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Incorporating Directional Information within a Differential Evolution Algorithm for Multiobjective Optimization

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First Author :
Antony Iorio, RMIT University, School of Computer Science and IT, 
GPO Box 2476v Melbourne, 3001 Victoria, Australia.
iantony@cs.rmit.edu.au, +61 402758676.
Second Author :
Xiaodong Li, RMIT University, School of Computer Science and IT, 
GPO Box 2476v Melbourne, 3001 Victoria, Australia.
 xiaodong@cs.rmit.edu.au, +61 3 9925 9585 

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Antony Iorio

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The field of Differential Evolution (DE) has demonstrated important advantages in single objective optimization. To date, no previous research has explored how the unique characteristics of DE can be applied to multi-objective optimization. This paper explains and demonstrates how DE can provide advantages in multi-objective optimization using directional information. We present three novel DE variants for multi-objective optimization, and a report of their performance on four multi-objective problems with different characteristics. The DE variants are compared with the NSGA-II (Non-dominated Sorting Genetic Algorithm). The results suggest that directional information yields improvements in convergence speed and spread of solutions.

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B, F

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Typically decision makers are required to choose weights to guide a search towards a single desired solution. EMO algorithms can discover a set of solutions from which a decision maker can select the most ideal solution best on their domain knowledge. EMO algorithms outperform human beings with respect to their ability to find non-dominated solution sets in complex problem domains with many parameters. 
Furthermore, the development of non-dominated sorting and crowding distances were an important development to the field of EMO (Evolutionary Multi-objective Optimization). The use of directional information in a Differential EMO algorithm dramatically improves the performance of EMO, with respect to the diversity of the non-dominated solutions, and the convergence speed of the non-dominated solutions.  
Referring to the eight criteria for establishing that an automatically created result is competitive with a human-produced result, the optimization of problems with parameter interactions using directional information satisfies the following  three of the eight criteria:

B - The result is equal to or better than a result that was accepted as a new scientific result at the time when it was published in a peer-reviewed scientific journal.

F - The result is equal to or better than a result that was considered an achievement in its field at the time it was first discovered.

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Iorio, A. and Li, X. (2006), Incorporating Directional Information within a Differential Evolution Algorithm for Multiobjective Optimization, In GECCO 2006: Proceedings of the Genetic and Evolutionary Computation Conference, July 2006. To appear.

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Any prize money, if any, is to be divided equally among the co-authors.

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This entry should be considered for the following reasons:
Most real world problems have parameter interactions, involve multiple possibly conflicting objectives, and have expensive evaluation functions that may take a long time to evaluate. It is impossible for a human being to be competitive with EMO algorithms in general. Furthermore, the proposed approach using Differential Evolution and directional information addresses these issues associated with an EMO algorithm; it can solve multi-objective problems with parameter interactions, and can do so more efficiently by minimizing the number of evaluations required by the algorithm.