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# Genetic local search for multi-objective combinatorial optimization

European Journal of Operational Research, no. 1 (2002): 50-71

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Abstract

The paper presents a new genetic local search (GLS) algorithm for multi-objective combinatorial optimization (MOCO). The goal of the algorithm is to generate in a short time a set of approximately efficient solutions that will allow the decision maker to choose a good compromise solution. In each iteration, the algorithm draws at random a...More

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Introduction

- Combinatorial optimization ®nds applications in many areas, e.g. in production scheduling, project scheduling, sta scheduling, time-tabling, production facilities design, vehicle routing, telecommunication routing, investment planning, location and many others.

Solutions of real-life combinatorial optimization problems usually have to be evaluated taking into account dierent points of view corresponding to multiple, often conicting objectives. *

Tel.: +48-61-66-52-371; fax: +48-61-877-1525.

www-idss.cs.put.poznan.pl/jaszkiewicz

The goal of multi-objective optimization is to

®nd the single solution giving the best compromise between multiple objectives. - Since usually there is no single solution that optimizes simultaneously all the objectives, selection of the best compromise solution requires taking into account preferences of the DM.
- Many multi-objective optimization methods reduce the search space to the set of ef®cient solutions
- Note that this approach is not valid if the DM searches for a sample of best solutions as the second best and other good solutions do not need to be ecient under the same assumptions about the DM's preferences

Highlights

- Combinatorial optimization ®nds applications in many areas, e.g. in production scheduling, project scheduling, sta scheduling, time-tabling, production facilities design, vehicle routing, telecommunication routing, investment planning, location and many others.

Solutions of real-life combinatorial optimization problems usually have to be evaluated taking into account dierent points of view corresponding to multiple, often conicting objectives. *

Tel.: +48-61-66-52-371; fax: +48-61-877-1525.

www-idss.cs.put.poznan.pl/jaszkiewicz

The goal of multi-objective optimization is to

®nd the single solution giving the best compromise between multiple objectives - Since usually there is no single solution that optimizes simultaneously all the objectives, selection of the best compromise solution requires taking into account preferences of the DM
- Many multi-objective optimization methods reduce the search space to the set of ef®cient solutions. Note that this approach is not valid if the DM searches for a sample of best solutions as the second best and other good solutions do not need to be ecient under the same assumptions about the DM's preferences
- The elite size in IM multi-objective genetic local search (MOGLS) was set equal to 10% of the population size

Results

- The elite size in IM MOGLS was set equal to 10% of the population size.

Conclusion

**Conclusions and directions for further research**

A new MOGLS algorithm has been described.

Summary

## Introduction:

Combinatorial optimization ®nds applications in many areas, e.g. in production scheduling, project scheduling, sta scheduling, time-tabling, production facilities design, vehicle routing, telecommunication routing, investment planning, location and many others.

Solutions of real-life combinatorial optimization problems usually have to be evaluated taking into account dierent points of view corresponding to multiple, often conicting objectives. *

Tel.: +48-61-66-52-371; fax: +48-61-877-1525.

www-idss.cs.put.poznan.pl/jaszkiewicz

The goal of multi-objective optimization is to

®nd the single solution giving the best compromise between multiple objectives.- Since usually there is no single solution that optimizes simultaneously all the objectives, selection of the best compromise solution requires taking into account preferences of the DM.
- Many multi-objective optimization methods reduce the search space to the set of ef®cient solutions
- Note that this approach is not valid if the DM searches for a sample of best solutions as the second best and other good solutions do not need to be ecient under the same assumptions about the DM's preferences
## Results:

The elite size in IM MOGLS was set equal to 10% of the population size.## Conclusion:

**Conclusions and directions for further research**

A new MOGLS algorithm has been described.

- Table1: Numbers of starting solutions for multi-objective TSP instancesa

Funding

- I would like to thank my colleagues Michael Hansen and Pedro Borges for fruitful discussions. This work has been supported by KBN grant No

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