Heuristic Optimization Method Research Articles

Global Optimization of Surface Warpage for Inverse Design of Ultra-Thin Electronic Packages Using Tensor Train Decomposition

As laptops get thinner and thinner, the electronic packages that go into these devices must shrink along the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$z$ </tex-math></inline-formula> -dimension as well. High warpage in these ultra-thin packages is the result of mismatch of coefficients of thermal expansion (CTE) between the silicon die (CTE = 2.6 ppm/C) and the organic substrate (CTE = 12 to 16 ppm/C) and the reduced flexural rigidity due to reduced thickness. This can result in decreased yield during assembly onto the board. Through the selection of low CTE materials and the implementation of stiffeners, warpage can be decreased. This work aims to optimize the metal density in the substrate to achieve low warpage. An inverse design framework is implemented to optimize the surface warpage profiles of the package using heuristic global optimization method viz. Particle Swarm Optimization (PSO) and Cross Entropy (CE) on a surrogate model that is built using finite element analysis (FEA), tensor train decomposition (TTD) and artificial neural networks (ANN). Results demonstrate that using this framework can result in more than 10% reduction in warpage by implementing up to 50% decrease in metal density on the ground and power layers in the substrate. Further analysis is required to determine the impact of these changes to signal and power integrity. In future, the framework can be implemented to realize even thinner packages without compromising on their functionality.

A Multiresolution Approach for Large Real-World Camera Placement Optimization Problems

There have been numerous attempts at solving the optimal camera placement problem across multiple applications. Exact linear programming-based, as well as, heuristic combinatorial optimization methods were shown to be successful in providing optimal or near-optimal solutions to this problem. Working over a discrete space model is the general practice when solving the camera placement problem. However, discretized environments often limit the methods&#x2019; usage only to small-scale datasets due to resource and time constraints that grow exponentially with the number of 3D points collected from the discrete space. We propose a multi-resolution approach that enables the usage of existing optimization algorithms on large real-world problems modelled using high resolution 3D grids. Our method works by grouping together the given discrete set of possible camera locations into clusters of points, multiple times, resulting in multiple resolution levels. Camera placement optimization is repeated for all resolution levels while propagating the optimized solution from low to high resolutions. Our experiments on both simulated and real data with grids of varying sizes show that using our multi-resolution approach, existing camera placement optimization methods can be used even on high resolution grids consisting of hundreds of thousands of points. Our results also show that the strategy of grouping points together by exploiting underlying 3D geometry to optimize camera poses is not only significantly faster than optimizing on the entire set of samples but, it also provides better camera coverage.

Development of Forked Divergence Particle Swarm Optimization

In this paper, we propose new type of particle swarm optimization named forked divergence particle swarm optimization (PSO). PSO is one of the powerful heuristic optimization methods due to its simple algorithm, good convergence, and ease of implementation for various problems. However, its performance is highly dependent on the velocity term in the gradient equation, the value of which is the same for all individuals, making it difficult to have diversity in the individuals. Therefore, when given an inappropriate velocity term parameter or when the problem is complex, premature convergence occurs and the search stalls. In proposed method, each individual has its own parameter values and diffuses at the individual and global level depending on each convergence status. By using forked divergence PSO, we can avoid premature convergence to the locality and continue the search. In this study, we demonstrate the proposed method by numerical examples and demonstrate its effectiveness and characteristics.

Development of exact and heuristic optimization methods for safety improvement projects at level crossings under conflicting objectives

A significant number of accidents occur each year at level crossings globally. Substantial efforts are being made by different railway authorities and other stakeholders to prevent accidents by installing various countermeasures at level crossings (e.g., mountable curbs, two-quad gates, four-quad gates). However, due to budgetary constraints, it is not possible to deploy countermeasures at all level crossings. Besides, countermeasures have certain effectiveness factors and the associated installation cost. Usually, the cost of the countermeasure increases with its effectiveness. Therefore, it is essential to select the most effective countermeasures at the riskiest level crossings. The implementation of countermeasures at level crossings may lead to certain negative externalities as well. In particular, the deployment of countermeasures can result in a decreased traffic flow, causing traffic delays and adversely affecting the continuity of freight and passenger train movements. This study proposes a multi-objective mathematical model for resource allocation among level crossings, which aims not only to minimize the total hazard severity due to potential accidents but the associated traffic delays as well. Exact and heuristic solution approaches are designed to solve the developed multi-objective model. A set of computational experiments are conducted for the level crossings located in the State of Florida (United States). The results demonstrate superiority of the exact optimization method, as it obtained optimal Pareto Fronts within acceptable computational time. Moreover, a number of sensitivity analyses are conducted to showcase certain managerial insights that would be of interest to railway authorities and other stakeholders involved in level crossing safety improvements.

Optimal tuning of sigmoid PID controller using Nonlinear Sine Cosine Algorithm for the Automatic Voltage Regulator system

Automatic Voltage Regulator (AVR) is fabricated to sustain the voltage level of a synchronous generator spontaneously. Several control strategies have been introduced into the AVR system with the aim of gaining a better dynamic response. One of the most universally utilized controllers is the Proportional–Integral–Derivative (PID) controller. Despite the PID controller having a relatively high dynamic response, there are still further possibilities to improve in order to obtain more appropriate responses. This paper designed a sigmoid-based PID (SPID) controller for the AVR system in order to allow for an accelerated settling to rated voltage, as well as increasing the control accuracy. In addition, the parameters of the proposed SPID controller are obtained using an enhanced self-tuning heuristic optimization method called Nonlinear Sine Cosine Algorithm (NSCA), for achieving a better dynamic response, particularly with regards to the steady-state errors and overshoot of the system. A time-response specifications index is used to validate the proposed SPID controller. The obtained simulation results revealed that the proposed method was not only highly effective but also greatly improved the AVR system transient response in comparison to those with the modern heuristic optimization based PID controllers.

A heuristic swarm-based optimization method using multi-variate normal distributions with self-adaptive variance matrices

In this paper a heuristic swarm-based optimization method developed based on stochastic search and concepts from statistics was presented for optimal design of problems in structural mechanics. Although in recent years many heuristic optimization methods have been developed, none of them can be considered as the most effective method for solving all types of optimization problems. In general, heuristic optimization methods are formulated to follow specific patterns and often include some random parameters. It has been shown that adding stochastic parameters and concepts from statistics to such algorithms can improve their performance and increase the chance of finding global optimal points. Based upon same notion, we have developed a new swarm-based optimization algorithm in which multi-variate normal distributions with self-adaptive variance matrices (MNSV) are used to generate superior solutions in each iteration. The self-adaptive variance matrix in each iteration was calculated using the variance of the best points from solution history. Such a choice improved both exploration and exploitation of the algorithm and led to a trade-off between them from beginning towards the end of the solution. Computational complexity of MNSV algorithm was comparable to that of other swarm-based optimization algorithms and performance of the algorithm was tested through optimal solution of several benchmarks from structural and mechanical engineering. While MNSV algorithm was simple in terms of both formulation and implementation, it was effective in finding optimal solutions and often converged using a smaller number of iterations when compared to other algorithms.

Determination of Maximum Acceptable Standing Phase Angle across Open Circuit Breaker as an Optimisation Task

There are several threats that require the control of the conditions of switching operations in the transmission grid. They result mainly from the negative effects of the high-value current, which may appear after the breaker is closed. Problems considering closing the power circuit breakers on a large standing phase angle (SPA) are often formulated by grid operators. The literature most often discusses the problem of SPA reduction, which allows the system to be restored without the risk of damaging the turbogenerator shafts. This reduction can be achieved by various operational solutions; most often, it is the appropriate adjustment of active power generation, sometimes backed up by partial load shedding. The subject of the presented article is a slightly different approach to the SPA problem. The method of determining the maximum value of SPA for which the connection operation allows to avoid excessive transitional torques was presented. With this approach, finding the maximum value of SPA between the two considered system nodes is treated as an optimisation task. In order to solve it, the original heuristic optimisation method described in the article was applied.

Flutter Derivatives Identification and Uncertainty Quantification for Bridge Decks Based on the Artificial Bee Colony Algorithm and Bootstrap Technique

This paper presents a novel parameter identification and uncertainty quantification method for flutter derivatives estimation of bridge decks. The proposed approach is based on free-decay vibration records of a sectional model in wind tunnel tests, which consists of parameter identification by a heuristic optimization algorithm in the sense of weighted least squares and uncertainty quantification by a bootstrap technique. The novel contributions of the method are on three fronts. Firstly, weighting factors associated with vertical and torsional motion in the objective function are determined more reasonably using an iterative procedure rather than preassigned. Secondly, flutter derivatives are identified using a hybrid heuristic and classical optimization method, which integrates a modified artificial bee colony algorithm with the Powell’s algorithm. Thirdly, a statistical bootstrap technique is used to quantify the uncertainties of flutter derivatives. The advantages of the proposed method with respect to other methods are faster and more accurate achievement of the global optimum, and refined uncertainty quantification in the identified flutter derivatives. The effectiveness and reliability of the proposed method are validated through noisy data of a numerically simulated thin plate and experimental data of a bridge deck sectional model.

Real-time heliostat field aiming strategy optimization based on reinforcement learning

The heliostat field aiming strategy optimization is a crucial topic in solar power tower (SPT) plants. The optimal aiming strategy attempts to maximize the thermal power output while preserving certain operational limits. While existing methods could produce high-optimality results, they cannot be applied to real-time optimization for ultra large scale problems due to high computational complexity. In this work, an effective and scalable optimization method is proposed to achieve real-time optimization for ultra large scale problems, enabling efficient and robust SPT plant operations under varying solar conditions (i.e., cloud shadowing variations). The real-time optimization problem is reformulated as a reinforcement learning problem, capturing the learning from the intrinsic sequential decision-making process, to minimize unnecessary repetitions of computations. A Crescent Dunes-like SPT plant is studied, with the allowable flux density as the optimization constraint, and the results show that the proposed method provides better or comparable performance compared to heuristic optimization methods with an order of magnitude less computation time.

Full-Waveform Inversion of Time-Lapse Crosshole GPR Data Using Markov Chain Monte Carlo Method

Crosshole ground-penetrating radar (GPR) is an important tool for a wide range of geoscientific and engineering investigations, and the Markov chain Monte Carlo (MCMC) method is a heuristic global optimization method that can be used to solve the inversion problem. In this paper, we use time-lapse GPR full-waveform data to invert the dielectric permittivity. An inversion based on the MCMC method does not rely on an accurate initial model and can introduce any complex prior information. Time-lapse ground-penetrating radar has great potential to monitor the properties of a subsurface. For the time-lapse inversion, we used the double difference method to invert the time-lapse target area accurately and full-waveform data. We propose a local sampling strategy taking advantage of the a priori information in the Monte Carlo method, which can sample only the target area with a sequential Gibbs sampler. This method reduces the calculation and improves the inversion accuracy of the target area. We have provided inversion results of the synthetic time-lapse waveform data that show that the proposed method significantly improves accuracy in the target area.

Assessment of two optimisation methods for renewable energy capacity expansion planning

When deciding on a country’s future energy policy, it is essential to accurately estimate the future generation mix and technology costs, as well as future generation site locations in electricity power grids. This estimate needs to allow for changing levels of demand and increasing levels of renewable energy supply, with both having high fluctuations geographically and temporally. This objective leads to high-dimensional mathematical models with high computational complexity that cannot be solved analytically. Various simplifications and heuristics are proposed globally, however, these need to be anchored in terms of an indication of their likely performance. We offer a novel parallel investigation of a near-optimal and heuristic optimisation approach on a country scale. The Linear Programming (LP) optimisation problem finds the global minimum for the chosen set of input variables, this however comes at the cost of limitations regarding model size due to complexity. The alternative heuristic model limits connectivity of model parameters but rather than aggregating variables over space or time, it maintains a high resolution to allow for more granular estimates. We compare the quality and performance of a heuristic and LP optimisation method, using two configurations for the example of Australia and find relevant solutions for both. The solution space requires substantial simplification for the LP to be solvable and leads to overly optimistic capacity factors, installed capacity and cost, due to spatial aggregation. The heuristic approach has a significant performance advantage requiring only 3% of the near-optimal runtime and a fraction of calculation iterations.

GENERATION OF OPTIMAL 2-D ROUTES USING GENETIC ALGORITHMS

The paper deals with practical issues of using the apparatus of genetic algorithms as one of the directions of optimization based on heuristic optimization methods. The adequacy of the application of genetic algorithms in the problem of two-dimensional optimal placement of a bit sequence in a bounded two-dimensonal space is shown. The probabilistic mechanism of application of the mutational genetic operator is used.

Surrogate-adjoint refine based global optimization method combining with multi-stage fuzzy clustering space reduction strategy for expensive problems

In engineering optimization, surrogate model (SM) is widely used to replace the involved time expensive model, due to the expensive model is complex and high precise requirement caused a long calculation cycle. In traditional process of engineering optimization, the separation of the surrogate model static construction stage and dynamic optimization stage depresses the optimization accuracy and efficiency. Moreover, in order to ensure the accuracy of the surrogate model, expensive model had to be intensively invoked to get enough representative samples in the design space for the SM training. In this paper, a surrogate model adjoint refine based global optimization method combining with the multi-stage fuzzy clustering space reduction strategy (MFCPR-SGO) is proposed to improve the optimization accuracy and efficiency. Firstly, the optimal Latin hypercube design method (OLHD) is used to sample in design space to assure the initial sample set with strong space filling property. Then, the design space is subdivided into three tiered subspaces by using the space reduction strategy of multi-stage fuzzy clustering, which has the ability of space focusing, space reduction and jumping out of local optimum. On this basis, the hierarchical optimization method with ADAM gradient descent is proposed to quickly and accurately search the local minimum value of the objective function in each subspaces. At the same time, combined with the extremum sampling and the gaussian process sampling, a dynamic sampling algorithm is given to realize the synchronization of optimization and surrogate model update. Finally, the benchmark test problems in 12 different dimensions are used to verify the proposed method. The results show that the optimization accuracy can be improved by 21.3% and expensive model invoking times are reduced by 31.5% compared with other three heuristic optimization methods and the three recent surrogate-based optimization (SGO) algorithms. It indicated that the optimization precision and efficiency can be greatly improved by synchronizing the dynamic updating of the surrogate model with the engineering optimization search.

A New Solar Assisted Heat Pump System with Underground Energy Storage: Modelling and Optimisation

The objectives of this work are: (a) to present a new system for building heating which is based on underground energy storage, (b) to develop a mathematical model of the system, and (c) to optimise the energy performance of the system. The system includes Photovoltaic Thermal Hybrid Solar Panels (PVT) panels with cooling, an evacuated solar collector and a water-to-water heat pump. Additionally, storage tanks, placed underground, are used to store the waste heat from PVT panels cooling. The thermal energy produced by the solar collectors is used for both domestic hot water preparation and thermal energy storage. Both PVT panels and solar collectors are assembled with a sun-tracking system to achieve the highest possible solar energy gain. Optimisation of the proposed system is considered to achieve the highest Renewable Energy Sources (RES) share during the heating period. Because the resulting optimisation problem is nonlinear, the classical gradient-based optimisation algorithm gives solutions that are not satisfying. As alternatives, three heuristic global optimisation methods are considered: the Genetic Algorithm (GA), the Particle Swarm Optimisation (PSO) algorithm, and the Jaya algorithm. It is shown that the Jaya algorithm outperforms the GA and PSO methods. The most significant result is that 93% of thermal energy is covered by using the underground energy storage unit consisting of two tanks.

PSO and GA tuned conventional and fractional order PID controllers for quadrotor control

Purpose This study aims to compare the performance of the conventional and fractional order proportional-integral-derivative (PID and FOPID) controllers tuned with a particle swarm optimization (PSO) and genetic algorithm (GA) for quadrotor control. Design/methodology/approach In this study, the gains of the controllers were tuned using PSO and GA, which are included in the heuristic optimization methods. The tuning processes of the controller’s gains were formulated as optimization problems. While generating the objective functions (cost functions), four different decision criteria were considered separately: integrated summation error (ISE), integrated absolute error, integrated time absolute error and integrated time summation error (ITSE). Findings According to the simulation results and comparison tables that were created, FOPID controllers tuned with PSO performed better performances than PID controllers. In addition, the ITSE criterion returned better results in control of all axes except for altitude control when compared to the other cost functions. In the control of altitude with the PID controller, the ISE criterion showed better performance. Originality/value While a conventional PID controller has three parameters (Kp, Ki, Kd) that need to be tuned, FOPID controllers have two additional parameters (µ). The inclusion of these two extra parameters means more flexibility in the controller design but much more complexity for parameter tuning. This study reveals the potential and effectiveness of PSO and GA in tuning the controller despite the increased number of parameters and complexity.

The impact of loading restrictions on the two-echelon location routing problem

The two-echelon location routing problem (2E-LRP) arises in freight distribution when goods available at different origins are delivered to their respective destinations via intermediate facilities. The literature concerning the 2E-LRP considers freight capacities of vehicles to be scalars, while customer demands are additive volumes of individual items. However, ignoring the real dimensions of items and vehicles can lead to infeasible load plans in practice. Further investigation is thus required to study the impact of realistic loading restrictions on the 2E-LRP, algorithms for the problem and the quality of the solutions produced by those algorithms. This paper introduces a generalized 2E-LRP with two-dimensional loading restrictions (2E-LRP2L). To investigate how exactly one should handle these restrictions we introduce a heuristic optimization method combined with different loading strategies and evaluate their performance on instances derived from real-world data. Given that we are introducing a new problem, the quality of our heuristic is assessed by comparing it against state-of-the-art 2E-LRP methods on benchmark instances. The results indicate that the proposed method is highly competitive, finding most best-known solutions as well as providing some new ones.

Electromagnetic Architectures: Structures, Properties, Functions and Their Intrinsic Relationships in Subwavelength Optics and Electromagnetics

In recent years, with the development of photonic crystals, metamaterials, metasurfaces, and other related disciplines, the relationship between the structures and functionalities of artificial optical/electromagnetic materials and devices has become a research hotspot. This article reviews the optical/electromagnetic properties and performance of typical artificial micro/nanostructures. Based on the analogy of mechanics and optics/electromagnetism, the concept of “Electromagnetic Architectures” is proposed. In particular, we reviewed several typical methods for the study of optical/electromagnetic structural‐functional relationships, including semi‐classical analytical models, heuristic optimization methods, deep neural networks, topological optimization methods, etc. The viewpoint of this paper may push further researches on the structural‐functional relationship of artificially structured materials and devices, and find broad application prospects in imaging, communication, photonic chips, among many others.

Halton-Chaos and ALPSO power allocation methods for passive optical CDMA networks

The allocation of minimum power with guarantee of minimum rate in passive optical network optical code division multiple access (PON-OCDMA) networks is analyzed considering heuristic optimization methods such as Particle Swarm Optimization (PSO) and four variants. The base of the power-rate adaptive PON-OCDMA is the multi-length 2-D wavelength-hopping/time-spreading code called multiple-length extended wavelength-hopping prime code (MLEWHPC) to support the services of different media in accordance with the bit-rate and quality of service (QoS). The Halton-Chaos-β-PSO (HC-PSO) algorithm is proposed for solving the optimal power and rate allocation in order to maximize the EE of the optical system, subject to QoS restrictions based on the signal-to-interference plus-noise ratio (SINR) in each class of optical user and minimum required power. The proposed HC-PSO and the analytical–iterative–heuristic approach based on the augmented Lagrangian and PSO (ALPSO) method demonstrate promising performance-complexity trade-off, specially for high dimensionality OCDMA systems. The proposed hybrid analytical-evolutionary resource allocation method is corroborated by numerical simulation results, considering the tuning of heuristic evolutionary input parameters, which have demonstrated to improve the EE of the optical system when the power-rate allocation procedure is deployed dynamically in real time applications.

Improving the efficiency of microseismic source locating using a heuristic algorithm-based virtual field optimization method

Improving the efficiency of microseismic source locating using a heuristic algorithm-based virtual field optimization method

PI+Feed Forward Controller Tuning Based on Genetic Algorithm for Liquid Level Control of Coupled-Tank System

One of the main problems in the control of the coupled tank liquid level systems, which are used frequently in water treatment systems and petrochemical industry today, is to determine the water flow rate between the two tanks. In this paper, proportional-integral +feed forward control method (PI+FF), whose parameters are determined using genetic algorithm (GA), one of the heuristic optimization methods, is used to solve this problem. In addition, in order to show the performance of the GA-based controller, the PI+FF controller that PI parameters obtained using the Ziegler-Nichols (Z-N) method are applied to the same system and the real-time application results of both controllers are compared. The experimental results showed that the controller, which parameters are determined by GA, reached the desired reference value with less settling time and less overshooting when it compared to the Z-N method based controller, and also it has given faster response to sudden changes in the system.