Biologically inspired computing framework for solving two-point boundary value problems using differential evolution

Backtracking search optimization heuristics for nonlinear Hammerstein controlled auto regressive auto regressive systems

In this work, novel application of evolutionary computational heuristics is presented for parameter identification problem of nonlinear Hammerstein controlled auto regressive auto regressive (NHCARAR) systems through global search competency of backtracking search algorithm (BSA), differential evolution (DE) and genetic algorithms (GAs). The mean squared error metric is used for the fitness function of NHCARAR system based on difference between actual and approximated design variables. Optimization of the cost function is conducted with BSA for NHCARAR model by varying degrees of freedom and noise variances. To verify and validate the worth of the presented scheme, comparative studies are carried out with its counterparts DE and GAs through statistical observations by means of weight deviation factor, root of mean squared error, and Thiel's inequality coefficient as well as complexity measures.

Solution of Linear and Non-Linear Boundary Value Problems Using Population-Distributed Parallel Differential Evolution

Cases where the derivative of a boundary value problem does not exist or is constantly changing, traditional derivative can easily get stuck in the local optima or does not factually represent a constantly changing solution. Hence the need for evolutionary algorithms becomes evident. However, evolutionary algorithms are compute-intensive since they scan the entire solution space for an optimal solution. Larger populations and smaller step sizes allow for improved quality solution but results in an increase in the complexity of the optimization process. In this research a population-distributed implementation for differential evolution algorithm is presented for solving systems of 2 nd -order, 2-point boundary value problems (BVPs). In this technique, the system is formulated as an optimization problem by the direct minimization of the overall individual residual error subject to the given constraint boundary conditions and is then solved using differential evolution in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. Four benchmark BVPs are solved using the proposed parallel framework for differential evolution to observe the speedup in the execution time. Meanwhile, the statistical analysis is provided to discover the effect of parametric changes such as an increase in population individuals and nodes representing features on the quality and behavior of the solutions found by differential evolution. The numerical results demonstrate that the algorithm is quite accurate and efficient for solving 2 nd -order, 2-point BVPs.

Urban Comprehensive Water Consumption: Nonlinear Control of Production Factor Input Based upon the C-D Function

Utilizing the urban water demand function and the Cobb-Douglas (C-D) production function, an economic control model for the multi-input-multi-output (MIMO) nonlinear system was designed and implemented to describe urban comprehensive water consumption, where the urban water demand function was expressed as the product of the number of water users and per capita comprehensive water consumption, and the urban water supply function was expressed as a C-D production function. The control variables included capital investment and labor input for the urban water supply. In contrast to the Solow model, Shell model and aggregate model with renewable labor resources, the proposed model eliminated value constraints on investment and labor input in the state equations and hence avoided the difficulty in applying these models to urban water supply institutions. Furthermore, the feedback linearization control design (FLCD) method was employed to accomplish stability of the system. In contrast to the optimal control method, the FLCD method possesses an explicit solution of the control law and does not require the solution of a two-point boundary value problem of an ordinary differential equation, making the method more convenient for application. Moreover, two different scenarios of urban water consumption, one for the growth period and the other for the decline period, were simulated to demonstrate the effectiveness of the proposed control scheme.