Multi-objective optimization: Difference between revisions

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'''Multi-objective optimization''' (or programming),<ref>{{cite book|last = Steuer|first = R.E.|title = Multiple Criteria Optimization: Theory, Computations, and Application|publisher = John Wiley & Sons, Inc|date = 1986|___location = New York|isbn = 047188846X}}</ref><ref>{{cite book|last = Sawaragi|first = Y.|coauthors = Nakayama, H. and Tanino, T.|title = Theory of Multiobjective Optimization (vol. 176 of Mathematics in Science and Engineering)|publisher = Academic Press Inc|___location = Orlando, FL|date = 1985|isbn = 0126203709}}</ref> also known as '''multi-criteria''' or '''multi-attribute''' optimization, is the process of simultaneously optimizing two or more conflicting objectives subject to certain constraints.

'''Multi-objective optimization''' (or programming)<ref>R. E. Steuer. Multiple Criteria Optimization, Theory Computations and

Applications. John Wiley & Sons, Inc., New York, 1986.</ref> <ref> Y. Sawaragi, H. Nakayama, and T. Tanino. Theory of Multiobjective Optimization, vol. 176 of Mathematics in Science and Engineering, Academic Press Inc., Orlando, FL, 1985. </ref> also known as multi-criteria optimization, 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, oil and gas industry, automobile design, or wherever optimal decisions need to be taken in the presence of trade-off between two conflicting objectives. For example, maximizing profit and minimizing cost of a product; maximizing performance and mimimzing fuel consumption of a vehicle; minimizing weight and maximizing the strength of a particular component, etc. If a multiobjective problem is well formed, there should not be a single solution that simultaneously minimizes each objective to its fullest. In each of these examples, we are looking for a solution for which we know that 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 of setting up and solving a multiobjective optimization problem.

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 mimimizing 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.

== Introduction ==