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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.

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.

We generalize the standard method of solving inverse optimization problems to allow for the solution of inverse problems that would otherwise be ill posed or infeasible. In multiobjective linear optimization, given a solution that is not a weakly efficient solution to the forward problem, our method generates objective function weights that make the given solution a near-weakly efficient solution. Our generalized inverse optimization model specializes to the standard model when the given solution is weakly efficient and retains the complexity of the underlying forward problem. We provide a novel interpretation of our inverse formulation as the dual of the well-known Benson's method and by doing so develop a new connection between inverse optimization and Pareto surface approximation techniques. We apply our method to prostate cancer data obtained from Princess Margaret Cancer Centre in Toronto, Canada. We demonstrate that clinically acceptable treatments can be generated using a small number of objective functions and inversely optimized weights-current treatments are designed using a complex formulation with a large parameter space in a trial-and-error reoptimization process. We also show that our method can identify objective functions that are most influential in treatment plan optimization.

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.

This paper proposes a robust control strategy to enhance the dynamic performance and power quality of standalone Doubly Fed Induction Generator (DFIG) systems under unbalanced loads. The approach employs metaheuristic optimization techniques the Cuckoo Search Algorithm (CSA) and Whale Optimization Algorithm (WOA) to optimally tune PI controllers in a direct-voltage control scheme for the rotor-side converter. Comprehensive simulation and experimental validation (using a dSPACE DS1104 platform) demonstrate the superiority of the optimized controllers over conventional PI tuning. Key experimental improvements include: overshoot reduced by up to 88% (from 36.8 to 4.2%), rise time accelerated by 99% (from 0.22 to 0.002 s), and stator voltage THD suppressed by 82% (from 31.8 to 5.9%) during load and voltage step variations. The results confirm that CSA and WOA optimization significantly boost transient response and power quality in off-grid DFIG wind energy systems.

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.