Many-objective ant lion optimizer (MaOALO): A new many-objective optimizer with its engineering applications.

Many-objective optimization (MaO) is an important aspect of engineering scenarios. In many-objective optimization algorithms (MaOAs), a key challenge is to strike a balance between diversity and convergence. MaOAs employs various tactics to either enhance selection pressure for better convergence and/or implements additional measures for sustaining diversity. With increase in number of objectives, the process becomes more complex, mainly due to challenges in achieving convergence during population selection. This paper introduces a novel Many-Objective Ant Lion Optimizer (MaOALO), featuring the widely-popular ant lion optimizer algorithm. This method utilizes reference point, niche preserve and information feedback mechanism (IFM), to enhance the convergence and diversity of the population. Extensive experimental tests on five real-world (RWMaOP1- RWMaOP5) optimization problems and standard problem classes, including MaF1-MaF15 (for 5, 9 and 15 objectives), DTLZ1-DTLZ7 (for 8 objectives) has been carried out. It is shown that MaOALO is superior compared to ARMOEA, NSGA-III, MaOTLBO, RVEA, MaOABC-TA, DSAE, RL-RVEA and MaOEA-IH algorithms in terms of GD, IGD, SP, SD, HV and RT metrics. The MaOALO source code is available at: https://github.com/kanak02/MaOALO.

Multi-objective liver cancer algorithm: A novel algorithm for solving engineering design problems.

This research introduces the Multi-Objective Liver Cancer Algorithm (MOLCA), a novel approach inspired by the growth and proliferation patterns of liver tumors. MOLCA emulates the evolutionary tendencies of liver tumors, leveraging their expansion dynamics as a model for solving multi-objective optimization problems in engineering design. The algorithm uniquely combines genetic operators with the Random Opposition-Based Learning (ROBL) strategy, optimizing both local and global search capabilities. Further enhancement is achieved through the integration of elitist non-dominated sorting (NDS), information feedback mechanism (IFM) and Crowding Distance (CD) selection method, which collectively aim to efficiently identify the Pareto optimal front. The performance of MOLCA is rigorously assessed using a comprehensive set of standard multi-objective test benchmarks, including ZDT, DTLZ and various Constraint (CONSTR, TNK, SRN, BNH, OSY and KITA) and real-world engineering design problems like Brushless DC wheel motor, Safety isolating transformer, Helical spring, Two-bar truss and Welded beam. Its efficacy is benchmarked against prominent algorithms such as the non-dominated sorting grey wolf optimizer (NSGWO), multiobjective multi-verse optimization (MOMVO), non-dominated sorting genetic algorithm (NSGA-II), decomposition-based multiobjective evolutionary algorithm (MOEA/D) and multiobjective marine predator algorithm (MOMPA). Quantitative analysis is conducted using GD, IGD, SP, SD, HV and RT metrics to represent convergence and distribution, while qualitative aspects are presented through graphical representations of the Pareto fronts. The MOLCA source code is available at: https://github.com/kanak02/MOLCA.

Optimizing brushless direct current motor design: An application of the multi-objective generalized normal distribution optimization.

In this study, we tackle the challenge of optimizing the design of a Brushless Direct Current (BLDC) motor. Utilizing an established analytical model, we introduced the Multi-Objective Generalized Normal Distribution Optimization (MOGNDO) method, a biomimetic approach based on Pareto optimality, dominance, and external archiving. We initially tested MOGNDO on standard multi-objective benchmark functions, where it showed strong performance. When applied to the BLDC motor design with the objectives of either maximizing operational efficiency or minimizing motor mass, the MOGNDO algorithm consistently outperformed other techniques like Ant Lion Optimizer (ALO), Ion Motion Optimization (IMO), and Sine Cosine Algorithm (SCA). Specifically, MOGNDO yielded the most optimal values across efficiency and mass metrics, providing practical solutions for real-world BLDC motor design. The MOGNDO source code is available at: https://github.com/kanak02/MOGNDO.

Multi-objective exponential distribution optimizer (MOEDO): a novel math-inspired multi-objective algorithm for global optimization and real-world engineering design problems.

The exponential distribution optimizer (EDO) represents a heuristic approach, capitalizing on exponential distribution theory to identify global solutions for complex optimization challenges. This study extends the EDO's applicability by introducing its multi-objective version, the multi-objective EDO (MOEDO), enhanced with elite non-dominated sorting and crowding distance mechanisms. An information feedback mechanism (IFM) is integrated into MOEDO, aiming to balance exploration and exploitation, thus improving convergence and mitigating the stagnation in local optima, a notable limitation in traditional approaches. Our research demonstrates MOEDO's superiority over renowned algorithms such as MOMPA, NSGA-II, MOAOA, MOEA/D and MOGNDO. This is evident in 72.58% of test scenarios, utilizing performance metrics like GD, IGD, HV, SP, SD and RT across benchmark test collections (DTLZ, ZDT and various constraint problems) and five real-world engineering design challenges. The Wilcoxon Rank Sum Test (WRST) further confirms MOEDO as a competitive multi-objective optimization algorithm, particularly in scenarios where existing methods struggle with balancing diversity and convergence efficiency. MOEDO's robust performance, even in complex real-world applications, underscores its potential as an innovative solution in the optimization domain. The MOEDO source code is available at: https://github.com/kanak02/MOEDO .