An improved fruit fly optimization algorithm to solve the homogeneous fuzzy series–parallel redundancy allocation problem under discount strategies

In this paper, a mathematical formulation is first derived for a homogenous fuzzy series–parallel redundancy allocation problem, where both the system and its subsystems can only take two states of complete perfect and complete failure. Identical redundant components are included in order to achieve desirable system reliability. The components of each subsystem characterized by their cost, weight, and reliability, are purchased from the market under all-unit discount and incremental quantity discount strategies. The goal is to find the optimum combination of the number of components for each subsystem that maximizes the system reliability under total fuzzy cost and weight constraints. An improved fruit fly optimization algorithm (IFOA) is proposed to solve the problem, where a particle swarm optimization, a genetic algorithm, and a Tabu search algorithm are utilized to validate the results obtained. These algorithms are the most common ones in the literature to solve series–parallel redundancy allocation problems. Moreover, design of experiments using the Taguchi approach is employed to calibrate the parameters of the algorithms. At the end, some numerical examples are solved to demonstrate the applicability of the proposed methodology. The results are generally in favor IFOA.     

A particle swarm–BFGS algorithm for nonlinear programming problems

This article proposes a hybrid optimization algorithm based on a modified BFGS and particle swarm optimization to solve medium scale nonlinear programs. The hybrid algorithm integrates the modified BFGS into particle swarm optimization to solve augmented Lagrangian penalty function. In doing so, the algorithm launches into a global search over the solution space while keeping a detailed exploration into the neighborhoods. To shed light on the merit of the algorithm, we provide a test bed consisting of 30 test problems to compare our algorithm against two of its variations along with two state-of-the-art nonlinear optimization algorithms. The numerical experiments illustrate that the proposed algorithm makes an effective use of hybrid framework when dealing with nonlinear equality constraints although its convergence cannot be guaranteed.     

A hybrid CBO–PSO algorithm for optimal design of truss structures with dynamic constraints

The vibration domain of structures can be reduced by imposing some constraints on their natural frequencies. For this purpose optimal design of structures under frequency constraints is required which involves highly non-linear and non-convex problems. In this paper an efficient hybrid algorithm is developed for solving such optimization problems. This algorithm utilizes the recently developed colliding bodies optimization (CBO) algorithm as the main engine and uses the positive properties of the particle swarm optimization (PSO) algorithm to increase the efficiency of the CBO. The distinct feature of the present hybrid algorithm is that it requires no parameter tuning. The CBO is known for being parameter independent, and avoiding the use of the traditional penalty method to handle the constraints upholds this property. Two mathematical constrained functions taken from the literature are studied to verify the performance of the algorithm. The algorithm is then applied to optimize truss structures with frequency limitations. The numerical results demonstrate the efficiency of the presented algorithm for this class of problems.     

Coupled particle swarm optimization method with genetic algorithm for the static–dynamic performance of the magneto-electro-elastic nanosystem

As a first attempt, Fourier series expansion (FSE), particle swarm optimization (PSO), and genetic algorithm (GA) methods are coupled for analysis of the static–dynamic performance and propagated waves in the magneto-electro-elastic (MEE) nanoplate. The FSE method is presented for solving the motion equations of the MEE nanoplate. For increasing the performance of genetic algorithms for solving the problem, the particle swarm optimization technique is added as an operator of the GA. Accuracy, convergence, and applicability of the proposed mixed approach are shown in the results section. Also, we prove that for obtaining the convergence results of the PSO and GA, we should consider more than 16 iterations. Finally, it is shown that if designers consider the presented algorithm in their model, the results of phase velocity of the nanosystem will be increased by 27%. A useful suggestion is that there is a region the same as a trapezium in which there are no effects from magnetic and electric potential of the MEE face sheet on the phase velocity of the smart nanoplate, and the region will be bigger by increasing the wavenumber.

     

A problem evolution algorithm with linear programming for the dynamic facility layout problem—A general layout formulation

Facility layout problems (FLPs) are quite common and important in many industries. This paper presents a mixed integer linear programming (MILP) model for the dynamic facility layout problem, which is a generalization of several special cases of FLPs studied in recent years. A new evolutionary meta-heuristic framework, named as the problem evolution algorithm (PEA), is developed as a general solution approach for FLPs. Computational experiments show that the PEA combined with the linear programming (LP), called PEA-LP in short, performs well in various types of FLPs. In addition, a new polyhedral inner-approximation method is proposed based on secant lines for the linearization of the non-linear constraint for department area requirements. This new method guarantees that the actual department area is always greater than or equal to the required area within a given maximum deviation error. Furthermore, two new symmetry-breaking constraints which help to improve the computational efficiency of the MILP model are also introduced. Computational experiments on several well-known problem instances from the literature are carried out to test the DFLP-FZ and the PEA-LP with promising results.     

A multi-dimensional shooting algorithm for the two-facility location–allocation problem with dense demand

We develop an efficient allocation-based solution framework for a class of two-facility location–allocation problems with dense demand data. By formulating the problem as a multi-dimensional boundary value problem, we show that previous results for the discrete demand case can be extended to problems with highly dense demand data. Further, this approach can be generalized to non-convex allocation decisions. This formulation is illustrated for the Euclidean metric case by representing the affine bisector with two points. A specialized multi-dimensional shooting algorithm is presented and illustrated on an example. Comparisons with two alternative methods through a computational study confirm the efficiency of the proposed methodology.     

Wei–Yao–Liu conjugate gradient projection algorithm for nonlinear monotone equations with convex constraints

In this paper, the Wei–Yao–Liu (WYL) conjugate gradient projection algorithm will be studied for nonlinear monotone equations with convex constraints, which can be viewed as an extension of the WYL conjugate gradient method for solving unconstrained optimization problems. These methods can be applied to solving large-scale nonlinear equations due to the low storage requirement. We can obtain global convergence of our algorithm without requiring differentiability in the case that the equation is Lipschitz continuous. The numerical results show that the new algorithm is efficient.     

A closed-form approximation for the fractional Black–Scholes model with transaction costs

In this paper, we investigate option valuation problems under the fractional Black–Scholes model. The aim is to propose a pricing formula for the European option with transaction costs, where the costs structure contains fixed costs, a cost propositional to the volume traded, and a cost proportional to the value traded. Precisely, we provide an approximate solution of the nonlinear Hoggard–Whalley–Wilmott equation. The comparison results reveal that our approximate solutions are close to the numerical computations. Moreover, the comparison results demonstrate that the price of the European option decreases as the Hurst exponent increases.     

A bound for the Rosenfeld–Gröbner algorithm

We consider the Rosenfeld–Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n$n$ indeterminates. For a set of ordinary differential polynomials F$F$, let M(F)$M\left(F\right)$ be the sum of maximal orders of differential indeterminates occurring in F$F$. We propose a modification of the Rosenfeld–Gröbner algorithm, in which for every intermediate polynomial system F$F$, the bound M(F)?(n−1)!M(_F0)$M\left(F\right)?(n-1)!M\left(F_0\right)$ holds, where _F0$F_0$ is the initial set of generators of the radical ideal. In particular, the resulting regular systems satisfy the bound. Since regular ideals can be decomposed into characterizable components algebraically, the bound also holds for the orders of derivatives occurring in a characteristic decomposition of a radical differential ideal.     

Agent–cellular automata model for the dynamic fluctuation of EV traffic and charging demands based on machine learning algorithm

Neural Computing and Applications - Electric vehicles (EV) comprise one of the foremost components of the smart grid and tightly link the power system with the road network. Spatial and temporal...     

A finite element method with discontinuous rotations for the Mindlin–Reissner plate model

We present a continuous-discontinuous finite element method for the Mindlin–Reissner plate model based on continuous polynomials of degree k ? 2 for the transverse displacements and discontinuous polynomials of degree k ? 1 for the rotations. We prove a priori convergence estimates, uniformly in the thickness of the plate, and thus show that locking is avoided. We also derive a posteriori error estimates based on duality, together with corresponding adaptive procedures for controlling linear functionals of the error. Finally, we present some numerical results.     

A new and improved version of particle swarm optimization algorithm with global–local best parameters

This paper presents a new and improved version of particle swarm optimization algorithm (PSO) combining the global best and local best model, termed GLBest-PSO. The GLBest-PSO incorporates global–local best inertia weight (GLBest IW) with global–local best acceleration coefficient (GLBest Ac). The velocity equation of the GLBest-PSO is also simplified. The ability of the GLBest-PSO is tested with a set of bench mark problems and the results are compared with those obtained through conventional PSO (cPSO), which uses time varying inertia weight (TVIW) and acceleration coefficient (TVAC). Fine tuning variants such as mutation, cross-over and RMS variants are also included with both cPSO and GLBest-PSO to improve the performance. The simulation results clearly elucidate the advantage of the fine tuning variants, which sharpen the convergence and tune to the best solution for both cPSO and GLBest-PSO. To compare and verify the validity and effectiveness of the GLBest-PSO, a number of statistical analyses are carried out. It is also observed that the convergence speed of GLBest-PSO is considerably higher than cPSO. All the results clearly demonstrate the superiority of the GLBest-PSO.

An improved model along with a spectral numerical simulation for fractional predator–prey interactions

Predator–prey models appear in various fields of bio-mathematics used for the analysis of interactions of biological systems. Due to the complexities of the physical context for the real-world problems of food chain dynamics, introducing new models compatible with experimental results stays ongoing research. Many models have been proposed and analyzed for these systems in recent years. In this paper, we propose a new fractional-order predator–prey model with negative feedback on both species with memory-dependent effects, which increases the compatibility level of the model. Then we present a novel Laguerre spectral numerical simulation for the proposed model by introducing Laguerre modal basis functions with collocation and Galerkin techniques. We then transfer the nonlinear model into a system of algebraic equations, which is solved by efficient numerical solvers. Finally, we provide some test problems to show the efficiency of the proposed model and the computational method.

     

A hybrid genetic algorithm for the discrete time–cost trade-off problem

In this paper we present a hybrid strategy developed using genetic algorithms (GAs), simulated annealing (SA), and quantum simulated annealing techniques (QSA) for the discrete time–cost trade-off problem (DTCTP). In the hybrid algorithm (HA), SA is used to improve hill-climbing ability of GA. In addition to SA, the hybrid strategy includes QSA to achieve enhanced local search capability. The HA and a sole GA have been coded in Visual C++ on a personal computer. Ten benchmark test problems with a range of 18 to 630 activities are used to evaluate performance of the HA. The benchmark problems are solved to optimality using mixed integer programming technique. The results of the performance analysis indicate that the hybrid strategy improves convergence of GA significantly and HA provides a powerful alternative for the DTCTP.     

A fast algorithm for solving the space–time fractional diffusion equation

In this paper, we propose a fast algorithm for efficient and accurate solution of the space–time fractional diffusion equations defined in a rectangular domain. The spatial discretization is done by using the central finite difference scheme and matrix transfer technique. Due to its nonlocality, numerical discretization of the spectral fractional Laplacian ${(?\Delta )}_s^{\alpha /2}$ results in a large dense matrix. This causes considerable challenges not only for storing the matrix but also for computing matrix–vector products in practice. By utilizing the compact structure of the discrete system and the discrete sine transform, our algorithm avoids to store the large matrix from discretizing the nonlocal operator and also significantly reduces the computational costs. We then use the Laplace transform method for time integration of the semi-discretized system and a weighted trapezoidal method to numerically compute the convolutions needed in the resulting scheme. Various experiments are presented to demonstrate the efficiency and accuracy of our method.     

A robust D–S fusion algorithm for multi-target multi-sensor with higher reliability

This paper addresses the problem of track fusion for unordered distributed sensors with unknown measurement noise. A robust Dempster–Shafer (D–S) fusion algorithm is proposed, which includes three parts, namely, the local track estimation, the track association, and the state fusion. First, a labeling VB-PHD filter is derived to present target states with track labels and the unknown measurement noises of local sensors. Next, a heuristic D–S method is proposed to determine the relationship of local tracks and fused tracks, where the accumulated information is taken into account. Finally, a fusion method is given to show the state fusion results, which can fully utilize local state estimates and measurement noise information. Simulation results are provided to illustrate the high precision of tracking and good robustness, comparing with the traditional methods.     

A new model for the preemptive earliness–tardiness scheduling problem

This paper addresses a new model for the one-machine earliness–tardiness scheduling problem where jobs can be interrupted. Some dominance rules and a lower bound are derived. A new timing algorithm is also presented and a local search algorithm based on this timing algorithm permits the computation of good feasible solutions. We experimentally compare our timing algorithm with a previously published timing algorithm. The tests show that the execution time of the new timing algorithm is significantly faster, especially for large instances. The values of the solutions are compared to the lower bound.     

Chebyshev polynomials for the numerical solution of fractal–fractional model of nonlinear Ginzburg–Landau equation

Engineering with Computers - This paper introduces a new version for the nonlinear Ginzburg–Landau equation derived from fractal–fractional derivatives and proposes a computational...