Solving initial and boundary value problems using learning automata particle swarm optimization

In this article, the particle swarm optimization (PSO) algorithm is modified to use the learning automata (LA) technique for solving initial and boundary value problems. A constrained problem is converted into an unconstrained problem using a penalty method to define an appropriate fitness function, which is optimized using the LA-PSO method. This method analyses a large number of candidate solutions of the unconstrained problem with the LA-PSO algorithm to minimize an error measure, which quantifies how well a candidate solution satisfies the governing ordinary differential equations (ODEs) or partial differential equations (PDEs) and the boundary conditions. This approach is very capable of solving linear and nonlinear ODEs, systems of ordinary differential equations, and linear and nonlinear PDEs. The computational efficiency and accuracy of the PSO algorithm combined with the LA technique for solving initial and boundary value problems were improved. Numerical results demonstrate the high accuracy and efficiency of the proposed method

A comparison of general-purpose optimization algorithms forfinding optimal approximate experimental designs

Several common general purpose optimization algorithms are compared for findingA- and D-optimal designs for different types of statistical models of varying complexity,including high dimensional models with five and more factors. The algorithms of interestinclude exact methods, such as the interior point method, the Nelder–Mead method, theactive set method, the sequential quadratic programming, and metaheuristic algorithms,such as particle swarm optimization, simulated annealing and genetic algorithms.Several simulations are performed, which provide general recommendations on theutility and performance of each method, including hybridized versions of metaheuristicalgorithms for finding optimal experimental designs. A key result is that general-purposeoptimization algorithms, both exact methods and metaheuristic algorithms, perform wellfor finding optimal approximate experimental designs

Porcellio scaber algorithm (PSA) for solving constrained optimization problems

In this paper, we extend a bio-inspired algorithm called the porcellio scaber algorithm (PSA) to solve constrained optimization problems, including a constrained mixed discrete-continuous nonlinear optimization problem. Our extensive experiment results based on benchmark optimization problems show that the PSA has a better performance than many existing methods or algorithms. The results indicate that the PSA is a promising algorithm for constrained optimization.Comment: 6 pages, 1 figur

Optimal analog wavelet bases construction using hybrid optimization algorithm

An approach for the construction of optimal analog wavelet bases is presented. First, the definition of an analog wavelet is given. Based on the definition and the least-squares error criterion, a general framework for designing optimal analog wavelet bases is established, which is one of difficult nonlinear constrained optimization problems. Then, to solve this problem, a hybrid algorithm by combining chaotic map particle swarm optimization (CPSO) with local sequential quadratic programming (SQP) is proposed. CPSO is an improved PSO in which the saw tooth chaotic map is used to raise its global search ability. CPSO is a global optimizer to search the estimates of the global solution, while the SQP is employed for the local search and refining the estimates. Benefiting from good global search ability of CPSO and powerful local search ability of SQP, a high-precision global optimum in this problem can be gained. Finally, a series of optimal analog wavelet bases are constructed using the hybrid algorithm. The proposed method is tested for various wavelet bases and the improved performance is compared with previous works.Peer reviewedFinal Published versio