Multi-objective optimization (or programming), also known as multi-criteria or multi-attribute optimization, is the process of simultaneously optimizing two or more conflicting objectives subject to certain constraints.
Multiobjective optimization problems can be found in various fields: product and process design, finance, aircraft design, the oil and gas industry, automobile design, or wherever optimal decisions need to be taken in the presence of trade-offs between two conflicting objectives. Maximizing profit and minimizing the cost of a product; maximizing performance and minimizing fuel consumption of a vehicle; and minimizing weight while maximizing the strength of a particular component are examples of multi-objective optimization problems.
If a multiobjective problem is well formed, there should not be a single solution that simultaneously minimizes each objective to its fullest. In each case we are looking for a solution for which each objective has been optimized to the extent that if we try to optimize it any further, then the other objective(s) will suffer as a result. Finding such a solution, and quantifying how much better this solution is compared to other such solutions (there will generally be many) is the goal when setting up and solving a multiobjective optimization problem.
Problems with multiple objectives arise in a natural fashion in most disciplines and their solution has been a challenge to researchers for a long time. Despite the considerable variety of techniques developed in Operations Research (OR) to tackle these problems, the complexities of their solution calls for alternative approaches. In multiobjective optimization (MOP), the notion of optimality is not at all obvious. If we refuse beforehand to interrelate the relative values of the different criteria – then we must come up with a different notion of optimality, one that respects the integrity of each of our separate criteria. The concept of Pareto Optimality helps us to do this in a rational way.
To illustrate the problem, suppose a widget manufacturer wishes to minimize both on-the-job accidents and widget cost. So in this case, the manufacturer identifies 7 possible ways of running the plant (scenarios A, B, C, D, E, F and G) as indicated in above Figure. Here we can say that A, B and C seem to like good possible choices: even though none of these three points is best along both dimensions, we can see that there are trade-offs from one of these three scenarios to another; there is gain along one dimension and loss along others. In optimization terminology, we say these three points are non-dominated because there are no points better than these on all criteria. Other points, D, E, F and G are called as dominated points. Our objective is to find these non-dominated points.
