Optimization algorithms play a crucial role in solving complex challenges across various fields, including engineering, finance, and data science. This study introduces a novel hybrid optimization algorithm, the Hybrid Crayfish Optimization Algorithm with Differential Evolution (HCOADE), which addresses the limitations of premature convergence and inadequate exploitation in the traditional Crayfish Optimization Algorithm (COA). By integrating COA with Differential Evolution (DE) strategies, HCOADE leverages DE’s mutation and crossover mechanisms to enhance global optimization performance. The COA, inspired by the foraging and social behaviors of crayfish, provides a flexible framework for exploring the solution space, while DE’s robust strategies effectively exploit this space. To evaluate HCOADE’s performance, extensive experiments are conducted using 34 benchmark functions from CEC 2014 and CEC 2017, as well as six engineering design problems. The results are compared with ten leading optimization algorithms, including classical COA, Particle Swarm Optimization (PSO), Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), Moth-flame Optimization (MFO), Salp Swarm Algorithm (SSA), Reptile Search Algorithm (RSA), Sine Cosine Algorithm (SCA), Constriction Coefficient-Based Particle Swarm Optimization Gravitational Search Algorithm (CPSOGSA), and Biogeography-based Optimization (BBO). The average rankings and results from the Wilcoxon Rank Sum Test provide a comprehensive comparison of HCOADE’s performance, clearly demonstrating its superiority. Furthermore, HCOADE’s performance is assessed on the CEC 2020 and CEC 2022 test suites, further confirming its effectiveness. A comparative analysis against notable winners from the CEC competitions, including LSHADEcnEpSin, LSHADESPACMA, and CMA-ES, using the CEC-2017 test suite, revealed superior results for HCOADE. This study underscores the advantages of integrating DE strategies with COA and offers valuable insights for addressing complex global optimization problems.

This paper proposes a new concept on transportation problem in which, we maximize the profit and minimize the transportation time while transporting an amount of quantity from a source to the destination. Here, we design two transportation models, in both the models; we maximize the profit and minimize the time of transportation. Here model-I having the unit purchase cost, unit selling price, unit transportation cost and transportation time as trapezoidal interval type-2 fuzzy number, while in model-II all the parameters are trapezoidal interval type-2 fuzzy number. To reduce these model-I and model-II into crisp equivalent, we use the expected value of a trapezoidal interval type-2 fuzzy number. Then the crisp equivalent problems are solved by employing the Interactive fuzzy satisficing method and LINGO 13.0 software to get the optimal solution. A numerical example is provided to demonstrate the models.

The occurrence of a sudden, calamitous, and unfortunate event requires a quick response that can reduce damage and save lives, fulfilling the basic humanitarian needs of the affected population. National or international organizations and agencies may be initiated to provide assistance but local agencies need to act as soon as possible, because they are familiar with the geographical location as well as the local conditions of the affected areas. Effective coordination of disaster assistance is often crucial, particularly when resources are limited in the local agencies and the demands are more. In such conditions, it becomes a challenging job for the agencies to distribute resources so that the resources are optimally used. This article is initiated to address the challenging fact by introducing the concept of priority measure for demands. In this regard, ranking of the affected areas based on resource requirement for a disaster scenario is evaluated through a multicriteria decision-making process. A formula is developed to find the numerical value of priority factor collecting the responses of requirement of relief materials using information crowdsourcing. To this contingent, a three-echelon emergency solid transportation problem is formulated, in which the demand with the most priority is fulfilled by the local agencies in echelon-I, and the remaining demand is fulfilled by the other national or international agencies in echelon-II along with a restoration of local agencies in echelon-III. A numerical example is presented for the sake of model performance and to test the convergence using LINGO and CPLEX optimization solvers. The model is also designed using a genetic algorithm to obtain the optimal solution. Moreover, a brief analysis of the model is presented by considering 11 different numerical instances to enhance the efficacy of the model in real-life applications.

This paper presents a novel hybrid metaheuristic, the Hybrid Coati Optimization Algorithm with Differential Evolution (HCOADE), developed to address complex global optimization tasks and constrained engineering design problems. HCOADE integrates the exploration-driven behaviour of the Coati Optimization Algorithm (COA)-inspired by the social foraging and predation strategies of coatis-with the powerful mutation and crossover mechanisms of Differential Evolution (DE), thereby achieving a balanced and adaptive search process. The hybridization enhances global exploration and local exploitation, enabling the algorithm to efficiently navigate diverse and challenging optimization landscapes. To rigorously evaluate its performance, HCOADE is tested on benchmark suites from CEC 2014, 2017, 2020, and 2022, which encompass unimodal, multimodal, hybrid, and composition functions. It is also applied to real-world constrained engineering problems, such as pressure vessel design, cantilever beam optimization, and reinforced concrete beam design. Comparative experiments against state-of-the-art algorithms—including COA, DE, RSA, PSO, SSA, BBO, QIO, DMOA, and others—demonstrate that HCOADE consistently delivers superior solution quality, faster convergence, and higher robustness. Quantitative results show that HCOADE achieved the 1st place average rank across all four benchmark suites. It obtained top performance on 80% of the functions in CEC 2014, 66.7% in CEC 2017, 70% in CEC 2020, and 66.7% in CEC 2022. Furthermore, HCOADE outperformed or matched CEC competition-winning algorithms such as LSHADE-cnEpSin, LSHADE-SPACMA, and CMA-ES on numerous challenging functions of CEC 2017. Statistical analyses, including Wilcoxon Rank Sum Tests and ranking evaluations, confirm the significance and reliability of HCOADE’s performance. Furthermore, convergence behaviour, measurement of exploration and exploitation, and sensitivity analysis highlight the algorithm’s adaptability and stability across varied problem domains. This study contributes a computationally efficient and generalizable hybrid optimization framework, offering a promising solution for theoretical benchmarks and real-world engineering applications.