Simulated Kalman Filter algorithms for solving optimization problems - Nor Hidayati, Abdul Aziz (2019)
Optimization is an important process in solving most engineering problems. Unfortunately, many practical optimization problems cannot be solved to optimality within reasonable computational effort. Optimization in drill path for example, can lead to a significant time reduction in the overall manufacturing process, thus reducing a significant amount of total production costs. Reduction of the total travelling time of the drilling machine in particular, is the most crucial issue in large production of electronics manufacturing industries involving printed circuit board (PCB). When the exact solution is not an option or probably unnecessary, one may use metaheuristic approach to obtain a near-optimal solution in some reasonable computational time. In this research, two novel estimation-based metaheuristic optimization algorithms, named as Simulated Kalman Filter (SKF), and single-solution Simulated Kalman Filter (ssSKF) algorithms are introduced for global optimization problems. These algorithms are inspired by the estimation capability of the well-known Kalman filter estimation method. Kalman filter, named after its developer, is a very rare algorithm that is provable to be an optimal linear Gaussian estimator. Its optimality has inspired the development of a metaheuristic algorithm called Heuristic Kalman Algorithm (HKA) in 2009. Applications and improvements to the HKA algorithm suggest that optimization algorithm based on estimation principle has a huge potential in solving a wide variety of optimization problems. However, the HKA algorithm has its own flaws. Although it was introduced as a population-based stochastic optimization algorithm, HKA is not exactly a population-based algorithm because it initializes and updates only a single solution. The computation in HKA also becomes expensive when dealing with high dimension. Last but not least, HKA has a very high dependency on the Gaussian assumption. The proposed population-based SKF algorithm and the single solution-based SKF algorithm use the scalar model of discrete Kalman filter algorithm as the search strategy to overcome these flaws. In principle, the optimization problem is regarded as a state estimation process. Each agent acts as a Kalman filter and finds solution to the optimization problem using a standard Kalman Filter framework which comprises of prediction, simulated measurement, and estimation phase that uses the best-so-far solution as a reference. The algorithms are evaluated using 30 benchmark functions of the CEC2014 benchmark suite, and then applied to solve PCB drill path optimization case study. The Wilcoxon signed ranked statistical test shows that the ssSKF algorithm that uses an adaptive local neighbourhood in the prediction phase performs statistically better than the SKF algorithm that uses the last estimated state as its prediction, especially in solving high dimensional functions. Benchmarking with recent algorithms tested on the CEC2014 benchmark suite shows that all compared algorithms perform statistically on par considering their average performance. The Friedman test ranked ssSKF and SKF algorithm in the third and fourth rank respectively when they are being benchmarked against three state-of-the-art algorithms that competed in the CEC2014 competition. In the benchmarking of the SKF and ssSKF algorithms’ performance in solving the 14-hole PCB drill path optimization case study with recent implementations, on average, both algorithms show the ability to converge to the optimal solution at a smaller number of function evaluations compared to the Gravitational Search Algorithm (GSA), Cuckoo Search (CS), and Intelligent Water Drop (IWD), although fall-short to the Taguchi- Genetic Algorithm optimization algorithm.