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Research in the field of multi-objective optimisation problem (MOP) has garnered ample interest in the last two decades. Majority of methods developed for solving the problem belong to the class of evolutionary algorithms (EA) which are population-based evolution search strategies involving exploration and exploitation in general. Multi-criteria decision making (MCDM) is another aspect of MOP which involves finding methods to help a decision maker (DM) in making most optimal decisions in a conflicting scenario. In this paper, we present a brief review of the methods and techniques developed in the last 15 years which try to solve the MOP and MCDM problems. The strengths and weaknesses of methods have been discussed to present a holistic view. This paper covers challenges associated with MOEAs, different solution approaches such as Pareto-based methods and non-Pareto methods, indicator-based …