SINGLE OBJECTIVE METAHEURISTIC ALGORITHM

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This paper presents an art-inspired optimization algorithm, which is called Stochastic Paint Optimizer (SPO). The SPO is a population-based optimizer inspired by the art of painting and the beauty of colors plays the main role in this algorithm. 

Puma Optimizer (PO) is proposed as a new optimization algorithm inspired from the intelligence and life of Pumas in. In this algorithm, unique and powerful mechanisms have been proposed in each phase of exploration and exploitation, which has increased the algorithm's performance against all kinds of optimization problems. In addition, a new type of intelligent mechanism, which is a type of hyper-heuristic for phase change, is presented (PI). 

The novelty of this article lies in introducing a novel stochastic technique named the Hippopotamus Optimization (HO) algorithm. The HO is conceived by drawing inspiration from the inherent behaviors observed in hippopotamuses, showcasing an innovative approach in metaheuristic methodology. The HO is conceptually defined using a trinary-phase model that incorporates their position updating in rivers or ponds, defensive strategies against predators, and evasion methods, which are mathematically formulated.

An original swarm-based, bio-inspired metaheuristic algorithm, named electric eel foraging optimization (EEFO) is developed and tested in this work. EEFO draws inspiration from the intelligent group foraging behaviors exhibited by electric eels in nature.

Quadratic Interpolation Optimization (QIO) is a new optimization approach for solving optimization problems. QIO is motivated derived from mathematics, specifically the newly proposed generalized quadratic interpolation (GQI) method. The GQI method can better find the minimizer of the quadratic interpolation function form any three points. The algorithm is simple and easy to implement.

The Mountain Gazelle Optimizer (MGO), a novel meta-heuristic algorithm inspired by the social life and hierarchy of wild mountain gazelles, is suggested in this paper. In this algorithm, gazelles' hierarchical and social life is formulated mathematically and used to develop an optimization algorithm. 

In this paper, a dynamic version of the arithmetic optimization algorithm (DAOA) is presented. During an optimization process, a new candidate solution change to regulate exploration and exploitation in a dynamic version in each iteration. The most remarkable attribute of DAOA is that it does not need to make any effort to preliminary fine-tuning parameters relative to the most present metaheuristic.

ICGO is an enhanced version of the Chaos Game Optimization (CGO) algorithm, with improvements made to the mutation phase of the traditional CGO method. The foundational mathematics of CGO is rooted in the self-resemblance properties of fractals in chaos theory and the fundamental principles of creating the Sierpinski triangle. The Sierpinski triangle is crafted by segmenting each equilateral triangle into three smaller triangles, each having half the edge length of the original. When the count of initial fractal vertices rises to N, a Sierpinski triangle of N − 1 dimensions can be established,

This research paper presents a novel optimization method called the Synergistic Swarm Optimization Algorithm (SSOA). The SSOA combines the principles of swarm intelligence and synergistic cooperation to search for optimal solutions efficiently. A synergistic cooperation mechanism is employed, where particles exchange information and learn from each other to improve their search behaviors. 

In MTV-SCA, a sufficient number of search strategies incorporating three control parameters are adapted through a multi-trial vector (MTV) approach to achieve specific objectives during the search process. The major contribution of this study is employing four distinct search strategies, each adapted to preserve the equilibrium between exploration and exploitation and avoid premature convergence during optimization. The strategies utilize different sinusoidal and cosinusoidal parameters to improve the algorithm’s performance.

This study introduces a novel optimization technique, the Divine Religions Algorithm (DRA), which employs an evolutionary socio-economic approach inspired by religious societies. The algorithm models interactions among followers, missionaries, and leaders, organizing followers into religious and political schools. Agents such as promotion, miracles, substitution, and reward-penalty mechanisms, along with an elitism-based search, enhance follower beliefs. 

This paper introduces a multi-objective adaptation of the Flow Direction Algorithm (FDA) to address the shortcomings of traditional evolutionary and meta-heuristic optimization methods in multi-objective optimization (MOO). These conventional methods often fail to find Pareto optimal solutions and to represent all objectives fairly. Building on the FDA's success in single-objective tasks, we expanded its application to MOO, creating the Multi-Objective Flow Direction Algorithm (MOFDA). MOFDA incorporates new mechanisms to accurately and uniformly find optimal solutions for MOO challenges. It features a fixed-size external archive to maintain Pareto optimal solutions, uses a grid mechanism to improve non-dominated solutions within this archive, and implements a leader selection process to guide searches in the multi-objective space. 

The GNDO algorithm, previously known for its effectiveness in single-objective optimization, has been enhanced with two key features for multi-objective optimization. The first is the addition of an archival mechanism to store non-dominated Pareto optimal solutions, ensuring a detailed record of the best outcomes. The second enhancement is a new leader selection mechanism designed to strategically identify and select the best solutions from the archive to guide the optimization process. This enhancement positions MOGNDO as a cutting-edge solution in multi-objective optimization, setting a new benchmark for evaluating its performance against leading algorithms in the field.

The single-objective version of stochastic paint optimizer (SPO) is appropriately changed to solve multi-objective optimization problems described as MOSPO. Color theory, the color wheel, and color combination methods are the main concepts of SPO. The SPO will be able to do excellent exploration and exploitation thanks to four simple color combination rules that do not have any internal parameters.

The Chaos Game Optimization (CGO) has only recently gained popularity, but its effective searching capabilities have a lot of potential for addressing single-objective optimization issues. Despite its advantages, this method can only tackle problems formulated with one objective. The multi-objective CGO proposed in this study is utilized to handle the problems with several objectives (MOCGO).

This paper presents the multi-objective version of a recently proposed metaheuristic algorithm called Crystal Structure Algorithm (CryStAl) which was inspired by the principles underlying the formation crystal structures.

The artificial hummingbird algorithm (AHA) is a recently developed bio-based metaheuristic and it shows superior performance in handling single-objective optimization problems. A multi-objective AHA (MOAHA) is developed in this study. In MOAHA, an external archive is employed to save Pareto optimal solutions, and a dynamic elimination-based crowding distance (DECD) method is developed to maintain this archive to effectively preserve the population diversity. 

In the present paper, a physics-inspired metaheuristic algorithm is presented to solve multi-objective optimization problems. The algorithm is developed based on the concept of Newtonian cooling law that recently has been employed by the thermal exchange optimization (TEO) algorithm to solve single-objective optimization problems efficiently. The performance of the multi-objective version of TEO (MOTEO) is examined through bi- and tri-objective mathematical and engineering problems as well as bi-objective structural design examples.

In this paper, we introduce the multi-objective version of a recently-developed single-objective metaheuristic algorithm known as Atomic Orbital Search (AOS), which will be called Multi-Objective Atomic Orbital Search (MOAOS). To this end, the general aspects and main searching loop of the AOS algorithm are modified to make it capable of dealing with problems with multiple objectives.

This paper presents a multi-objective version of the artificial vultures optimization algorithm (AVOA) for a multi-objective optimization problem called a multi-objective AVOA (MOAVOA). The inspirational concept of the AVOA is based on African vultures' lifestyles. Archive, grid, and leader selection mechanisms are used for developing the MOAVOA.  

his research proposes an Archive-based Multi-Objective Arithmetic Optimization Algorithm (MAOA) as an alternative to the recently established Arithmetic Optimization Algorithm (AOA) for multi-objective problems (MAOA). The original AOA approach was based on the distribution behavior of vital mathematical arithmetic operators, such as multiplication, division, subtraction, and addition.

 this paper, the multi-objective version of the Material Generation Algorithm (MGA) is proposed as MOMGA, one of the recently developed metaheuristic algorithms for single-objective optimization.