By Estefania Yap, RMIT University
As we grow up we are often told to make the most of what we have, but then comes the question of what and how? This is where multiple objective programming comes in.
Multi-objective programming is a decision making tool that aids a decision maker in finding the best solution to a problem. Real life problems tend to have more than one objective that needs to be optimised and most of the time these objectives will conflict with each other. E.g. School takes up a lot of our time and this often results in less time for our hobbies and social life. Ideally, every student wants to sit at home watching T.V. without worrying about homework, but then how will we be prepared for tests at school? If you, the decision maker, wanted to maximise your two objectives of happiness and good school results but have time constraints i.e. hours left in the day, how would you assign your free time to get the most out of both your social and school life? Since there is no single solution that can lead to the best outcome for all objectives, we must make trade-offs whereby increasing the value of one objective will lead to decreasing the value of some other objectives. These trade-offs are the problems that are addressed in multi-objective programming. Anything that requires a trade-off leads to multi-objective programming, and this is often seen in fields such as finance, engineering and manufacturing.
There are three types of multi-objective problems. These problems are known as the multi-objective linear (MOLP), integer (MOIP) and mixed integer (MOMIP) problems. MOLP problems deal with objectives that are continuous, e.g. minimising the amount of time it takes you to wash the dishes. MOIP problems have objectives which must be integers, e.g. maximising the amount of friends you have. It is not physically possible to have half a friend! MOMIP problems are the most difficult and have yet to be solved in a general setting because they can have any mix of continuous and integer variables.
My project reviews some of the more recently available methods that are used in solving these three types of problems and aims to contribute towards the ongoing research in multi-objective programming so we can better solve some of life’s problems.
Estefania Yap was one of the recipients of a 2013/14 AMSI Vacation Research Scholarship.