Simulated Kalman Filter Research Articles

Multi-Agent cubature Kalman optimizer: A novel metaheuristic algorithm for solving numerical optimization problems

Optimization problems arise in diverse fields such as engineering, economics, and industry. Metaheuristic algorithms, including the Simulated Kalman Filter (SKF), have been developed to solve these problems. SKF, inspired by the Kalman Filter (KF) in control engineering, requires three parameters (initial error covariance P(0), measurement noise Q, and process noise R). However, studies have yet to focus on tuning these parameters. Furthermore, no significant improvement is shown by the parameter-less SKF (with randomized P(0), Q, and R). Randomly choosing values between 0 and 1 may lead to too small values. As an estimator, KF raises concerns with excessively small Q and R values, which can introduce numerical stability issues and result in unreliable outcomes. Tuning parameters for SKF is a challenging and time-consuming task. The Multi-Agent Cubature Kalman Filter (MACKO), inspired by the Cubature Kalman filter (CKF), was introduced in this work. The nature of the Cubature Kalman filter (CKF) allows the use of small values for parameters P(0), Q, and R. In the MACKO algorithm, Cubature Transformation Techniques (CTT) are employed. CTT can use small values for parameters P(0), Q, and R, so CKF was developed to overcome KF and other estimation algorithms. Moreover, in CTT, the term local neighborhoods is used to propagate the cubature point in local search, where the radius, δ, of local search is updated in every iteration to balance between the exploration and exploitation processes. MACKO is evaluated on the CEC 2014 benchmark suite with 30 optimization problems, and its performance is compared with nine existing metaheuristic algorithms. Simulation results demonstrate that MACKO is superior, outperforming the benchmark algorithms, as indicated by Friedman's test with a 5 % significance level.

FPGA Implementation of Metaheuristic Optimization Algorithm

Metaheuristic algorithms are gaining popularity amongst researchers due to their ability to solve nonlinear optimization problems as well as the ability to be adapted to solve a variety of problems. There is a surge of novel metaheuristics proposed recently, however it is uncertain whether they are suitable for FPGA implementation. In addition, there exists a variety of design methodologies to implement metaheuristics upon FPGA which may improve the performance of the implementation. The project begins by researching and identifying metaheuristics which are suitable for FPGA implementation. The selected metaheuristic was the Simulated Kalman Filter (SKF) which proposed an algorithm that was low in complexity and used a small number of steps. Then the Discrete SKF was adapted from the original metaheuristic by rounding all floating-point values to integers as well as setting a fixed Kalman gain of 0.5. The Discrete SKF was then modeled using behavioral modeling to produce the Binary SKF which was then implemented onto FPGA. The design was made modular by producing separate modules that managed different parts of the metaheuristic and Parallel-In-Parallel-Out configuration of ports was also implemented. The Discrete SKF was then simulated on MATLAB meanwhile the Binary SKF was implemented onto FPGA and their performance were measured based on chip utilization, processing speed, and accuracy of results. The Binary SKF produced speed increment of up to 69 times faster than the Discrete SKF simulation.

Cubature Kalman Optimizer: A Novel Metaheuristic Algorithm for Solving Numerical Optimization Problems

This study introduces a new single-agent metaheuristic algorithm, named cubature Kalman optimizer (CKO). The CKO is inspired by the estimation ability of the cubature Kalman filter (CKF). In control system, the CKF algorithm is used to estimate the true value of a hidden quantity from an observation signal that contain an uncertainty. As an optimizer, the CKO agent works as individual CKF to estimate an optimal or a near-optimal solution. The agent performs four main tasks: solution prediction, measurement prediction, and solution update phases, which are adopted from the CKF. The proposed CKO is validated on CEC 2014 test suite on 30 benchmark functions. To further validate the performance, the proposed CKO is compared with well-known algorithms, including single-agent finite impulse response optimizer (SAFIRO), single-solution simulated Kalman filter (ssSKF), simulated Kalman filter (SKF), asynchronous simulated Kalman filter (ASKF), particle swarm optimization algorithm (PSO), genetic algorithm (GA), grey wolf optimization algorithm (GWO), and black hole algorithm (BH). Friedman's test for multiple algorithm comparison with 5% of significant level shows that the CKO offers better performance than the benchmark algorithms.

Feature Selection of Microarray Data Using Simulated Kalman Filter with Mutation

Microarrays have been proven to be beneficial for understanding the genetics of disease. They are used to assess many different types of cancers. Machine learning algorithms, like the artificial neural network (ANN), can be trained to determine whether a microarray sample is cancerous or not. The classification is performed using the features of DNA microarray data, which are composed of thousands of gene values. However, most of the gene values have been proven to be uninformative and redundant. Meanwhile, the number of the samples is significantly smaller in comparison to the number of genes. Therefore, this paper proposed the use of a simulated Kalman filter with mutation (SKF-MUT) for the feature selection of microarray data to enhance the classification accuracy of ANN. The algorithm is based on a metaheuristics optimization algorithm, inspired by the famous Kalman filter estimator. The mutation operator is proposed to enhance the performance of the original SKF in the selection of microarray features. Eight different benchmark datasets were used, which comprised: diffuse large b-cell lymphomas (DLBCL); prostate cancer; lung cancer; leukemia cancer; “small, round blue cell tumor” (SRBCT); brain tumor; nine types of human tumors; and 11 types of human tumors. These consist of both binary and multiclass datasets. The accuracy is taken as the performance measurement by considering the confusion matrix. Based on the results, SKF-MUT effectively selected the number of features needed, leading toward a higher classification accuracy ranging from 95% to 100%.

A Performance of AFIRO among Asynchronous Iteration Strategy Metaheuristic Algorithms

Asynchronous Finite Impulse Response Optimizer (AFIRO) is a metaheuristic algorithm that has been developed as a population-based solution with an asynchronous update mechanism. AFIRO is inspired by the Ultimate Unbiased Finite Impulse Response filter framework. AFIRO works with a group of agents where each agent performs the iteration update asynchronously. In the original paper, AFIRO was compared with the Particle Swarm Optimisation algorithm, Genetic Algorithm, and Grey Wolf Optimizer. Although AFIRO shows a better performance, the comparison seems unfair since the iteration strategy of AFIRO is different from those compared algorithms. Hence, this article further investigates the potential of AFIRO against three existent metaheuristic algorithms with the same iteration strategy, namely Asynchronous PSO (A-PSO), Asynchronous Gravitational Search Algorithm (A-GSA), and Asynchronous Simulated Kalman Filter (A-SKF). The CEC2014 test suite was applied to evaluate the performance, where the results revealed that AFIRO leads 18 out of 30 functions. The Holm post hoc showed that AFIRO performs significantly better than A-SKF and A-GSA while having the same performance as A- PSO. Moreover, the Friedman test disclosed that AFIRO has the highest ranking than A-PSO, A-SKF, and A-GSA. Therefore, it can be concluded that AFIRO performs well in the same iteration strategy category.

A brief review of simulated Kalman Filter Algorithm – variants and applications

Simulated Kalman Filter (SKF) solves optimization problems by finding the estimate of the optimum solution. As a multi-agent algorithm, every agent in the population acts as a Kalman filter by using a standard Kalman filter framework, which includes a simulated measurement process and a best-so-far solution as a reference. This paper presented an overview of the research progress in SKF from the day it was introduced until the present day, discussing the progress, improvements, modifications, and applications of SKF. The fundamental and standard algorithm were first introduced. Then, the work on the algorithm improvements was surveyed. Finally, the remaining unresolved problems and some directions of SKF research were discussed. We reviewed 57 SKF papers. 16 of them on fundamental improvements, 9 on extension of the algorithm to discrete problems and 25 on their applications. Researchers have worked on ideas to improve exploration capability to prevent premature convergence by trying prediction operators, opposition-based learning, and different iteration strategies. There were also attempts to hybridize SKF with other famous algorithms such as Particle Swarm Optimization (PSO), Gravitational Search Algorithm (GSA), and Sine Cosine Algorithm (SCA) to improve its performance. Lastly, a single-agent variant of SKF and a multi-objective SKF were introduced. SKF algorithms and its variants have been implemented in at least nine areas of applications: drill path optimization, airport gate allocation problem (AGAP), assembly sequence planning (ASP), system identification, feature selection, image template matching, controller tuning, wireless sensor network, and engineering design problem. The literature reviewed solely depended on the keyword search that contained the terms simulated Kalman filter from December 2015 to the present date. This is the first review paper on SKF. It is hoped that this survey would be beneficial for the researchers of this area and attracting interest towards the algorithm.

Solving Assembly Sequence Planning Using Distance Evaluated Simulated Kalman Filter

This paper presents an implementation of simulated Kalman filter (SKF) algorithm for optimizing an assembly sequence planning (ASP) problem. The SKF search strategy contains three simple steps; predict-measure-estimate. The main objective of the ASP is to determine the sequence of component installation to shorten assembly time or save assembly costs. Initially, permutation sequence is generated to represent each agent. Each agent is then subjected to a precedence matrix constraint to produce feasible assembly sequence. In this paper, the distance evaluated SKF (DESKF) is proposed for solving ASP problem. The performance of the proposed DESKF is compared against previous works in solving ASP by applying BGSA, BPSO, and MSPSO. Using a case study of ASP, the results show that DESKF outperformed all the algorithms in obtaining the best solution.

Single-agent Finite Impulse Response Optimizer vs Simulated Kalman Filter Optimizer


 
 
 
 Single-agent Finite Impulse Response Optimizer (SAFIRO) is a new estimation-based optimization algorithm which mimics the work procedure of the ultimate unbiased finite impulse response (UFIR) filter. In a real UFIR filter, the horizon length, N, plays an important role to obtain the optimal estimation. In SAFIRO, N represents the repetition number of estimation part that needs to be done in find-ing an optimal solution. On the other hand, Simulated Kalman Filter (SKF) is also an estimation- based optimization algorithm inspired by the estimation capability of Kalman filtering. In literature, substantial amount of works has been devoted to SKF, both in applied research and fundamental enhancements. Thus, in this paper, a performance comparison of both SAFIRO and SKF is presented. It is found that the SAFIRO outperforms the SKF significantly.
 
 
 

A Tutorial on Population-based Simulated Kalman Filter


 
 
 
 Simulated Kalman Filter (SKF) is an estimation-based optimization algorithm which is established based on the Kalman filtering framework. Even since the SKF algorithm is introduced in 2015, there is no tutorial been published on SKF. One may find that the equations and flowchart of the algorithm is not easy to understand. Hence, this paper provides a tutorial on SKF algorithm that emphasizes on a numerical example for easy and intuitive explanations. This tutorial would be important to those who work on the fundamentals and applications of SKF as well as to students who are new to optimization research.
 
 
 

A Tutorial on Single-solution Simulated Kalman Filter


 
 
 
 Simulated Kalman Filter (SKF) is an estimation-based optimization algorithm which is established based on the Kalman filtering framework. A variant of SKF which operates using one agent is called single-solution simulated Kalman filter (ssSKF). At present, there is no tutorial been published on ssSKF. One may find that the equations and flowchart of the algorithm is not easy to understand. Hence, this paper provides a tutorial on ssSKF algorithm that emphasizes on a numerical example for easy and intuitive explanations. This tutorial would be important to those who work on the fundamentals and applications of ssSKF as well as to students who are new to optimization research.
 
 
 

Design of an Helical Spring using Single-solution Simulated Kalman Filter Optimizer


 
 
 
 Optimization is one of the important process in solving engineering problems. Regrettably, there are numerous problems in practical optimization that cannot be solved flawlessly within reasonable computational effort. Thus, metaheuristic approach is often useful to get near-optimal solution when the best solution is not achievable. This paper demonstrates the usefullness of a metaheuristic algorithm called single-solution simulated Kalman filter (ssSKF) in helical spring design, which is an example of structural engineering design problem. The ssSKF is a single agent-based optimization algorithm based on the Kalman filtering. The solution obtained by the ssSKF is compared againsts the genetic algorithm, co-evolutionary particle swarm optimization, co-evolutionary differential evolution, bat algorithm, and artificial bee colony.
 
 
 

A Three-bar Truss Design using Single-solution Simulated Kalman Filter Optimizer


 
 
 
 Three-bar truss is a structure that is important in the field of civil engineering. Design of the three-bar truss is thus an interesting problem in engineering. Metaheuristic approach has been employed to get near-optimal solution of this problem. A study to investigate the effectiveness of a new single-solution simulated Kalman filter (ssSKF) algorithm in three-bar truss design is presented in this paper. The solution obtained by the ssSKF is as good as hybrid lightning search algorithm-simplex method and better than solutions produced other algorithms in literature.
 
 
 

Fitness-evaluated Adaptive Switching Simulated Kalman Filter Algorithm with Randomness


 
 
 
 The original Simulated Kalman Filter (SKF) is an optimizer that employs synchronous update mechanism. The agents in SKF update their solutions after all fitness calculations, prediction process, and measurement process are completed. An alternative to synchronous update is asynchronous update. In asynchronous update, only one agent does fitness calculation, prediction, measurement, and estimation processes at one time. A recent study shows that the asynchronous SKF outperforms synchronous SKF. In this study, synchronous and asynchronous mechanisms are combined in SKF. At first, the SKF starts with either synchronous or asynchronous update. By evaluating the fitness, if no improved solution is found, the SKF changes its update mechanism. The decision to switch from synchronous to asynchronous or vice versa is made randomly. Using the CEC2014 benchmark test suite, experimental results indicate that the proposed adaptive switching SKF randomness outperforms the original SKF algorithm.
 
 
 

Enhancing Simulated Kalman Filter Algorithm using Current Optimum Opposition-based Learning

Simulated Kalman filter (SKF) is a new population-based optimization algorithm inspired by estimation capability of Kalman filter. Each agent in SKF is regarded as a Kalman filter. Based on the mechanism of Kalman filtering, the SKF includes prediction, measurement, and estimation process to search for global optimum. The SKF has been shown to yield good performance in solving benchmark optimization problems. However, the exploration capability of SKF could be further improved. From literature, current optimum opposition-based learning (COOBL) has been employed to increase the diversity (exploration) of search algorithm by allowing current population to be compared with an opposite population. By employing this concept, more potential agents are generated to explore more promising regions that exist in the solution domain. Therefore, this paper intends to improve the exploration capability of SKF through the application of COOBL. The COOBL is employed after the estimation process of SKF. Experimental results over the IEEE congress on evolutionary computation (CEC) 2014 benchmark functions indicate that current optimum opposition-based simulated Kalman filter (COOBSKF) improved the exploration capability of SKF significantly. The COOBSKF also has been compared with five other optimization algorithms and outperforms them all.

A Simulated Kalman Filter Optimizer with White Hole Operator

The simulated Kalman filter (SKF) is a population-based optimization algorithm that was developed based on a well-known estimator called Kalman filter. Meanwhile, a white hole operator has been recently introduced to prevent premature convergence in black hole algorithm (BHA). The computation of white hole operator begins by selecting the worst agent as the white hole with event horizon. If an agent is located within the event horizon of white hole, the agent is pushed by the white hole. In this study, the white hole operator is used to improve the effectiveness of the SKF optimizer. A comprehensive experiment is done to evaluate the proposed SKF with white hole operator (SKFWH).

Distance Evaluated Simulated Kalman Filter with State Encoding for Combinatorial Optimization Problems

Simulated Kalman Filter (SKF) is a population-based optimization algorithm which exploits the estimation capability of Kalman filter to search for a solution in a continuous search space. The SKF algorithm only capable to solve numerical optimization problems which involve continuous search space. Some problems, such as routing and scheduling, involve binary or discrete search space. At present, there are three modifications to the original SKF algorithm in solving combinatorial optimization problems. Those modified algorithms are binary SKF (BSKF), angle modulated SKF (AMSKF), and distance evaluated SKF (DESKF). These three combinatorial SKF algorithms use binary encoding to represent the solution to a combinatorial optimization problem. This paper introduces the latest version of distance evaluated SKF which uses state encoding, instead of binary encoding, to represent the solution to a combinatorial problem. The algorithm proposed in this paper is called state-encoded distance evaluated SKF (SEDESKF) algorithm. Since the original SKF algorithm tends to converge prematurely, the distance is handled differently in this study. To control and exploration and exploitation of the SEDESKF algorithm, the distance is normalized. The performance of the SEDESKF algorithm is compared against the existing combinatorial SKF algorithm based on a set of Traveling Salesman Problem (TSP).

Asynchronous Simulated Kalman Filter Optimization Algorithm

Simulated Kalman filter (SKF) is an optimization algorithm which is inspired by Kalman filtering method. SKF was introduced as synchronous population-based algorithm. This work introduced a new variation of SKF which is SKF with asynchronous update mechanism, asynchronous-SKF (ASKF). In contrast to the synchronous implementation where the whole population go through each optimization step as a group, in ASKF an agent starts its optimization steps only after its preceding agent has completed all optimization steps. The performance of ASKF is compared against SKF using CEC2014 benchmark functions, where the ASKF is found to perform significantly better than the original SKF.

Single-solution Simulated Kalman Filter algorithm for global optimisation problems

This paper introduces single-solution Simulated Kalman Filter (ssSKF), a new single-agent optimisation algorithm inspired by Kalman Filter, for solving real-valued numerical optimisation problems. In comparison, the proposed ssSKF algorithm supersedes the original population-based Simulated Kalman Filter (SKF) algorithm by operating with only a single agent, and having less parameters to be tuned. In the proposed ssSKF algorithm, the initialisation parameters are not constants, but they are produced by random numbers taken from a normal distribution in the range of [0, 1], thus excluding them from tuning requirement. In order to balance between the exploration and exploitation in ssSKF, the proposed algorithm uses an adaptive neighbourhood mechanism during its prediction step. The proposed ssSKF algorithm is tested using the 30 benchmark functions of CEC 2014, and its performance is compared to that of the original SKF algorithm, Black Hole (BH) algorithm, Particle Swarm Optimisation (PSO) algorithm, Grey Wolf Optimiser (GWO) algorithm and Genetic Algorithm (GA). The results show that the proposed ssSKF algorithm is a promising approach and able to outperform GWO and GA algorithms, significantly.

Solving Assembly Sequence Planning using Angle Modulated Simulated Kalman Filter

This paper presents an implementation of Simulated Kalman Filter (SKF) algorithm for optimizing an Assembly Sequence Planning (ASP) problem. The SKF search strategy contains three simple steps; predict-measure-estimate. The main objective of the ASP is to determine the sequence of component installation to shorten assembly time or save assembly costs. Initially, permutation sequence is generated to represent each agent. Each agent is then subjected to a precedence matrix constraint to produce feasible assembly sequence. Next, the Angle Modulated SKF (AMSKF) is proposed for solving ASP problem. The main idea of the angle modulated approach in solving combinatorial optimization problem is to use a function, g(x), to create a continuous signal. The performance of the proposed AMSKF is compared against previous works in solving ASP by applying BGSA, BPSO, and MSPSO. Using a case study of ASP, the results show that AMSKF outperformed all the algorithms in obtaining the best solution.

Adaptive Beamforming Algorithm Based on a Simulated Kalman Filter

Adaptive beamforming is a technique used to steer the radiation pattern towards the desired signal and cancel out any interference signal by finding the appropriate weights for every element in an array antenna, to achieve maximum signal to interference plus noise ratio (SINR). There are many methods to perform adaptive beamforming and one of the method is to use metaheuristic algorithm, to estimate the weights for individual elements in an array. Over the years, various metaheuristic algorithms have been applied to adaptive beamforming. Some of the metaheuristic algorithms have been modified from the original algorithms to improve the algorithms performance in adaptive beamforming application. A new metaheuristic algorithm named Simulated Kalman Filter (SKF), is inspired by the estimation capabilities of Kalman filter, has not been applied to adaptive beamforming application. Therefore, this research presents the first-time application of SKF algorithm to adaptive beamforming. The SKF algorithm, however, often converge prematurely at local optimum due to lack of exploration, preventing it from finding better solution. A modified version of the SKF algorithm, named Opposition-Based SKF (OBSKF), introduced by K. Zakwan, applies Opposition-Based Learning method to improve the exploration capabilities of SKF algorithm. Moreover, a new modified version of the SKF algorithm named SKF with Modified Measurement (SKFMM) is introduced to further improve the exploration capabilities of SKF algorithm by modifying the measurement-update equation. The SKF, OBSKF and SKFMM is applied to an array antenna with 10 elements arranged linearly with 0.5