Multiobjective Optimisation - Falmouth-Games-Academy/comp350-research-journal GitHub Wiki

Multiobjective optimisation is an area of multiple criteria decision making, that is concerned with mathematical optimisation problems involving more than one function that can be solved simultaneously 1(http://www.mcda-school18.tuc.gr/Slides/Miettinen2018.pdf). This type of optimisation can arise in many different fields, such as engineering, economics and logistics, when there are two conflicting objectives and an optimal decision needs to be decided in the presence of trade-offs. For example, developing a new component might involve minimizing weight but maximising strength 2(https://www.researchgate.net/profile/Jasbir_Arora4/publication/225153273_Survey_of_Multi-Objective_Optimization_Methods_for_Engineering/links/5462358d0cf2c0c6aec1ab30/Survey-of-Multi-Objective-Optimization-Methods-for-Engineering.pdf).

Generally, there does not involve a single solution that will optimise each problem at the same time. Instead, there exists a set of Pareto optimal solutions, which is a state of allocation of resources from which it is impossible to reallocate resources to one criterion without making another criterion worse off 3(https://thereaderwiki.com/en/Pareto_optimum). A solution is called nondominated, Pareto optimal, Pareto efficient or non-inferior, that is if none of the objectives can be improved in value without degrading another value 4(http://www.cs.tufts.edu/comp/150GA/handouts/zitzler04.pdf). For example, when employing Object pooling in your program you may reduce the number of CPU cycles when you destroy and spawn an object but the trade off is it takes up more memory.

In mathematical terms, a multiobjective optimisation can be formulated as:

References

[1] Miettinen, Kaisa. Nonlinear multiobjective optimization. Vol. 12. Springer Science & Business Media, 2012.

[2] Marler, R. Timothy, and Jasbir S. Arora. "Survey of multi-objective optimization methods for engineering." Structural and multidisciplinary optimization 26.6 (2004): 369-395.

[3] Proximedia. "Pareto Front", www.cenaero.be. Retrieved 2018-10-08

[4] Zitzler, Eckart, Marco Laumanns, and Stefan Bleuler. "A tutorial on evolutionary multiobjective optimization." Metaheuristics for multiobjective optimisation. Springer, Berlin, Heidelberg, 2004. 3-37.