The compact Genetic Algorithm for likelihood estimator of first order moving average model

Abstract

Recently Genetic Algorithms (GAs) have frequently been used for optimizing the solution of estimation problems. One of the main advantages of using these techniques is that they require no knowledge or gradient information about the response surface. The poor behavior of genetic algorithms in some problems, sometimes attributed to design operators, has led to the development of other types of algorithms. One such class of these algorithms is compact Genetic Algorithm (cGA), it dramatically reduces the number of bits reqyuired to store the poulation and has a faster convergence speed. In this paper compact Genetic Algorithm is used to optimize the maximum likelihood estimator of the first order moving avergae model MA(1). Simulation results based on MSE were compared with those obtained from the moments method and showed that the Canonical GA and compact GA can give good estimator of for the MA(1) model. Another comparison has been conducted to show that the cGA method has less number of function evaluations, minimum searched space percentage, faster convergence speed and has a higher optimal precision than that of the Canonical GA.

A combined compact genetic algorithm and local search method for optimizing the ARMA(1,1) model of a likelihood estimator

“…Moreover, MSE of I-CGA-SDA and HGA when the model parameters (φ 1 , θ 1 ) take positive values is smaller than that when these parameters are assigned to negative ones. Table 2 illustrates the average simulation results of HGA and I-CGA-SDA, respectively, with population size P s = 50 over 100 runs, where F is the number of function evaluations taken until convergence for the various numbers of generations, and PSS is the percentage of the searched space which can be calculated as follows 13 :…”

“…is the sum of squared errors, while (a t | θ 1 , φ 1 , w) denotes the conditional expectation of a t given θ 1 , φ 1 and w. The sum of squared errors can be found by unconditional calculation of the a t 's, which is computed recursively by taking expectations in (13), it is also called Least Square Estimate in which the parameter estimated is obtained by minimizing the sum of squares in (13), it usually provides very close approximation to the maximum likelihood estimator. Back-forecasting is a popular technique, it estimates the parameters which are crudely put into the model and run backwards in time.…”

Metaheuristics in the Balance: A Survey on Memory-Saving Approaches for Platforms with Seriously Limited Resources

“…Te most interesting areas of application of compact optimisation in the discrete domain include the Travelling Salesman Problem (TSP) [224,261]; determining minimum set primers in Polymerase Chain Reaction (PCR) [262]; task scheduling in grid computing environments [263]; protein folding [264]; object recognition [265,266]; soft decision decoding [267,268]; minimising the number of coding operations required in multicast based on network coding [222]; estimating the parameters of the maximum log-likelihood function of a frst-order moving average model MA [269] and a mixed model ARMA (1, 1) [223]; optimising the aggregation of multiple similarity measures to obtain a single similarity metric for ontology matching [270]; optimising ontology alignment [271]; designing multiple input multiple output wireless communication systems [272].…”

Multiobjective Optimization Based Vessel Collision Avoidance Strategy Optimization

“…With the appearance and development of new navigation equipment like AIS [5,6], advanced computer technology, and so forth, the application of intelligent optimization algorithm has been used for collision avoidance strategy searching. Genetic algorithm (GA) is a popular heuristic algorithm, which has been used for many subjects, such as system identification [7,8], supply chain [9], and scheduling problem [10].Ś mierzchalski and Michalewicz [11], Szlapczynski [12], and Szlapczynski and Szlapczynska [13] first made use of genetic algorithm to plan the route of vessel in static or dynamic environment in order to avoid obstacles. Similar heuristic optimization algorithms have been used by other 2 Mathematical Problems in Engineering researchers: GA is used to find the optimal path and manoeuvres in collision avoidance [14][15][16].…”