Metaheuristic algorithms are methods devised to efficiently solve computationally challenging optimization problems. Researchers have taken inspiration from various natural and physical processes alike to formulate meta-heuristics that have successfully provided near-optimal or optimal solutions to several engineering tasks. This chapter focuses on meta-heuristic algorithms modelled upon non-linear physical phenomena having a concrete optimization paradigm, having shown formidable exploration and exploitation abilities for such optimization problems. Specifically, this chapter focuses on several popular physics-based metaheuristics as well as describing the underlying unique physical processes associated with each algorithm.
The simplified modeling of a complex system allied with a low-order controller structure can lead to poor closed-loop performance and robustness. A feasible solution is to avoid the necessity of a model by using data for the controller design. The Virtual Reference Feedback Tuning (VRFT) is a data-driven design method that only requires a single batch of data and solves a reference tracking problem, although with no guarantee of robustness. In this work, the inclusion of an $\mathcal{H}_{\infty}$ robustness constraint to the VRFT cost function is addressed. The estimation of the $\mathcal{H}_{\infty}$ norm of the sensitivity transfer function is extended to maintain the one-shot characteristic of the VRFT. Swarm intelligence algorithms are used to solve the non-convex cost function. The proposed method is applied in two real-world inspired problems with four different swarm intelligence algorithms, which are compared with each other through a Monte Carlo experiment of 50 executions. The obtained results are satisfactory, achieving the desired robustness criteria.
Mathematical models are widely recognized as an important tool for analyzing and understanding the dynamics of infectious disease outbreaks, predict their future trends, and evaluate public health intervention measures for disease control and elimination. We propose a novel stochastic metapopulation state-space model for COVID-19 transmission, based on a discrete-time spatio-temporal susceptible/exposed/infected/recovered/deceased (SEIRD) model. The proposed framework allows the hidden SEIRD states and unknown transmission parameters to be estimated from noisy, incomplete time series of reported epidemiological data, by application of unscented Kalman filtering (UKF), maximum-likelihood adaptive filtering, and metaheuristic optimization. Experiments using both synthetic data and real data from the Fall 2020 Covid-19 wave in the state of Texas demonstrate the effectiveness of the proposed model.
Inverse molecular design, i.e., designing molecules with specific target properties, can be posed as an optimization problem. High-dimensional optimization tasks in the natural sciences are commonly tackled via population-based metaheuristic optimization algorithms such as evolutionary algorithms. However, expensive property evaluation, which is often required, can limit the widespread use of such approaches as the associated cost can become prohibitive. Herein, we present JANUS, a genetic algorithm that is inspired by parallel tempering. It propagates two populations, one for exploration and another for exploitation, improving optimization by reducing expensive property evaluations. Additionally, JANUS is augmented by a deep neural network that approximates molecular properties via active learning for enhanced sampling of the chemical space. Our method uses the SELFIES molecular representation and the STONED algorithm for the efficient generation of structures, and outperforms other generative models in common inverse molecular design tasks achieving state-of-the-art performance.
The Ebola virus and the disease in effect tend to randomly move individuals in the population around susceptible, infected, quarantined, hospitalized, recovered, and dead sub-population. Motivated by the effectiveness in propagating the disease through the virus, a new bio-inspired and population-based optimization algorithm is proposed. This paper presents a novel metaheuristic algorithm named Ebola optimization algorithm (EOSA). To correctly achieve this, this study models the propagation mechanism of the Ebola virus disease, emphasising all consistent states of the propagation. The model was further represented using a mathematical model based on first-order differential equations. After that, the combined propagation and mathematical models were adapted for developing the new metaheuristic algorithm. To evaluate the proposed method's performance and capability compared with other optimization methods, the underlying propagation and mathematical models were first investigated to determine how they successfully simulate the EVD. Furthermore, two sets of benchmark functions consisting of forty-seven (47) classical and over thirty (30) constrained IEEE CEC-2017 benchmark functions are investigated numerically. The results indicate that the performance of the proposed algorithm is competitive with other state-of-the-art optimization methods based on scalability analysis, convergence analysis, and sensitivity analysis. Extensive simulation results indicate that the EOSA outperforms other state-of-the-art popular metaheuristic optimization algorithms such as the Particle Swarm Optimization Algorithm (PSO), Genetic Algorithm (GA), and Artificial Bee Colony Algorithm (ABC) on some shifted, high dimensional and large search range problems.
The success of metaheuristic optimization methods has led to the development of a large variety of algorithm paradigms. However, no algorithm clearly dominates all its competitors on all problems. Instead, the underlying variety of landscapes of optimization problems calls for a variety of algorithms to solve them efficiently. It is thus of prior importance to have access to mature and flexible software frameworks which allow for an efficient exploration of the algorithm design space. Such frameworks should be flexible enough to accommodate any kind of metaheuristics, and open enough to connect with higher-level optimization, monitoring and evaluation softwares. This article summarizes the features of the ParadisEO framework, a comprehensive C++ free software which targets the development of modular metaheuristics. ParadisEO provides a highly modular architecture, a large set of components, speed of execution and automated algorithm design features, which are key to modern approaches to metaheuristics development.
This paper presents a new algorithm named spherical vector-based particle swarm optimization (SPSO) to deal with the problem of path planning for unmanned aerial vehicles (UAVs) in complicated environments subjected to multiple threats. A cost function is first formulated to convert the path planning into an optimization problem that incorporates requirements and constraints for the feasible and safe operation of the UAV. SPSO is then used to find the optimal path that minimizes the cost function by efficiently searching the configuration space of the UAV via the correspondence between the particle position and the speed, turn angle and climb/dive angle of the UAV. To evaluate the performance of SPSO, eight benchmarking scenarios have been generated from real digital elevation model maps. The results show that the proposed SPSO outperforms not only other particle swarm optimization (PSO) variants including the classic PSO, phase angle-encoded PSO and quantum-behave PSO but also other state-of-the-art metaheuristic optimization algorithms including the genetic algorithm (GA), artificial bee colony (ABC), and differential evolution (DE) in most scenarios. In addition, experiments have been conducted to demonstrate the validity of the generated paths for real UAV operations. Source code of the algorithm can be found at https://github.com/duongpm/SPSO.
Artificial bee colony algorithm (ABC) developed by inspiring the foraging phenomena of the natural honey bees is a simple and powerful metaheuristic optimization algorithm. The performance of single objective ABC performance has been well demonstrated by implemented to different design optimization problems from elec-trical and mechanical to civil engineering. Its efficacy is anticipated in the multi-objective design optimization of multilayer microwave dielectric filters (MMDFs) which is a challenging multi-objective problem falls into the context of electromagnetic (EM) design in electrical engineering. The MMDF is composed of superimposed multiple dielectric layers in order to pass or stop the EM wave at the desired frequency bands. An accurate dual-objective EM model of MMDF is constituted to be the total reflection coefficients for oblique incident wave angular range with transverse electric (TE) or transverse magnetic (TM) polarizations. The objective functions depend on the total reflection (TR) at the pass and stop band re-gions. Three types of the MDFs that are low pass (LP), high pass (HP) and band pass (BP) MMDFs are optimally designed across the constituted dual-objective EM model with a frequency dependent material database through using the multi-objective ABC (MO-ABC) strategy. The Pareto optimal solutions are refined within the possible solutions for synchronously minimizing the objective func-tions. The global optimal MMDF designs are selected from the Pare-to optimal solutions by providing the trade-off therein between the objective functions. The performance study regarding the frequen-cy characteristics of the designed MMDFs are well presented via numerical and graphical results. It is hence demonstrated that MO-ABC is even versatile and robust in the multi-objective design of MMDFs.
Purpose: The development of metaheuristic algorithms has increased by researchers to use them extensively in the field of business, science, and engineering. One of the common metaheuristic optimization algorithms is called Grey Wolf Optimization (GWO). The algorithm works based on imitation of the wolves' searching and the process of attacking grey wolves. The main purpose of this paper to overcome the GWO problem which is trapping into local optima. Design or Methodology or Approach: In this paper, the K-means clustering algorithm is used to enhance the performance of the original Grey Wolf Optimization by dividing the population into different parts. The proposed algorithm is called K-means clustering Grey Wolf Optimization (KMGWO). Findings: Results illustrate the efficiency of KMGWO is superior to GWO. To evaluate the performance of the KMGWO, KMGWO applied to solve 10 CEC2019 benchmark test functions. Results prove that KMGWO is better compared to GWO. KMGWO is also compared to Cat Swarm Optimization (CSO), Whale Optimization Algorithm-Bat Algorithm (WOA-BAT), and WOA, so, KMGWO achieves the first rank in terms of performance. Statistical results proved that KMGWO achieved a higher significant value compared to the compared algorithms. Also, the KMGWO is used to solve a pressure vessel design problem and it has outperformed results. Originality/value: Results prove that KMGWO is superior to GWO. KMGWO is also compared to cat swarm optimization (CSO), whale optimization algorithm-bat algorithm (WOA-BAT), WOA, and GWO so KMGWO achieved the first rank in terms of performance. Also, the KMGWO is used to solve a classical engineering problem and it is superior
Deep learning techniques, such as Deep Boltzmann Machines (DBMs), have received considerable attention over the past years due to the outstanding results concerning a variable range of domains. One of the main shortcomings of these techniques involves the choice of their hyperparameters, since they have a significant impact on the final results. This work addresses the issue of fine-tuning hyperparameters of Deep Boltzmann Machines using metaheuristic optimization techniques with different backgrounds, such as swarm intelligence, memory- and evolutionary-based approaches. Experiments conducted in three public datasets for binary image reconstruction showed that metaheuristic techniques can obtain reasonable results.
In this paper is proposed an evaluation of ten metaheuristic optimization algorithms applied on the inverse optimization of the Interfacial Heat Transfer Coefficient (IHTC) coupled on the solidification phenomenon. It was considered an upward directional solidification system for Al-7wt.% Si alloy and, for IHTC model, a exponential time function. All thermophysical properties of the alloy were considered constant. Scheil Rule was used as segregation model ahead phase-transformation interface. Optimization results from Markov Chain Monte Carlo method (MCMC) were considered as reference. Based on average, quantiles 95% and 5%, kurtosis, average iterations and absolute errors of the metaheuristic methods, in relation to MCMC results, the Flower Pollination Algorithm (FPA) and Moth-Flame Optimization (MFO) presented the most appropriate results, outperforming the other methods in this particular phenomenon, based on these metrics. The regions with the most probable values for parameters in IHTC time function were also determined.
This paper presents a novel algorithm named the motion-encoded particle swarm optimization (MPSO) for finding a moving target with unmanned aerial vehicles (UAVs). From the Bayesian theory, the search problem can be converted to the optimization of a cost function that represents the probability of detecting the target. Here, the proposed MPSO is developed to solve that problem by encoding the search trajectory as a series of UAV motion paths evolving over the generation of particles in a PSO algorithm. This motion-encoded approach allows for preserving important properties of the swarm including the cognitive and social coherence, and thus resulting in better solutions. Results from extensive simulations with existing methods show that the proposed MPSO improves the detection performance by 24\% and time performance by 4.71 times compared to the original PSO, and moreover, also outperforms other state-of-the-art metaheuristic optimization algorithms including the artificial bee colony (ABC), ant colony optimization (ACO), genetic algorithm (GA), differential evolution (DE), and tree-seed algorithm (TSA) in most search scenarios. Experiments have been conducted with real UAVs in searching for a dynamic target in different scenarios to demonstrate MPSO merits in a practical application.
In the power and energy systems area, a progressive increase of literature contributions containing applications of metaheuristic algorithms is occurring. In many cases, these applications are merely aimed at proposing the testing of an existing metaheuristic algorithm on a specific problem, claiming that the proposed method is better than other methods based on weak comparisons. This 'rush to heuristics' does not happen in the evolutionary computation domain, where the rules for setting up rigorous comparisons are stricter, but are typical of the domains of application of the metaheuristics. This paper considers the applications to power and energy systems, and aims at providing a comprehensive view of the main issues concerning the use of metaheuristics for global optimization problems. A set of underlying principles that characterize the metaheuristic algorithms is presented. The customization of metaheuristic algorithms to fit the constraints of specific problems is discussed. Some weaknesses and pitfalls found in literature contributions are identified, and specific guidelines are provided on how to prepare sound contributions on the application of metaheuristic algorithms to specific problems.
Research on new optimization algorithms is often funded based on the motivation that such algorithms might improve the capabilities to deal with real-world and industrially relevant optimization challenges. Besides a huge variety of different evolutionary and metaheuristic optimization algorithms, also a large number of test problems and benchmark suites have been developed and used for comparative assessments of algorithms, in the context of global, continuous, and black-box optimization. For many of the commonly used synthetic benchmark problems or artificial fitness landscapes, there are however, no methods available, to relate the resulting algorithm performance assessments to technologically relevant real-world optimization problems, or vice versa. Also, from a theoretical perspective, many of the commonly used benchmark problems and approaches have little to no generalization value. Based on a mini-review of publications with critical comments, advice, and new approaches, this communication aims to give a constructive perspective on several open challenges and prospective research directions related to systematic and generalizable benchmarking for black-box optimization.
All metaheuristic optimization algorithms require some initialization, and the initialization for such optimizers is usually carried out randomly. However, initialization can have some significant influence on the performance of such algorithms. This paper presents a systematic comparison of 22 different initialization methods on the convergence and accuracy of five optimizers: differential evolution (DE), particle swarm optimization (PSO), cuckoo search (CS), artificial bee colony (ABC) algorithm and genetic algorithm (GA). We have used 19 different test functions with different properties and modalities to compare the possible effects of initialization, population sizes and the numbers of iterations. Rigorous statistical ranking tests indicate that 43.37\% of the functions using the DE algorithm show significant differences for different initialization methods, while 73.68\% of the functions using both PSO and CS algorithms are significantly affected by different initialization methods. The simulations show that DE is less sensitive to initialization, while both PSO and CS are more sensitive to initialization. In addition, under the condition of the same maximum number of function evaluations (FEs), the population size can also have a strong effect. Particle swarm optimization usually requires a larger population, while the cuckoo search needs only a small population size. Differential evolution depends more heavily on the number of iterations, a relatively small population with more iterations can lead to better results. Furthermore, ABC is more sensitive to initialization, while such initialization has little effect on GA. Some probability distributions such as the beta distribution, exponential distribution and Rayleigh distribution can usually lead to better performance. The implications of this study and further research topics are also discussed in detail.
In recent years, there has been an increasing interest in building video summarization tools, where the goal is to automatically create a short summary of an input video that properly represents the original content. We consider shot-based video summarization where the summary consists of a subset of the video shots which can be of various lengths. A straightforward approach to maximize the representativeness of a subset of shots is by minimizing the total distance between shots and their nearest selected shots. We formulate the task of video summarization as an optimization problem with a knapsack-like constraint on the total summary duration. Previous studies have proposed greedy algorithms to solve this problem approximately, but no experiments were presented to measure the ability of these methods to obtain solutions with low total distance. Indeed, our experiments on video summarization datasets show that the success of current methods in obtaining results with low total distance still has much room for improvement. In this paper, we develop ILS-SUMM, a novel video summarization algorithm to solve the subset selection problem under the knapsack constraint. Our algorithm is based on the well-known metaheuristic optimization framework -- Iterated Local Search (ILS), known for its ability to avoid weak local minima and obtain a good near-global minimum. Extensive experiments show that our method finds solutions with significantly better total distance than previous methods. Moreover, to indicate the high scalability of ILS-SUMM, we introduce a new dataset consisting of videos of various lengths.
This paper presents the application of a newly developed nature-inspired metaheuristic optimization method, namely the Adaptive Wind Driven Optimization (AWDO), to the training of feedforward artificial neural networks (NN) and presents a discussion into the future research of AWDO implementation in Deep Learning (DL). Application example of digit classification with MNIST dataset reveals interesting behavior of the derivative-free AWDO method compared to steepest descent method where results and future work on the implementation of AWDO in deep neural networks are discussed.
We propose a novel, flexible algorithm for combining together metaheuristicoptimizers for non-convex optimization problems. Our approach treatsthe constituent optimizers as a team of complex agents that communicateinformation amongst each other at various intervals during the simulationprocess. The information produced by each individual agent can be combinedin various ways via higher-level operators. In our experiments on keybenchmark functions, we investigate how the performance of our algorithmvaries with respect to several of its key modifiable properties. Finally,we apply our proposed algorithm to classification problems involving theoptimization of support-vector machine classifiers.
Swarm Intelligence is a metaheuristic optimization approach that has become very predominant over the last few decades. These algorithms are inspired by animals' physical behaviors and their evolutionary perceptions. The simplicity of these algorithms allows researchers to simulate different natural phenomena to solve various real-world problems. This paper suggests a novel algorithm called Donkey and Smuggler Optimization Algorithm (DSO). The DSO is inspired by the searching behavior of donkeys. The algorithm imitates transportation behavior such as searching and selecting routes for movement by donkeys in the actual world. Two modes are established for implementing the search behavior and route-selection in this algorithm. These are the Smuggler and Donkeys. In the Smuggler mode, all the possible paths are discovered and the shortest path is then found. In the Donkeys mode, several donkey behaviors are utilized such as Run, Face & Suicide, and Face & Support. Real world data and applications are used to test the algorithm. The experimental results consisted of two parts, firstly, we used the standard benchmark test functions to evaluate the performance of the algorithm in respect to the most popular and the state of the art algorithms. Secondly, the DSO is adapted and implemented on three real-world applications namely; traveling salesman problem, packet routing, and ambulance routing. The experimental results of DSO on these real-world problems are very promising. The results exhibit that the suggested DSO is appropriate to tackle other unfamiliar search spaces and complex problems.
Software development effort estimation is considered a fundamental task for software development life cycle as well as for managing project cost, time and quality. Therefore, accurate estimation is a substantial factor in projects success and reducing the risks. In recent years, software effort estimation has received a considerable amount of attention from researchers and became a challenge for software industry. In the last two decades, many researchers and practitioners proposed statistical and machine learning-based models for software effort estimation. In this work, Firefly Algorithm is proposed as a metaheuristic optimization method for optimizing the parameters of three COCOMO-based models. These models include the basic COCOMO model and other two models proposed in the literature as extensions of the basic COCOMO model. The developed estimation models are evaluated using different evaluation metrics. Experimental results show high accuracy and significant error minimization of Firefly Algorithm over other metaheuristic optimization algorithms including Genetic Algorithms and Particle Swarm Optimization.