Hybrid Ant Colony-Genetic Algorithm (GAAPI) for Global Continuous Optimization

Many real–world problems are modeled as global continuous optimization problems with a nonlinear objective function. Stochastic methods are used to solve these problems approximately, when solving them exactly is impractical. In this class of methods, swarm intelligence (SI) presents metaheuristics that exploit a population of interacting agents able to self–organize, such as ant colony optimization (ACO), particle swarm optimization (PSO), and artificial bee colony (ABC). This paper presents a new SI-based method for solving continuous optimization problems. The new algorithm, called Swarm Random Walk (SwarmRW), is based on a random walk of a swarm of potential solutions. SwarmRW is validated on test functions and compared to PSO and ABC. Results show improved performance on most of the test functions.KeywordsContinuous OptimizationSwarm IntelligenceMeta- heuristic

Deterministic branch-and-bound algorithms for continuous global optimization often visit a large number of boxes in the neighborhood of a global minimizer, resulting in the so-called cluster problem (Du and Kearfott in J Glob Optim 5(3):253---265, 1994). This article extends previous analyses of the cluster problem in unconstrained global optimization (Du and Kearfott 1994; Wechsung et al. in J Glob Optim 58(3):429---438, 2014) to the constrained setting based on a recently-developed notion of convergence order for convex relaxation-based lower bounding schemes. It is shown that clustering can occur both on nearly-optimal and nearly-feasible regions in the vicinity of a global minimizer. In contrast to the case of unconstrained optimization, where at least second-order convergent schemes of relaxations are required to mitigate the cluster problem when the minimizer sits at a point of differentiability of the objective function, it is shown that first-order convergent lower bounding schemes for constrained problems may mitigate the cluster problem under certain conditions. Additionally, conditions under which second-order convergent lower bounding schemes are sufficient to mitigate the cluster problem around a global minimizer are developed. Conditions on the convergence order prefactor that are sufficient to altogether eliminate the cluster problem are also provided. This analysis reduces to previous analyses of the cluster problem for unconstrained optimization under suitable assumptions.

In this paper shape control optimization of piezoelectric bimorph is done by piezo response function (PRF) and global optimization technique. PRF is used to formulate the optimization problem and global optimization algorithm is used to minimize the error between the target and the achieved shape. The performance of four global optimization techniques, simulated annealing (SA), genetic algorithm, particle swarm optimization and teacher learning based optimization are compared for the shape control of piezoelectric bimorph. 28 piezoelectric actuators are used in the piezoelectric bimorph to generate the sinusoidal profile, elliptical profile and arbitrary deformation profile by the external load. PRF is calculated by solving finite element model of piezoelectric bimorph and, optimization of electric potential with safety limit is done to achieve the target profiles by using all the aforementioned optimization techniques. SA gives best value of the objective function. At optimum electrode potential, the target and, achieved sinusoidal, elliptical and arbitrary deformation profiles obtained by SA at 5 × 107 computation, matches closely with root mean square (RMS) errors of 0.72, 12.18 and 28.86 nm, respectively. Subsequently, a robust and fully reproducible method for the shape control of piezo actuated deformable mirrors and smart structures is developed.

Prestack amplitude versus offset (AVO) inversion is an essential tool to estimate elastic properties. Approximations of P-wave reflection coefficients based on the Zoeppritz equation are limited by the assumption of weak contrast and are inaccurate for far offset, and the existing nonlinear inversion method, like ant colony optimization (ACO), cannot converge to the global optimal solution within a limited time. Consequently, we propose a nonlinear AVO inversion method based on the exact Zoeppritz equation using hybrid quantum ant colony optimization (HQACO). The Zoeppritz equation is a forward modeling approach with high accuracy at far offset and is valid at the strong-contrast interface. HQACO, as a global optimization algorithm, not only has the potential of ACO to search global solutions but also exploits the power of quantum computing to speed up optimization procedures. The self-adaptive rotating strategy is proposed to improve the flexibility and efficiency of the conventional quantum rotating gate largely. Moreover, the quantum gate is introduced to enhance the global search ability. Numerical results show that the average evaluation number required for the global solution decreases largely and the solution converges to the global optimal solution closely using the proposed method. Synthetic applications verify that HQACO shows the most reliable exploring competence to find the global solution. The new inversion method is not only suitable for the strong-contrast interface with noise but also shows promising accuracy using the wide offset range.

Since there were few chaotic neural networks applicable to the global optimization, in this paper, we propose a new neural network model — chaotic parameters disturbance annealing (CPDA) network, which is superior to other existing neural networks, genetic algorithms, and simulated annealing algorithms in global optimization. In the present CPDA network, we add some chaotic parameters in the energy function, which make the Hopfield neural network escape from the attraction of a local minimal solution and with the parameter annealing, our model will converge to the global optimal solutions quickly and steadily. The converge ability and other characters are also analyzed in this paper. The benchmark examples show the present CPDA neural network's merits in nonlinear global optimization.

Optimization problems are ubiquitous and consequential. In fact every sphere of human activity that can be quantified can be formulated as an optimization problem. The focus of my work is on Global Optimization which is not only desirable but also necessary in many cases. In the past few decades several Global optimization algorithms have been suggested in literature out of which stochastic, population based search algorithms like Genetic algorithms (GA), Evolutionary Strategies (ES), Swarm Algorithms (Ant Colony (ACO) and Particle Swarm (PSO)), differential Evolution etc. have become immensely popular for solving real life optimization problems. The reason, being the efficiency with which these algorithms can tackle the complex and intricate models of real life problems. My research is concentrated on Differential Evolution which is relatively a newer addition to the population based search algorithms. DE was first suggested by Storn and Price in 1995 as a search technique for solving optimization problems. It uses the same operators like mutation, crossover and selection as that of GA but manipulates them in a manner different to that of GA.

Computer analysis and simulation based design optimization requires more computationally efficient global optimization tools. In this work, a new global optimization algorithm based on design experiments, region elimination and response surface model, namely Approximated Unimodal Region Elimination Method (AUREM), is introduced. The approach divides the field of interest into several unimodal regions using design experiment data; identify and rank the regions that most likely contain the global minimum; form a response surface model with additional design experiment data over the most promising region; identify its minimum, remove this processed region, and move to the next most promising region. By avoiding redundant searches, the approach identifies the global optimum with reduced number of objective function evaluations and computation effort. The new algorithm was tested using a variety of benchmark global optimization problems and compared with several widely used global optimization algorithms. The experiments results present comparable search accuracy and superior computation efficiency, making the new algorithm an ideal tool for computer analysis and simulation black-box based global design optimization.

We use the simple, but little-known, result that a uniformly continuous function on a convex set is e-Lipschitz (as defined below) to extend Piyavskii‘s algorithm for Lipschitz global optimization to the larger domain of continuous (not-necessarily-Lipschitz) global optimization.

An inverse design framework incorporating a physics-based surrogate model and global optimization is proposed to assist in the design of low warpage ultra-thin packages by adjusting the metal densities over substrate subsections and layers. The surrogate model is derived from two finite element analysis (FEA) models. The first one describes the relationship between the metal density in the substrate layer to the coefficient of thermal expansion (CTE) while the second one describes the relationship between in-plane CTE variation of the substrate to the warpage profile. Results from these two FEA models are used to train separate artificial neural networks (ANN). When these ANNs are run sequentially, the surrogate model can accurately determine the warpage profile for any set of metal densities. Three global optimization algorithms, Particle Swarm Optimization (PSO), Genetic Algorithm (GA) and Cross Entropy (CE) were then evaluated using this surrogate model. Three case studies consisting of different warpage profiles (original and 20% reduced warpage) and constraints to the optimization search space (±20% or ±50% change to metal density) were then evaluated using these algorithms. For all three cases, the three algorithms converged to similar solutions, indicating that indeed the global minimum has been attained and determined. However, GA took a significantly longer time to converge than PSO and CE. Based on these results, PSO and CE are recommended to be suitable algorithms to carry out inverse design for this type of problem.

Groundwater is a crucial source of water supply in drought conditions, and an auxiliary water source in wet seasons. Due to its increasing importance in view of climate change, predicting groundwater level (GWL) needs to be improved to enhance management. We used adaptive neuro-fuzzy inference systems (ANFIS) to predict the GWL of the Urmia aquifer in northwestern Iran under various input scenarios using precipitation, temperature, groundwater withdrawal, GWL during the previous month, and river flow. In total, 11 input patterns from various combinations of variables were developed. About 70% of the data were used to train the models, while the rest were used for validation. In a second step, several metaheuristic algorithms, such as genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization for continuous domains (ACOR), and differential evolution (DE) were used to improve the model and, consequently, prediction performance. The results showed that (i) RMSE, MAPE, and NSE of 0.51 m, 0.00037 m, and 0.86, respectively, were obtained for the ANFIS model using all input variables, indicating a rather poor performance, (ii) metaheuristic algorithms were able to optimize the parameters of the ANFIS model in predicting GWL, (iii) the input pattern that included all input variables resulted in the most appropriate performance with RMSE, MAPE, and NSE of 0.28 m, 0.00019 m, and 0.97, respectively, using the ANIFS-ACOR hybrid model, (iv) results of Taylor’s diagram (CC = 0.98, STD = 0.2, and RMSD = 0.30), as well as the scatterplot (R2 = 0.97), showed that best prediction was achieved by ANFIS-ACOR, and (v) temperature and evaporation exerted stronger influence on GWL prediction than groundwater withdrawal and precipitation. The findings of this study reveal that metaheuristic algorithms can significantly improve the performance of the ANFIS model in predicting GWL.

In this article, we introduce a new global optimization method to the field of multiview 3D reconstruction. While global minimization has been proposed in a discrete formulation in form of the maxflow-mincut framework, we suggest the use of a continuous convex relaxation scheme. Specifically, we propose to cast the problem of 3D shape reconstruction as one of minimizing a spatially continuous convex functional. In qualitative and quantitative evaluation we demonstrate several advantages of the proposed continuous formulation over the discrete graph cut solution. Firstly, geometric properties such as weighted boundary length and surface area are represented in a numerically consistent manner: The continuous convex relaxation assures that the algorithm does not suffer from metrication errors in the sense that the reconstruction converges to the continuous solution as the spatial resolution is increased. Moreover, memory requirements are reduced, allowing for globally optimal reconstructions at higher resolutions. We study three different energy models for multiview reconstruction, which are based on a common variational template unifying regional volumetric terms and on-surface photoconsistency. The three models use data measurements at increasing levels of sophistication. While the first two approaches are based on a classical silhouette-based volume subdivision, the third one relies on stereo information to define regional costs. Furthermore, this scheme is exploited to compute a precise photoconsistency measure as opposed to the classical estimation. All three models are compared on standard data sets demonstrating their advantages and shortcomings. For the third one, which gives the most accurate results, a more exhaustive qualitative and quantitative evaluation is presented.

Recent advances in networked control and distributed systems require the development of scalable algorithms that consider the decentralized characteristic of the problem and communication restrictions. The interest in solving distributed consensus optimization problems of multi-agent systems has been growing. Distributed consensus optimization problems are modeled as minimizing a global objective function by multiple agents over a network. The formulation of distributed consensus optimization has been paid extensive attention due to its widespread applications, e.g., large-scale machine learning [1, 2], model predictive control [3], cognitive networks [4, 5], source localization [6, 7], resource allocation or scheduling [8], message routing [9], distributed spectrum sensing [5], statistical inference and learning [6, 10, 11, 12]. In these applications, without need of putting all the parameters together which define the optimization problem, decentralized nodes that only have a local subcollection of such parameters, collaboratively achieve the minimizer of the global objective function. In light of commonly used distributed optimization algorithms, by introducing a large number of nodes with a certain ability of calculation and communication, a complex global optimization problem is spit and distributed to those nodes. Through locally calculating and communicating with neighboring nodes, global optimal solutions can be obtained.

This paper presents a comprehensive analysis of hybrid electric vehicle (HEV) classification and energy management strategies (EMS), with a particular emphasis on the application and potential of genetic algorithms (GAs) in optimizing energy management strategies for hybrid electric vehicles. Initially, the paper categorizes hybrid electric vehicles based on mixing rates and power source configurations, elucidating the operational principles and the range of applicability for different hybrid electric vehicle types. Following this, the two primary categories of energy management strategies—rule-based and optimization-based—are introduced, emphasizing their significance in enhancing energy efficiency and performance, while also acknowledging their inherent limitations. Furthermore, the advantages of utilizing genetic algorithms in optimizing energy management systems for hybrid vehicles are underscored. As a global optimization technique, genetic algorithms are capable of effectively addressing complex multi-objective problems by circumventing local optima and identifying the global optimal solution. The adaptability and versatility of genetic algorithms allow them to conduct real-time optimization across diverse driving conditions. Genetic algorithms play a pivotal role in hybrid vehicle energy management and exhibit a promising future. When combined with other optimization techniques, genetic algorithms can augment the optimization potential for tackling complex tasks. Nonetheless, the advancement of this technique is confronted with challenges such as cost, battery longevity, and charging infrastructure, which significantly influence its widespread adoption and application.

GGA: A modified genetic algorithm with gradient-based local search for solving constrained optimization problems

<p>The topic of this Ph.D. thesis is the application of evolution-based algorithms (EAs) to various highly constrained combinatorial optimization problems arising in layout synthesis of VLSI integrated circuits. The purpose is to investigate which performance can be obtained by EAs compared to traditional methods, to identify strengths and weaknesses of EAs within this application domain and to identify possible EA design principles yielding the best performance.</p><p>In particular, the study focuses on genetic algorithms (GAs) for placement and global routing of macro-cell layouts. GAs for the these problems are developed, and their performance compared to that of existing state-of-the-art tools, in terms of absolute solution quality and absolute runtime. The main results are new GAs for both macro-cell placement and global routing, which are comparable to or better than the current state-of-the-art approaches. Especially, a GA for the Steiner problem in a graph is presented, which to our knowledge is the current best heuristic for this problem, in terms of solution quality as well as runtime.</p><p>Finally, various design principles significantly affecting algorithm performance are identified, of which the constraint handling method is of utmost importance. Within the application domain considered, enforcing constraint satisfaction at all times is found to consistently outperform methods based on penalty terms.</p>