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A fuzzy reinforced Jaya algorithm for solving mathematical and structural optimization problems
Jaya is a metaheuristic algorithm that uses a pair of random internal parameters to adjust its exploration and exploitation search behaviors. Such a random setting can negatively affect the search performance of the algorithm by causing inappropriate search behavior in some iterations. To tackle this issue, the present study deals with developing a new fuzzy decision-making mechanism for dynamic adjusting the trade-off between the exploration and exploitation search behaviors of the Jaya method. The new algorithm is named Fuzzy Reinforced Jaya (FRJ) method. The search capability of the FRJ is evaluated in solving a suite of unconstrained mathematical benchmarks and constrained mechanical and structural optimization problems with buckling and natural frequency constraints. Also, the relevant decision variables are selected from both continuous and discrete domains. To provide a deeper insight into the effect of the defined auxiliary fuzzy module, the performance of the algorithm is evaluated and discussed using normalized diversity concept and behavioral diagrams. Also, employing different statistical analyses (e.g.,
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diagrams, Wilcoxson and Friedman tests), the significance of the outcomes is evaluated. Also, the numeric achievements are compared with six other well-stablished techniques. Attained outcomes indicate that the proposed FRJ, as a self-adaptive and parameter-free method, provides superior and promising results in the terms of stability, accuracy, and computational cost in solving mathematical and structural optimization problems.
Journal Article
Adaptive Fuzzy Swarm-based Search Algorithm (AFSSA) for Complex Engineering Optimization
In recent years, swarm intelligence metaheuristic algorithms have emerged as powerful tools for solving real-world engineering optimization problems. However, their performance often degrades when applied to complex, high-dimensional problems. To address this limitation, we propose an Adaptive Fuzzy Swarm-based Search Algorithm (AFSSA), which incorporates a Fuzzy Dynamic Control Mechanism to dynamically adjust the optimization coefficients of swarm intelligence algorithms. AFSSA employs a Mamdani fuzzy inference system to enable smooth phase transitions during optimization, ensuring adaptability to the problem's unique characteristics. In this study, AFSSA is applied to enhance the acceleration coefficients of Particle Swarm Optimization (PSO) and Golden Search Optimization (GSO), resulting in AFSSA-PSO and AFSSA-GSO. The performance of these modified algorithms is evaluated on 23 standard benchmark functions (with dimensions of 30, 100, and 500) and the CEC2019 test suite, showing competitive results compared to other well-known optimization methods. Additionally, AFSSA is tested on data clustering problems, further demonstrating its versatility in handling complex real-world applications.
Journal Article
Discrete Puma Optimizer to Solve Combinatorial Optimization Problems
Discrete and combinatorial optimization problems such as routing, scheduling, and resource allocation present high computational complexity, limiting the effectiveness of classical exact optimization methods. Most existing metaheuristic (MH) algorithms are originally designed for continuous domains and require transformation procedures that often degrade performance when applied to discrete problems. This study introduces the discrete puma optimizer (DPO), a new variant metaheuristic algorithm developed to operate directly within discrete search spaces by employing discrete-specific operators and adaptive exploration–exploitation strategies. DPO is applied to 7 real-world optimization problems, including the Traveling Salesman Problem, Smart Grid Optimization, Factory Production Planning, Vehicle Routing Problem, Modern TSP, Team Orienteering Problem, and Electric Vehicle Charging Station Location Optimization, and evaluated on a total of 22 small-, medium-, and large-scale dataset instances. The performance of DPO is benchmarked against 9 various and well-known MH algorithms. Experimental results show that DPO attains superior best and mean solutions, lower variance, and faster stabilization in convergence behavior. Wilcoxon signed-rank tests confirm the statistical significance of the observed improvements, particularly in large-scale scenarios where competing methods show marked degradation. Comprehensive cross-problem rankings further illustrate DPO’s enhanced generalizability and scalability. These results position DPO as an effective and robust approach for real-world large-scale discrete optimization tasks.
Journal Article
Optimal Task Allocation Algorithm Based on Queueing Theory for Future Internet Application in Mobile Edge Computing Platform
For 5G and future Internet, in this paper, we propose a task allocation method for future Internet application to reduce the total latency in a mobile edge computing (MEC) platform with three types of servers: a dedicated MEC server, a shared MEC server, and a cloud server. For this platform, we first calculate the delay between sending a task and receiving a response for the dedicated MEC server, shared MEC server, and cloud server by considering the processing time and transmission delay. Here, the transmission delay for the shared MEC server is derived using queueing theory. Then, we formulate an optimization problem for task allocation to minimize the total latency for all tasks. By solving this optimization problem, tasks can be allocated to the MEC servers and cloud server appropriately. In addition, we propose a heuristic algorithm to obtain the approximate optimal solution in a shorter time. This heuristic algorithm consists of four algorithms: a main algorithm and three additional algorithms. In this algorithm, tasks are divided into two groups, and task allocation is executed for each group. We compare the performance of our proposed heuristic algorithm with the solution obtained by three other methods and investigate the effectiveness of our algorithm. Numerical examples are used to demonstrate the effectiveness of our proposed heuristic algorithm. From some results, we observe that our proposed heuristic algorithm can perform task allocation in a short time and can effectively reduce the total latency in a short time. We conclude that our proposed heuristic algorithm is effective for task allocation in a MEC platform with multiple types of MEC servers.
Journal Article
CGWRIME: collaboration and competition-boosted RIME optimizer for engineering optimization problems
RIME, a physics-based heuristic algorithm, simulates the natural phenomenon of rime generation and possesses a robust capacity for global exploration, enabling it to escape local optima. However, testing revealed that RIME suffers from slow convergence during the later stages of evaluation, weak individual exploitation capabilities, and subpar population quality when addressing numerical function optimization problems. This paper proposes a fast-convergence soft-rime search strategy to address these issues by enhancing the soft-rime coefficient, a critical parameter, to mitigate slow convergence in RIME's later evaluation stages. Additionally, the concepts of collaboration and competition, inherent in swarm intelligence-based algorithms, are introduced through the hard-rime puncture strategy, aimed at improving individual exploitation and population quality in RIME. An improved version, termed CGWRIME, is developed by integrating the proposed strategy with a comprehensive learning approach. Subsequently, qualitative analyses and ablation experiments validate the algorithm's search characteristics and the proposed strategy's effectiveness. Comparative experiments with well-known heuristic algorithms and high-performing metaheuristic algorithms confirm CGWRIME's advantages in unconstrained mathematical optimization. Finally, it is applied to five engineering design optimization cases, demonstrating that CGWRIME excels in managing unconstrained numerical functions and provides significant benefits in solving practical engineering optimization problems with constraints.
Journal Article
Multi-objective enhanced interval optimization problem
In this paper, we consider a multiple objective optimization problem whose decision variables and parameters are intervals. Existence of solution of this problem is studied by parameterizing the intervals. A methodology is developed to find the tω-efficient solution of the problem. The original problem is transformed to an equivalent deterministic problem and the relation between solutions of both is established. Finally, the methodology is verified in numerical examples.
Journal Article
Multi-tracker Optimization Algorithm: A General Algorithm for Solving Engineering Optimization Problems
In this paper, a new computational population-based optimization algorithm, which is designed based on the advantages and disadvantages of other evolutionary optimization algorithms introduced so far, is proposed. This new algorithm, which is named as “multi-tracker optimization algorithm,” due to a multi-level structure of trackers within it, has some unique features, such as increasing the accuracy of the optimal point and continuous local search after convergence in order to escape from local minima simultaneously. Another important advantage of this algorithm is optimizing time-varying dynamical problems and tracking the optimal point. These characteristics make the algorithm very efficient for optimization problems, especially in the field of engineering. For a thorough investigation and comparison of this algorithm with other efficient optimization algorithms, different optimization problems such as static, dynamic, unconstrained and constrained, each of which has different challenges, are considered. The results of applying this algorithm on the abovementioned basic problems show the superiority of this algorithm over other efficient evolutionary algorithms.
Journal Article
Moboa: a proposal for multiple objective bean optimization algorithm
The primary objective of multi-objective evolutionary algorithms (MOEAs) is to find a set of evenly distributed nondominated solutions that approximate the Pareto front (PF) of a multi-objective optimization problem (MOP) or a many-objective optimization problem (MaOP). This implies that the approximated solution set obtained by MOEAs should be as close to PF as possible while remaining diverse, adhering to criteria of convergence and diversity. However, existing MOEAs exhibit an imbalance between achieving convergence and maintaining diversity in the objective space. As far as the diversity criterion is concerned, it is still a challenge to achieve an evenly distributed approximation set with different sizes for a problem with a complicated PF shape. Furthermore, Pareto dominance has its own weaknesses as the selection criterion in evolutionary multiobjective optimization. Algorithms based on Pareto criterion (PC) can suffer from problems such as slow convergence to the optimal front and inferior performance on problems with many objectives. To effectively address these challenges, we propose a multi-objective bean optimization algorithm (MOBOA). Given that the selection of parent species, representing global optimal solutions, directly influences the convergence and diversity of the algorithm, MOBOA incorporates a preference order equilibrium parent species selection strategy (POEPSS). By extending the Pareto criterion with the preference order optimization criterion, the algorithm effectively enhances parent species selection pressure across multiple objectives. To balance convergence and diversity, MOBOA proposes a multi-population global search strategy explicitly maintaining an external archive during the search process. Leveraging the inherent multi-population advantages of bean optimization algorithm (BOA), the algorithm facilitates information sharing among the main population, auxiliary populations, and historical archive solution sets. Additionally, a diversity enhancement strategy is employed in the environmental selection stage, introducing the environmental selection strategy of the SPEA2 algorithm to generate a set of evenly distributed nondominated solutions. Experimental results on a series of widely used MOPs and MaOPs demonstrate that the proposed algorithm exhibits higher effectiveness and competitiveness compared to state-of-the-art algorithms.
Journal Article
A survey on evolutionary computation for complex continuous optimization
Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.
Journal Article