Evolutionary multiobjective optimization

Many real-world search and optimization problems are naturally posed as non-linear programming problems having multiple conflicting objectives. Due to lack of suitable solution techniques, such problems are usually artificially converted into a single-objective problem and solved. The difficulty arises because multi-objective optimization problems give rise to a set of Pareto-optimal solutions, each corresponding to a certain trade-off among the objectives. It then becomes important to find not just one Pareto-optimal solution but as many of them as possible. Classical methods are found to be not efficient because they require repetitive applications to find multiple Pareto-optimal solutions and in some occasions repetitive applications do not guarantee finding distinct Pareto-optimal solutions. The population approach of evolutionary algorithms (EAs) allows an efficient way to find multiple Pareto-optimal solutions simultaneously in a single simulation run. In this tutorial, we shall contrast the differences in philosophies between classical and evolutionary multi-objective methodologies and provide adequate fundamentals needed to understand and use both methodologies in practice. Particularly, major state-of-the-art evolutionary multi-objective optimization (EMO) methodologies will be presented and various related issues such as performance assessment and preference articulation will be discussed. Thereafter, three main application areas of EMO will be discussed with adequate case studies from practice -- (i) applications showing better decision-making abilities through EMO, (ii) applications exploiting the multitude of trade-off solutions of EMO in extracting useful information in a problem, and (iii) applications showing better problem-solving abilities in various other tasks (such as, reducing bloating, solving single-objective constraint handling, and others). Clearly, EAs have a niche in solving multi-objective optimization problems compared to classical methods. This is why EMO methodologies are getting a growing attention in the recent past. Since this is a comparatively new field of research, in this tutorial, a number of future challenges in the research and application of multi-objective optimization will also be discussed. This tutorial is aimed for both novices and users of EMO. Those without any knowledge in EMO will have adequate ideas of the procedures and their importance in computing and problem-solving tasks. Those who have been practicing EMO will also have enough ideas and materials for future research, know state-of-the-art results and techniques, and make a comparative evaluation of their research.