In recent years, multi-objective optimization techniques have gained popularity as a powerful approach to the solution of complex engineering problems that involve multiple competing objectives. This popularity can be attributed to the fact that multi-objective optimization techniques can solve complex engineering problems. Engineers are able to think about many goals at the same time using this method, which enables them to discover the best solution that fits all of their requirements. Yet, there are obstacles connected with setting objectives, dealing with high computational costs, comprehending complicated Pareto fronts, coping with uncertainty, and having limited accessibility to data from the real world. The purpose of this paper is to present a literature review of multi-objective optimization techniques for the solution of complex engineering problems. The review covers a variety of techniques that are available for multi-objective optimization as well as their applications in a variety of engineering fields. It also draws attention to the difficulties involved with their application and the necessity of giving serious consideration to these difficulties while attempting to solve actual engineering problems that occur in the real world. The research comes to the conclusion that multi-objective optimization is an effective method that can assist engineers in solving complicated engineering issues by concurrently taking into consideration numerous competing objectives.