function parsing process. Numerical results show that PME can solve the symbolic regression problems effectively.

Some modifications of low-dimensional simplex evolution and their convergence

Low-dimensional simplex evolution (LDSE) is a real-coded evolutionary algorithm for global optimization. In this paper, we introduce three techniques to improve its performance: low-dimensional reproduction (LDR), normal struggle (NS) and variable dimension (VD). LDR tries to preserve the elite by keeping some of its (randomly chosen) components. LDR can also help the offspring individuals to escape from the hyperplane determined by their parents. NS tries to enhance its local search capability by allowing unlucky individual search around the best vertex of m-simplex. VD tries to draw lessons from recent failure by making further exploitation on its most promising sub-facet. Numerical results show that these techniques can improve the efficiency and reliability of LDSE considerably. The convergence properties are then analysed by finite Markov chains. It shows that the original LDSE might fail to converge, but modified LDSE with the above three techniques will converge for any initial population. To evaluate the convergence speed of modified LDSE, an estimation of its first passage time (of reaching the global minimum) is provided.

A Genetic Algorithm for Finding Minimal Multi-homogeneous Bézout Number

Homotopy continuation is a most efficient numerical method for finding all isolated solutions of system of polynomial equations, and finding minimal multi-homogeneous Bezout number is a basic problem of homotopy continuation. This paper presents a problem-specific genetic algorithm for finding minimal multi-homogeneous Bezout number. The algorithm is easy to implement and easy to be parallelized for large scale problems. It can find the minimal multi-homogeneous Bezout number in probability 1. Numerical results indicate that the proposed algorithm is reliable and efficient. The algorithm offers a competitive alternative for minimal multi-homogeneous Bezout number problem. Meanwhile, it extends the application fields of genetic algorithms.

Block building programming for symbolic regression

Abstract Symbolic regression that aims to detect underlying data-driven models has become increasingly important for industrial data analysis. For most existing algorithms such as genetic programming (GP), the convergence speed might be too slow for large-scale problems with a large number of variables. This situation may become even worse with increasing problem size. The aforementioned difficulty makes symbolic regression limited in practical applications. Fortunately, in many engineering problems, the independent variables in target models are separable or partially separable. This feature inspires us to develop a new approach, block building programming (BBP). BBP divides the original target function into several blocks, and further into factors. The factors are then modeled by an optimization engine (e.g. GP). Under such circumstances, BBP can make large reductions to the search space. The partition of separability is based on a special method, block and factor detection. Two different optimization engines are applied to test the performance of BBP on a set of symbolic regression problems. Numerical results show that BBP has a good capability of structure and coefficient optimization with high computational efficiency.

Adaptive space transformation

When developing a new hypersonic vehicle, thousands of wind tunnel tests to study its aerodynamic performance are needed. Due to limitations of experimental facilities and/or cost budget, only a part of flight parameters could be replicated. The point to predict might locate outside the convex hull of sample points. This makes it necessary but difficult to predict its aerodynamic coefficients under flight conditions so as to make the vehicle under control and be optimized. Approximation based methods including regression, nonlinear fit, artificial neural network, and support vector machine could predict well within the convex hull (interpolation). But the prediction performance will degenerate very fast as the new point gets away from the convex hull (extrapolation). In this paper, we suggest regarding the prediction not just a mathematical extrapolation, but a mathematics-assisted physical problem, and propose a supervised self-learning scheme, adaptive space transformation (AST), for the prediction. AST tries to automatically detect an underlying invariant relation with the known data under the supervision of physicists. Once the invariant is detected, it will be used for prediction. The result should be valid provided that the physical condition has not essentially changed. The study indicates that AST can predict the aerodynamic coefficient reliably, and is also a promising method for other extrapolation related predictions.

A multilevel block building algorithm for fast modeling generalized separable systems

Data-driven modeling plays an increasingly important role in different areas of engineering. For most of existing methods, such as genetic programming (GP), the convergence speed might be too slow for large scale problems with a large number of variables. It has become the bottleneck of GP for practical applications. Fortunately, in many applications, the target models are separable in some sense. In this paper, we analyze different types of separability of some real-world engineering equations and establish a mathematical model of generalized separable system (GS system). In order to get the structure of the GS system, a multilevel block building (MBB) algorithm is proposed, in which the target model is decomposed into a number of blocks, further into minimal blocks and factors. Compare to the conventional GP, MBB can make large reductions to the search space. This makes MBB capable of modeling a complex system. The minimal blocks and factors are optimized and assembled with a global optimization search engine, low dimensional simplex evolution (LDSE). An extensive study between the proposed MBB and a state-of-the-art data-driven fitting tool, Eureqa, has been presented with several man-made problems, as well as some real-world problems. Test results indicate that the proposed method is more effective and efficient under all the investigated cases.

Force measurement using strain-gauge balance in a shock tunnel with long test duration

Force tests were conducted at the long-duration-test shock tunnel JF12, which has been designed and built in the Institute of Mechanics, Chinese Academy of Sciences. The performance tests demonstrated that this facility is capable of reproducing a flow of dry air at Mach numbers from 5 to 9 at more than 100 ms test duration. Therefore, the traditional internal strain-gauge balance was considered for the force tests use in this large impulse facility. However, when the force tests are conducted in a shock tunnel, the inertial forces lead to low-frequency vibrations of the test model and its motion cannot be addressed through digital filtering because a sufficient number of cycles cannot be found during a shock tunnel run. The post-processing of the balance signal thus becomes extremely difficult when an averaging method is employed. Therefore, the force measurement encounters many problems in an impulse facility, particularly for large and heavy models. The objective of the present study is to develop pulse-type sting balance by using a strain-gauge sensor that can be applied in the force measurement of 100 ms test time, especially for the force test of the large-scale model. Different structures of the S-series (i.e., sting shaped balances) strain-gauge balance are proposed and designed, and the measuring elements are further optimized to overcome the difficulties encountered during the measurement of aerodynamic force in a shock tunnel. In addition, the force tests were conducted using two large-scale test models in JF12 and the S-series strain-gauge balances show good performance in the force measurements during the 100 ms test time.

Force measurement in a shock tunnel with 100 milliseconds test duration

Force tests were conducted at the long-duration-test shock tunnel JF12, which has been designed and built in the Institute of Mechanics, Chinese Academy of Sciences. The performance tests demonstrated that this facility is capable of reproducing a flow of dry air at Mach numbers from 5–9 at more than 100 ms test duration. Therefore, the traditional internal strain-gauge balance was considered for the force tests use in this large impulse facility. However, when the force tests are conducted in a shock tunnel, the inertial forces lead to low-frequency vibrations of the test model and its motion cannot be addressed through digital filtering because a sufficient number of cycles cannot be found during a shock tunnel run. The post-processing of the balance signal thus becomes extremely difficult when an averaging method is employed. Therefore, the force measurement encounters many problems in an impulse facility, particularly for large and heavy models. The objective of the present study is to develop pulse-type sting balance by using a strain-gauge sensor, that can be applied in the force measurement that 100 ms test time, especially for the force test of the large-scale model. Different structures of the S-series (i.e., sting shaped balances) strain-gauge balance are proposed and designed, and the measuring elements are further optimized to overcome the difficulties encountered during the measurement of aerodynamic force in a shock tunnel. In addition, the force tests were conducted using two large-scale test models in JF12 and the S-series strain-gauge balances show good performance in the force measurements during the 100 ms test time.