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This review aims to exploit a study on different benchmark test functions used to evaluate the performance of Meta-Heuristic (MH) optimization techniques. The performance of the MH optimization techniques is evaluated with the different sets of mathematical benchmark test functions and various real-world engineering design problems. These benchmark test functions can help to identify the strengths and weaknesses of newly proposed MH optimization techniques. This review paper presents 215 mathematical test functions, including mathematical equations, characteristics, search space and global minima of the objective function and 57 real-world engineering design problems, including mathematical equations, constraints, and boundary conditions of the objective functions carried out from the literature. The MATLAB code references for mathematical benchmark test functions and real-world design problems, including the Congress of Evolutionary Computation (CEC) and Genetic and Evolutionary Computation Conference (GECCO) test suite, are presented in this paper. Also, the winners of CEC are highlighted with their reference papers. This paper also comprehensively reviews the literature related to benchmark test functions and real-world engineering design challenges using a bibliometric approach. This bibliometric analysis aims to analyze the number of publications, prolific authors, academic institutions, and country contributions to assess the field's growth and development. This paper will inspire researchers to innovate effective approaches for handling inequality and equality constraints.

In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ -divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on φ -divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with φ -divergence uncertainty is tractable for most of the choices of φ typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach. This paper was accepted by Gérard P. Cachon, optimization.

A well-regarded as well as powerful method named the ‘analytic hierarchy process’ (AHP) uses mathematics and psychology for making and analysing complex decisions. This article aims to present a brief review of the consistency measure of the judgments in AHP. Judgments should not be random or illogical. Several researchers have developed different consistency measures to identify the rationality of judgments. This article summarises the consistency measures which have been proposed so far in the literature. Moreover, this paper describes briefly the functional relationships established in the literature among the well-known consistency indices. At last, some thoughtful research directions that can be helpful in further research to develop and improve the performance of AHP are provided as well.

The use of FACTS devices in power systems has become increasingly popular in recent years, as they offer a number of benefits, including improved voltage profile, reduced power losses, and increased system reliability and safety. However, determining the optimal type, location, and size of FACTS devices can be a challenging optimization problem, as it involves mixed integer, nonlinear, and nonconvex constraints. To address this issue, researchers have applied various optimization techniques to determine the optimal configuration of FACTS devices in power systems. The paper provides an in-depth and comprehensive review of the various optimization techniques that have been used in published works in this field. The review classifies the optimization techniques into four main groups: classical optimization techniques, metaheuristic methods, analytic methods, and mixed or hybrid methods. Classical optimization techniques are conventional optimization approaches that are widely used in optimization problems. Metaheuristic methods are stochastic search algorithms that can be effective for nonconvex constraints. Analytic methods involve sensitivity analysis and gradient-based optimization techniques. Mixed or hybrid methods combine different optimization techniques to improve the solution quality. The paper also provides a performance comparison of these different optimization techniques, which can be useful in selecting an appropriate method for a specific problem. Finally, the paper offers some advice for future research in this field, such as developing new optimization techniques that can handle the complexity of the optimization problem and incorporating uncertainties into the optimization model. Overall, the paper provides a valuable resource for researchers and practitioners in the field of power systems optimization, as it summarizes the various optimization techniques that have been used to solve the FACTS optimization problem and provides insights into their performance and applicability.

This paper proposes a simulation-based optimization (SO) method that enables the efficient use of complex stochastic urban traffic simulators to address various transportation problems. It presents a metamodel that integrates information from a simulator with an analytical queueing network model. The proposed metamodel combines a general-purpose component (a quadratic polynomial), which provides a detailed local approximation, with a physical component (the analytical queueing network model), which provides tractable analytical and global information. This combination leads to an SO framework that is computationally efficient and suitable for complex problems with very tight computational budgets. We integrate this metamodel within a derivative-free trust region algorithm. We evaluate the performance of this method considering a traffic signal control problem for the Swiss city of Lausanne, different demand scenarios, and tight computational budgets. The method leads to well-performing signal plans. It leads to reduced, as well as more reliable, average travel times.

Manta Ray Foraging Optimization Algorithm (MRFO) is a new bio-inspired, meta-heuristic algorithm. MRFO algorithm has been used for the first time to optimize a multi-objective problem. The best size and location of distributed generations (DG) units have been determined to optimize three different objective functions. Minimization of active power loss, minimization of voltage deviation, and maximization of voltage stability index has been achieved through optimizing DG units under different power factor values, unity, 0.95, 0.866, and optimum value. MRFO has been applied to optimize DGs integrated with two well-known radial distribution power systems: IEEE 33-bus and 69-bus systems. The simulation results have been compared to different optimization algorithms in different cases. The results provide clear evidence of the superiority of MRFO that defind before (Manta Ray Foraging Optimization Algorithm. Quasi-Oppositional Differential Evolution Lévy Flights Algorithm (QODELFA), Stochastic Fractal Search Algorithm (SFSA), Genetics Algorithm (GA), Comprehensive Teaching Learning-Based Optimization (CTLBO), Comprehensive Teaching Learning-Based Optimization (CTLBO (ε constraint)), Multi-Objective Harris Hawks Optimization (MOHHO), Multi-Objective Improved Harris Hawks Optimization (MOIHHO), Multi-Objective Particle Swarm Optimization (MOPSO), and Multi-Objective Particle Swarm Optimization (MOWOA) in terms of power loss, Voltage Stability Index (VSI), and voltage deviation for a wide range of operating conditions. It is clear that voltage buses are improved; and power losses are decreased in both IEEE 33-bus and IEEE 69-bus system for all studied cases. MRFO algorithm gives good results with a smaller number of iterations, which means saving the time required for solving the problem and saving energy. Using the new MRFO technique has a promising future in optimizing different power system problems.

For improving the energy efficacy and control performance, integration of swarm optimization with controller design could successfully reach this objective. In this study, a comparative analysis has been conducted between two decentralized control structures based on optimized Proportional-Integral-Derivative (PID) and PID-Proportional (PID-P) controllers for optimal controlling of heating system in multi-zone building. Based on the energy balance equation, the mathematical dynamics model of the heating system is established in the building. In order to enhance and optimize the performances of both controllers, their design parameters are tuned based on Whale Optimization Algorithm (WOA). Two objectives have been considered in the optimization process of heating system. The first objective is to minimize the error in temperature, between the desired and real temperatures, based on IAE (Integral of Absolute Error) index, while the second objective is the minimization of the heat energy consumption. The normalization method has been used to adjust between the two differently-scaled objectives. Simulation results based on MATLAB reveal that the PID-P controller achieved better performance in terms of providing comfort indoor temperature with energy savings as compared to the PID controller.

This paper provides a comprehensive review of machine learning strategies and optimization formulations employed in energy management systems (EMS) tailored for plug-in hybrid electric vehicles (PHEVs). EMS stands as a pivotal component facilitating optimized power distribution, predictive and adaptive control strategies, component health monitoring, and energy harvesting, thereby enabling the maximal exploitation of resources through optimal operation. Recent advancements have introduced innovative solutions such as Model Predictive Control (MPC), machine learning-based techniques, real-time optimization algorithms, hybrid optimization approaches, and the integration of fuzzy logic with neural networks, significantly enhancing the efficiency and performance of EMS. Additionally, multi-objective optimization, stochastic and robust optimization methods, and emerging quantum computing approaches are pushing the boundaries of EMS capabilities. Remarkable advancements have been made in data-driven modeling, decision-making, and real-time adjustments, propelling machine learning and optimization to the forefront of enhanced control systems for vehicular applications. However, despite these strides, there remain unexplored research avenues and challenges awaiting investigation. This review synthesizes existing knowledge, identifies gaps, and underscores the importance of continued inquiry to address unanswered research questions, thereby propelling the field toward further advancements in PHEV EMS design and implementation.

Robust optimization (RO) is a technique to tractably model uncertain parameters in optimization problems. More recently, it has attracted interest in applications from machine learning and statistics. These recent applications present algorithmic challenges in which the scalability of RO algorithms with problem dimension becomes crucial. The traditional solution method for RO is to transform it into an equivalent—yet more complex—deterministic problem. The alternate solution technique is to iteratively solve sequences of the underlying deterministic model with different values of the uncertain parameters. However, such iterative approaches have been rather prohibitive in practice, especially when solving even the underlying deterministic model is expensive. In “Online First-Order Framework for Robust Convex Optimization,” by analyzing the structure of an underlying convex–nonconcave saddle point problem, N. Ho-Nguyen and F. Kılınç-Karzan develop an iterative framework for RO in which the cost of each iteration can be remarkably reduced. In particular, they show that, without scarifying from the guarantees on the number of iterations needed, it is possible to use cheap first-order updates instead of deterministic optimization solvers in each iteration. Robust optimization (RO) has emerged as one of the leading paradigms to efficiently model parameter uncertainty. The recent connections between RO and problems in statistics and machine learning domains demand for solving RO problems in ever larger scales. However, the traditional approaches for solving RO formulations based on building and solving robust counterparts or the iterative approaches utilizing nominal feasibility oracles can be prohibitively expensive and thus significantly hinder the scalability of the RO paradigm. In this paper, we present a general and flexible iterative framework to approximately solve robust convex optimization problems that is built on a fully online first-order paradigm. In comparison with the existing literature, a key distinguishing feature of our approach is that it requires access to only first-order oracles that are remarkably cheaper than pessimization or nominal feasibility oracles, while maintaining the same convergence rates. This, in particular, makes our approach much more scalable and hence preferable in large-scale applications, specifically those from machine learning and statistics domains. We also provide new interpretations of existing iterative approaches in our framework and illustrate our framework on robust quadratic programming. The e-companion is available at https://doi.org/10.1287/opre.2018.1764 .

The field of data exploration relies heavily on clustering techniques to organize vast datasets into meaningful subgroups, offering valuable insights across various domains. Traditional clustering algorithms face limitations in terms of performance, often getting stuck in local minima and struggling with complex datasets of varying shapes and densities. They also require prior knowledge of the number of clusters, which can be a drawback in real-world scenarios. In response to these challenges, we propose the \"hybrid raven roosting intelligence framework\" (HRIF) algorithm. HRIF draws inspiration from the dynamic behaviors of roosting ravens and computational intelligence. What distinguishes HRIF is its effective capacity to adeptly navigate the clustering landscape, evading local optima and converging toward optimal solutions. An essential enhancement in HRIF is the incorporation of the Gaussian mutation operator, which adds stochasticity to improve exploration and mitigate the risk of local minima. This research presents the development and evaluation of HRIF, showcasing its unique fusion of nature-inspired optimization techniques and computational intelligence. Extensive experiments with diverse benchmark datasets demonstrate HRIF's competitive performance, particularly its capability to handle complex data and avoid local minima, resulting in accurate clustering outcomes. HRIF's adaptability to challenging datasets and its potential to enhance clustering efficiency and solution quality position it as a promising solution in the world of data exploration.