This paper introduces the multi-objective heterogeneous comprehensive learning symbiotic organism search algorithm (MOHCLSOS), designed to overcome the limitations of the multi-objective symbiotic organism search algorithm (MOSOS) when dealing with complex optimization problems. These limitations include improper initial population distribution, lack of diversity, premature convergence, and ineffective archiving of non-dominated solutions. MOHCLSOS enhances the optimization process through several key innovations. Initially, it employs opposition-based learning combined with fast non-dominated sorting to partition the initial population into exploration and exploitation subpopulations based on fitness values. This strategy helps in maintaining a balance between global exploration and local exploitation. Furthermore, MOHCLSOS integrates the heterogeneous comprehensive learning symbiotic organism search algorithm (HCLSOS) learning operators, and introduces a higher dominance level archiving strategy. This strategy expands the range of high quality solutions to be stored in the external archive. Meanwhile, the archive management process utilizes dominance-based sorting, genetic operators and an adaptive crowding distance computation that account for both objective and decision spaces to maintain a diverse and high-quality set of solutions. The efficacy of MOHCLSOS was evaluated using 22 benchmark functions from the ZDT, DTLZ, and UF test suites, as well as 5 real-world problems. Comparative analysis against 12 state-of-the-art algorithms revealed that MOHCLSOS consistently delivers competitive or significantly superior performance to both classical and advanced methods in handling multi-objective optimization problems (MOPs). Moreover, we implemented a binary version of our proposed method called MOHCLSOS-Prune, to solve the convolutional neural network (CNN) filter pruning problem, formulated as a two-objective optimization problem. Experimental results demonstrate that MOHCLSOS-Prune is both effective and competitive in practical applications, further highlighting the versatility and robustness of MOHCLSOS.