This research article presents the Multi-Objective Hippopotamus Optimizer (MOHO), a unique approach that excels in tackling complex structural optimization problems. The Hippopotamus Optimizer (HO) is a novel approach in meta-heuristic methodology that draws inspiration from the natural behaviour of hippos. The HO is built upon a trinary-phase model that incorporates mathematical representations of crucial aspects of Hippo’s behaviour, including their movements in aquatic environments, defense mechanisms against predators, and avoidance strategies. This conceptual framework forms the basis for developing the multi-objective (MO) variant MOHO, which was applied to optimize five well-known truss structures. Balancing safety precautions and size constraints concerning stresses on individual sections and constituent parts, these problems also involved competing objectives, such as reducing the weight of the structure and the maximum nodal displacement. The findings of six popular optimization methods were used to compare the results. Four industry-standard performance measures were used for this comparison and qualitative examination of the finest Pareto-front plots generated by each algorithm. The average values obtained by the Friedman rank test and comparison analysis unequivocally showed that MOHO outperformed other methods in resolving significant structure optimization problems quickly. In addition to finding and preserving more Pareto-optimal sets, the recommended algorithm produced excellent convergence and variance in the objective and decision fields. MOHO demonstrated its potential for navigating competing objectives through diversity analysis. Additionally, the swarm plots effectively visualize MOHO’s solution distribution of MOHO across iterations, highlighting its superior convergence behaviour. Consequently, MOHO exhibits promise as a valuable method for tackling complex multi-objective structure optimization issues.

This paper presents a new multi-objective optimization algorithm called the Multi-Objective Crested Porcupines Optimization (MOCPO) Algorithm, which uses an elitist, non-dominated sorting and crowding distance mechanism. MOCPO is motivated by the predator-prey behavior of crested porcupines and is based on the newly proposed Crested Porcupines Algorithm. MOCPO is formulated to efficiently manage conflicting objectives in multi-objective optimization problems. Through the use of non-dominated sorting and crowding distance mechanisms, MOCPO promotes solution diversity and convergence towards the Pareto front. MOCPO employs a new Information Feedback Mechanism (IFM) and an enhanced solution updating strategy to enhance convergence and diversity control. The performance of MOCPO is tested on a variety of benchmark problems, including the ZDT and DTLZ series, as well as real-world engineering design problems from the RWMOP suite. These test problems represent a variety of optimization problems with linear, nonlinear, continuous, and discrete nature. MOCPO performance is compared with state-of-the-art algorithms like the Multi-Objective Gradient Based Optimizer (MOGBO), Preference inspired Differential Evolution (Pre-DEMO), Multi-Objective Exponential Distribution Algorithm (MOEDO), Pivot solution based Multi-Objective Evolutionary Algorithm (Pi-MOEA), and Clustering aided Grid based Multi-Objective Evolutionary Algorithm (ClGrMOEA). Qualitative and quantitative analyses using standard performance metrics show the effectiveness of the algorithm. Experimental results verify that MOCPO provides substantial improvements in convergence and solution diversity, making it a viable choice for solving complex multi-objective optimization problems.

The study suggests a better multi-objective optimization method called 2-Archive Multi-Objective Cuckoo Search (MOCS2arc). It is then used to improve eight classical truss structures and six ZDT test functions. The optimization aims to minimize both mass and compliance simultaneously. MOCS2arc is an advanced version of the traditional Multi-Objective Cuckoo Search (MOCS) algorithm, enhanced through a dual archive strategy that significantly improves solution diversity and optimization performance. To evaluate the effectiveness of MOCS2arc, we conducted extensive comparisons with several established multi-objective optimization algorithms: MOSCA, MODA, MOWHO, MOMFO, MOMPA, NSGA-II, DEMO, and MOCS. Such a comparison has been made with various performance metrics to compare and benchmark the efficacy of the proposed algorithm. These metrics comprehensively assess the algorithms' abilities to generate diverse and optimal solutions. The statistical results demonstrate the superior performance of MOCS2arc, evidenced by enhanced diversity and optimal solutions. Additionally, Friedman's test & Wilcoxon’s test corroborate the finding that MOCS2arc consistently delivers superior optimization results compared to others. The results show that MOCS2arc is a highly effective improved algorithm for multi-objective truss structure optimization, offering significant and promising improvements over existing methods.

Complex many-objective optimization problems (MaOPs) generate multiple challenges for obtaining convergence alongside diversity within extensive multi-dimensional solution areas. Optimization approaches currently face limitations when trying to balance exploration and exploitation especially when resources become limited. MaOCO represents the Many-Objective Cheetah Optimization Algorithm which draws its concepts from the hunting behavior of cheetahs. MaOCO includes adaptive search functions that use attack and sit-and-wait approaches to optimize exploration and exploitation capabilities. MaOCO produces hypervolume (HV) results that exceed NSGA-III and MaOMVO by 50% while also delivering inverse generational distance (IGD) results which reach 40% better than both competing methods. The algorithm demonstrates superior efficiency in solving complex MaOPs, because it requires lower computational costs by 15%. MaOCO successfully traverses Pareto-optimal fronts according to theoretical evaluations, and its modular structure allows for both scale-up and hybridization features. The implemented applications of this approach include optimizing energy systems along with designing structures for engineering projects. Future researchers plan to integrate MaOCO with additional metaheuristic techniques to improve its performance when dealing with dynamic and irregular Pareto front problems.