Starting point selection in grouping design method for lithographic objectives

Non-convex optimization problems are prevalent in scientific and engineering applications, often characterized by multiple local minima that challenge standard optimization techniques. Global optimization methods, such as Genetic Algorithms (GA) (1992) [4] and Particle Swarm Optimization (PSO) (1995) [6], provide robust global exploration but tend to converge slowly. Conversely, local search methods, such as Newton’s method (2004) [1], (2006) [7], and the Conjugate Gradient (CG) (1964) [3] method, offer rapid convergence but are susceptible to local minima. In this paper, we present four hybrid optimization algorithms that integrate the exploratory strength of global algorithms with the refinement ability of local methods. The proposed hybrids, Genetic Algorithms (GA) + Newton, GA + CG, PSO + Newton, and PSO + CG, are evaluated against their standalone counterparts on standard benchmark functions (2013) [5], including Rosenbrock, Rastrigin, Ackley, and Himmelblau. This work builds upon our previous research on the hybridization of two global search algorithms, the Nelder–Mead (simplex) algorithm and the Bat algorithm, which resulted in the Hybrid Simplex Bat Algorithm (HSBA) [2], recently Published. Results demonstrate that the hybrid approaches consistently outperform traditional methods in terms of accuracy, convergence rate, and computational efficiency.

Harmony Search (HS) algorithm is a new meta-heuristic global search algorithm. To solve the algorithm easily fall into the local optimal problem, this paper proposes an adaptive novel global harmony search (ANGHS) algorithm based on NGHS algorithm. First, a new location update strategy is given using the adjustment parameter F. Then, the mutation operation is introduced in the case of excluding the small probability Pm. In order to avoid blind adjustment of the step size in the late search and effectively adjust the structure of the solution, the definition of the norm is introduced to adjust parameter bw dynamically. In this paper, 7 standard Benchmark functions are used to simulate the experiment. The results show that the algorithm avoids the premature problem of the algorithm and enhances the global search ability of the algorithm, with obvious improvement in convergence speed and stability, and has good optimize performance.

ABSTRACTEngineering design often involves different types of simulation, which results in expensive computational costs. Variable fidelity approximation-based design optimization approaches can realize effective simulation and efficiency optimization of the design space using approximation models with different levels of fidelity and have been widely used in different fields. As the foundations of variable fidelity approximation models, the selection of sample points of variable-fidelity approximation, called nested designs, is essential. In this article a novel nested maximin Latin hypercube design is constructed based on successive local enumeration and a modified novel global harmony search algorithm. In the proposed nested designs, successive local enumeration is employed to select sample points for a low-fidelity model, whereas the modified novel global harmony search algorithm is employed to select sample points for a high-fidelity model. A comparative study with multiple criteria and an engineering application are employed to verify the efficiency of the proposed nested designs approach.

Coupling Response Surface and Differential Evolution for Parameter Identification Problems

Imposing suitably designed nonconvex regularization is effective to enhance sparsity, but the corresponding global search algorithm has not been well established. In this article, we propose a global search algorithm for the nonconvex two-level l1 penalty based on its piecewise linear property and apply it to machine learning tasks. With the search capability, the optimization performance of the proposed algorithm could be improved, resulting in better sparsity and accuracy than most state-of-the-art global and local algorithms. Besides, we also provide an approximation analysis to demonstrate the effectiveness of our global search algorithm in sparse quantile regression.

This paper describes an improved global harmony search (IGHS) algorithm for identifying the nonlinear discrete-time systems based on second-order Volterra model. The IGHS is an improved version of the novel global harmony search (NGHS) algorithm, and it makes two significant improvements on the NGHS. First, the genetic mutation operation is modified by combining normal distribution and Cauchy distribution, which enables the IGHS to fully explore and exploit the solution space. Second, an opposition-based learning (OBL) is introduced and modified to improve the quality of harmony vectors. The IGHS algorithm is implemented on two numerical examples, and they are nonlinear discrete-time rational system and the real heat exchanger, respectively. The results of the IGHS are compared with those of the other three methods, and it has been verified to be more effective than the other three methods on solving the above two problems with different input signals and system memory sizes.

Shunt capacitors are broadly applied in distribution systems to scale down power losses, improve voltage profile and boost system capacity. The amount of capacitors added and location of deployment in the system highly determine the advantage of compensation. A novel global harmony search (GHS) algorithm in parallel with the backward/ forward sweep power flow technique and radial harmonic power flow was used to investigate the optimal placement and sizing of capacitors in radial distribution networks for minimizing power loss and total cost by taking account load unbalancing, mutual coupling and harmonics. The optimal capacitor placement outcomes show that the GHS algorithm can reduce total power losses up to 60 kW and leads to more than 18% of cost saving. The results also demonstrate that the GHS algorithm is more effective in minimization of power loss and total costs compared with genetic algorithm (GA), particle swarm optimization (PSO) and harmony search (HS) algorithm. Moreover, the proposed algorithm converges within 800 iterations and is faster in terms of computational time and gives better performance in finding optimal capacitor location and size compared with other optimization techniques.

The paper presents the application of the Taguchi's global optimisation algorithm to analyse the self-excited induction generator performances. The analysis is based essentially on finding the root of the equivalent circuit's admittance (or the impedance) being equated to zero. This equation has two unknowns the magnetizing reactance and the frequency. The two variables depend strongly on the equivalent circuit parameters and the external parameters which are the load, the excitation capacitance and the prime mover rotor speed. Previous work on the subject have used either gradient based or global search algorithms. In this work, a new global search technique is used to solve this equation. Besides its global search features, this optimization algorithm is superior in terms of accuracy and ease of implementation. A study of some simulations results carried out using Matlab software has been done to corroborate the above advantages.

Optimization Solution Task is a typical and important task in many applications. Many optimization problems have been proved to be NP-hard problems, which cannot be solved by some predefined mathematic formulae. In this case, computer aided method is very helpful. While some local search algorithms are easily to fall into a local optimum solution. On contrast, the population based methods, such as Genetic Algorithms, Artificial Immune System, Autonomy Oriented Computing, are global search algorithms. However, they are not good at the local search. In this paper, an improved method is proposed by combining the local and global search ability, so as to improve the performance in terms of the convergence speed and the convergence reliability. We construct a generic form to deal with the common objective function space or the objective function with the partial derivative. In addition, we present an n-hold method in population based evolution method. The experiments indicate that our approach can effectively improve the convergence reliability, which is much concerned in some applications with the expensive executing expense.

This paper proposes an improved Pelican optimization algorithm (IPOA) based on comprehansive strategy for the parameter identification of photovoltaic models. Firstly, the cubic chaotic mapping and the refraction reverse learning strategy are used to initialize the pelican population and enhance its diversity. Secondly, the position update formula of the Pelican optimization algorithm in the global detection phase is replaced by the position update formula of the red-tailed Eagle optimization algorithm in the soaring phase to obtain the adequacy of the Pelican optimization algorithm in solution space search. Further introducing the catchy variation strategy aims to improve the algorithm's global search ability. Finally, the reverse solution generated by the lens imaging principle can provide a new search direction through the mirror reverse learning strategy when the Pelican optimization algorithm falls into the local optimal. The CEC2022 test function performed analysis and comparison with eight meta-heuristic algorithms. The Wilcoxon rank sum test verified the significance of the algorithm. In addition, the IPOA was used to optimize the critical parameters of the PV model to solve the problem of actual parameter identification of the single-diode and double-diode photovoltaic module models. The experimental results indicate that the IPOA outperforms other classical swarm intelligence algorithms in both convergence speed and solving accuracy. Furthermore, this optimization method yields the smallest mean square error across all types of solar cells, demonstrating the superiority of the proposed algorithm.

Reliability vs. Efficiency When Solving Multiphase Equilibrium Problems with Hybrid Optimization Codes

We use an effective global harmony search algorithm (EGHS) to solve two kinds of pressure vessel design problems. In general, the two problems are formulated as mixed-integer non-linear programming problems with several constraints. The EGHS combines harmony search algorithm (HS) with concepts from the swarm intelligence of particle swarm optimization algorithm (PSO) to solve the two optimization problems. The EGHS algorithm has been applied to two typical problems with results better than previously reported. The results have demonstrated that the EGHS has strong convergence and capacity of space exploration on solving pressure vessel design problems.

An investigation is presented that considers various aspects of an aerodynamic shape optimization framework. A two-dimensional aerofoil transonic zero-lift drag minimization test case is used to investigate the effect of dimensionality, shape deformation parameters, and optimizer on the results from the shape optimization process. A flexible control point-based parameterization is implemented which decouples the design variables from the surface, such that control point deformations determine the surface and volume mesh deformations in a unified manner. A gradient-based optimizer (feasible sequential quadratic programming) and global search algorithm (gravitational search algorithm) are tested on the constrained optimization case. The results show, as expected, that an increase in the number of dimensions produces a greater design space coverage and better optimization results, and the gradient-based method is prone to terminating in local optima or at constraint boundaries, so the global search algorithm is more reliable at locating optima. Efficient, reduced, and orthogonal shape deformation parameters are defined here by singular value decomposition extraction, and are shown to be particularly effective, demonstrating a 99.7% drag reduction for the case considered.

According to the features of order-type vulcanization workshop scheduling, deficiencies of PSO, as well as the excellent characteristics of the chaos principle, target mutations, and cooperation particles, a new particle swarm optimization algorithm, that is, chaos double-mutations cooperation particles swarm optimization was proposed. This can maintain the diversity of particles, avoid results falling into local optimum and improve the algorithm's global search ability. Four optimization algorithm convergences were compared and the change orders of vulcanization workshop scheduling were stimulated by testing. Results show that it is very effective and the chaos double-mutations cooperation particles swarm optimization in solving the order-type vulcanization workshop scheduling was verified.

The extraction of solar cell model parameters is of great value for diagnosing the ageing fault of solar cells and predicting the life of solar cells. Aiming at improving the accuracy of solar cell parameter extraction, quantum theory is introduced to enhance the algorithm's global search ability and local mining ability of whale optimization algorithm. The extraction of solar cell model parameters are carried out with the whale optimization algorithm and the Harris Eagle algorithm at the same time. The comparison and results proved that the QWOA(quantum whale optimization algorithm) has high accuracy and rapidity in the extraction of solar cell model parameters.