On investigation of interdependence between sub-problems of the Travelling Thief Problem
Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematica...
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| Autor*in: |
Mei, Yi [verfasserIn] Li, Xiaodong [verfasserIn] Yao, Xin [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Soft Computing - Springer-Verlag, 2003, 20(2014), 1 vom: 17. Okt., Seite 157-172 |
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| Übergeordnetes Werk: |
volume:20 ; year:2014 ; number:1 ; day:17 ; month:10 ; pages:157-172 |
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| DOI / URN: |
10.1007/s00500-014-1487-2 |
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| 520 | |a Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP. | ||
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10.1007/s00500-014-1487-2 doi (DE-627)SPR006487750 (SPR)s00500-014-1487-2-e DE-627 ger DE-627 rakwb eng Mei, Yi verfasserin aut On investigation of interdependence between sub-problems of the Travelling Thief Problem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP. Combinatorial optimization (dpeaa)DE-He213 Evolutionary computation (dpeaa)DE-He213 Cooperative Co-evolution (dpeaa)DE-He213 Travelling Thief Problem (dpeaa)DE-He213 Interdependence (dpeaa)DE-He213 Li, Xiaodong verfasserin aut Yao, Xin verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 20(2014), 1 vom: 17. Okt., Seite 157-172 (DE-627)SPR006469531 nnns volume:20 year:2014 number:1 day:17 month:10 pages:157-172 https://dx.doi.org/10.1007/s00500-014-1487-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2014 1 17 10 157-172 |
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10.1007/s00500-014-1487-2 doi (DE-627)SPR006487750 (SPR)s00500-014-1487-2-e DE-627 ger DE-627 rakwb eng Mei, Yi verfasserin aut On investigation of interdependence between sub-problems of the Travelling Thief Problem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP. Combinatorial optimization (dpeaa)DE-He213 Evolutionary computation (dpeaa)DE-He213 Cooperative Co-evolution (dpeaa)DE-He213 Travelling Thief Problem (dpeaa)DE-He213 Interdependence (dpeaa)DE-He213 Li, Xiaodong verfasserin aut Yao, Xin verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 20(2014), 1 vom: 17. Okt., Seite 157-172 (DE-627)SPR006469531 nnns volume:20 year:2014 number:1 day:17 month:10 pages:157-172 https://dx.doi.org/10.1007/s00500-014-1487-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2014 1 17 10 157-172 |
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10.1007/s00500-014-1487-2 doi (DE-627)SPR006487750 (SPR)s00500-014-1487-2-e DE-627 ger DE-627 rakwb eng Mei, Yi verfasserin aut On investigation of interdependence between sub-problems of the Travelling Thief Problem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP. Combinatorial optimization (dpeaa)DE-He213 Evolutionary computation (dpeaa)DE-He213 Cooperative Co-evolution (dpeaa)DE-He213 Travelling Thief Problem (dpeaa)DE-He213 Interdependence (dpeaa)DE-He213 Li, Xiaodong verfasserin aut Yao, Xin verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 20(2014), 1 vom: 17. Okt., Seite 157-172 (DE-627)SPR006469531 nnns volume:20 year:2014 number:1 day:17 month:10 pages:157-172 https://dx.doi.org/10.1007/s00500-014-1487-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2014 1 17 10 157-172 |
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10.1007/s00500-014-1487-2 doi (DE-627)SPR006487750 (SPR)s00500-014-1487-2-e DE-627 ger DE-627 rakwb eng Mei, Yi verfasserin aut On investigation of interdependence between sub-problems of the Travelling Thief Problem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP. Combinatorial optimization (dpeaa)DE-He213 Evolutionary computation (dpeaa)DE-He213 Cooperative Co-evolution (dpeaa)DE-He213 Travelling Thief Problem (dpeaa)DE-He213 Interdependence (dpeaa)DE-He213 Li, Xiaodong verfasserin aut Yao, Xin verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 20(2014), 1 vom: 17. Okt., Seite 157-172 (DE-627)SPR006469531 nnns volume:20 year:2014 number:1 day:17 month:10 pages:157-172 https://dx.doi.org/10.1007/s00500-014-1487-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2014 1 17 10 157-172 |
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10.1007/s00500-014-1487-2 doi (DE-627)SPR006487750 (SPR)s00500-014-1487-2-e DE-627 ger DE-627 rakwb eng Mei, Yi verfasserin aut On investigation of interdependence between sub-problems of the Travelling Thief Problem 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP. Combinatorial optimization (dpeaa)DE-He213 Evolutionary computation (dpeaa)DE-He213 Cooperative Co-evolution (dpeaa)DE-He213 Travelling Thief Problem (dpeaa)DE-He213 Interdependence (dpeaa)DE-He213 Li, Xiaodong verfasserin aut Yao, Xin verfasserin aut Enthalten in Soft Computing Springer-Verlag, 2003 20(2014), 1 vom: 17. Okt., Seite 157-172 (DE-627)SPR006469531 nnns volume:20 year:2014 number:1 day:17 month:10 pages:157-172 https://dx.doi.org/10.1007/s00500-014-1487-2 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER AR 20 2014 1 17 10 157-172 |
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Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP. |
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Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP. |
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Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP. |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR006487750</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20201124002809.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201005s2014 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00500-014-1487-2</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR006487750</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00500-014-1487-2-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Mei, Yi</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">On investigation of interdependence between sub-problems of the Travelling Thief Problem</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2014</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, the interdependence between sub-problems in a complex overall problem is investigated using a benchmark problem called Travelling Thief Problem (TTP), which is a combination of Travelling Salesman Problem (TSP) and Knapsack Problem (KP). First, the analysis on the mathematical formulation shows that it is impossible to decompose the problem into independent sub-problems due to the non-linear relationship in the objective function. Therefore, the algorithm for TTP is not straightforward although each sub-problem alone has been investigated intensively. Then, two meta-heuristics are proposed for TTP. One is the Cooperative Co-evolution (CC) that solves the sub-problems separately and transfers the information between them in each generation. The other is the Memetic Algorithm (MA) that solves TTP as a whole. The comparative results showed that MA consistently obtained much better results than both the standard and dynamic versions of CC within comparable computational budget. This indicates the importance of considering the interdependence between sub-problems in an overall problem like TTP.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Combinatorial optimization</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Evolutionary computation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cooperative Co-evolution</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Travelling Thief Problem</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Interdependence</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Li, Xiaodong</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Yao, Xin</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Soft Computing</subfield><subfield code="d">Springer-Verlag, 2003</subfield><subfield code="g">20(2014), 1 vom: 17. Okt., Seite 157-172</subfield><subfield code="w">(DE-627)SPR006469531</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:20</subfield><subfield code="g">year:2014</subfield><subfield code="g">number:1</subfield><subfield code="g">day:17</subfield><subfield code="g">month:10</subfield><subfield code="g">pages:157-172</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00500-014-1487-2</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">20</subfield><subfield code="j">2014</subfield><subfield code="e">1</subfield><subfield code="b">17</subfield><subfield code="c">10</subfield><subfield code="h">157-172</subfield></datafield></record></collection>
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