PENERAPAN METODE CROSS ENTROPYdigilib.its.ac.id/public/ITS-Undergraduate-10663-Presentation.pdf ·...
Transcript of PENERAPAN METODE CROSS ENTROPYdigilib.its.ac.id/public/ITS-Undergraduate-10663-Presentation.pdf ·...
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PENERAPAN METODE CROSS ENTROPY
DALAM PENYELESAIAN CAPACITATED
VEHICLE ROUTING PROBLEM(Study Kasus : Distribusi Koran Jawa Pos Surabaya)(Study Kasus : Distribusi Koran Jawa Pos Surabaya)
Dosen Pembimbing:
Ir. Budi Santosa, M.Sc., Ph.D
Gladiez Florista Rera
(2506 100 024)
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Latar Belakang
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pustaka
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permasalahan
‘’ Bagaimana aplikasi metode Cross
Entropy untuk menyelesaikan permasalahan
Capacitated Vehicle Routing agar
didapatkan waktu komputasi yang lebihdidapatkan waktu komputasi yang lebih
baik dengan total cost transportation
yang minimum’’
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pustaka
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tujuan
• Mendapatkan algoritma Cross entropyuntuk kasus CVRP
• Menghasilkan program komputer untukimplementasi CE-CVRP
• Membandingkan performansi CE CVRP dengan metoda lain misalnya tabusearch.
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pustaka
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Ruang lingkup
Batasan
∃ Vehicle yang dimaksud adalah pick up dengan kapasitas 5000
eksemplar
∃ Permintaan akan kebutuhan koran di setiap agen dianggap sama
dengan besarnya jumlah permintaan, yang merupakan rata-rata
permintaan koran per periode pengiriman
∃ Pada permasalahan yang diangkat, digunakan satu depot utama
sebagai penyuplai utama koran ke seluruh agen yang besar di
seluruh surabayaseluruh surabaya
∃ Dalam konsep perhitungan jarak, digunakan metode symetric
distance
∃ Penentuan subtour menggunakan konsep route first cluster
second
Asumsi
Penentuan koordinat yang digunakan dalam perhitungan jarak
menetapkan depot utama sebagai pusat koordinat (pengukuran
relative)
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Tinjauan pustaka
CVRP
CE
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Metodologi penelitian
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Metodologipenelitian
Metodologi
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Pengujian algoritma
validasi • Validasi
menggunakan datayang berupapermasalahandistribusi
Data uji • Pengujian
menggunakan datayang meliputi 43 agen koran dengan1 depot utama
Data validasi
distribusisederhana denganmellibatkan 3 simpul agen dan 1 simpul depot
Data
1 depot utama
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Pengujian algoritma
1 2 3 4
1 0 7 5 4
2 7 0 2 5
3 5 2 0 3
4 4 5 3 0
Matriks Jarak Simpul Validasi
simpul demand
1 0
2 2
Data Demand Simpul Validasi
4 4 5 3 03 5
4 3
Tabu Search CE-CVRP
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pustaka
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Pengujian algoritma
Tahap
inisialisasi
Generate
Kandidat
Solusi
Pemilihan
solusi terbaik
pada
kandidat
solusi
Update Tabu
List
Stopping
criterion
terpenuhi?
current tour cost = 16 best obj =16
best tour
best_tour = 1 4 3 2 1
best obj =16
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Pengujian algoritma
Tahap
inisialis
asi
Tahap
pemban
gkitan
matriks
transisi
Tahap
pemba
ngkitan
Nℓ
lintasan
Tahap
penghit
ungan
expecte
d cost
T(r)
Tahap
pemilih
an
sample
elits
Update
parame
ter
Stopping
criterion
terpenuhi
?
Pembu
atan
subtour
Ropt : 1-4-3-2-1
Subtour
Rute 1: 1-4-3-2-1 dengan TC= 16, kapasitas 10
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Pengujian algoritma
Metode
Waktu
komputasi
(detik)
T (i) Subtour
Tabu Search 150,703 16 1-4-3-2-1
CE-CVRP 0.0625 16 1-4-3-2-1
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Pengujian algoritma
Data UJI
Data uji 8
simpul
Data uji 10
simpul
Data uji 20
simpul
Data uji 44
simpul
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Pengujian algoritma
8 simpul agen
Metode
waktu
komputasi
(detik)
ropt subtour T (i)
CE-CVRP 15.625 1-8-6-5-7-4-3-2-1 1-8-6-5-1 169,8CE-CVRP 15.625 1-8-6-5-7-4-3-2-1 1-8-6-5-1 169,8
1-7-4-1
1-3-2-1
Tabu
Search 59.718 1-8-6-5-2-3-4-7-1 1-8-6-5-1 170,1
1-3-4-1
1-7-1
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pustaka
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Pengujian algoritma
10 simpul
Metode
waktu
komputasi
(detik)
ropt subtour T (i)
CE-CVRP 19,68751-8-9-10-5-6-7-4-3-2-1 1-8-9-10-5-1 190,2
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pustaka
CE-CVRP 19,68751-8-9-10-5-6-7-4-3-2-1 1-8-9-10-5-1 190,2
1-6-7-4-1
1-3-2-1
Tabu Search 62,1251-8-9-6-5-10-2-3-4-7-1 1-8-9-6-1 211,4
1-5-10-2-1
1-3-4-1
1-7-1
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Pengujian algoritma
Metode
waktu
komputasi
(detik)
ropt subtour T (i)
CE-CVRP 205,593751-12-16-11-7-14-10-5-15-9-
17-6-18-4-2-3-13-4-16-1
1-12-16-11-7-14-10-5-
15-9-1238
1-17-6-18-4-2-3-13-1
1-4-16-1
20 simpul
1-4-16-1
Tabu Search 80,06251-12-19-8-9-15-17-6-5-10-14-
20-7-11-18-13-2-3-4-16-1
1-12-19-8-9-15-17-6-5-
10-14-1216,824
1-20-7-11-18-13-2-3-1
1-4-16-1
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pustaka
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Pengujian algoritma
44 simpul 10000 sampel
44 simpul 20000 sampel44 simpul 20000 sampel
44 simpul 40000 sampel
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Pengujian algoritma
Metode roptwaktu
komputasisubtour T (i)
CE-CVRP 285,14 1-8-40-37-30-29-16-27-11 620,1
1-21-15-6-20-9-36-34-7-32-1
1-26-4-25-14-17-24-38-10-44-5-35-31-
1
10000 sampel rute
1-8-40-37-30-29-16-27-11-21-15-6-20-9-36-34-
7-32-26-4-25-14-17-24-38-10-44-5-35-31-12-19-
13-18-22-33-23-42-39-41-28-2-3-43-1
1-12-19-13-18-22-33-23-1
1-42-39-41-28-2-3-43-1
Tabu Search
1-12-36-35-19-8-15-17-21-22-10-5-6-38-14-11-
37-43-42-18-32-2-3-29-26-27-25-4-41-16-30-24-
40-28-34-39-7-44-23-20-13-33-9-31-1
215,5631-12-36-35-19-8-15-17-21-22-10-5-6-
38-1363.71
1-14-11-37-43-42-18-32-2-3-29-26-1
1-27-25-4-41-16-30-24-1
1-40-28-34-39-7-44-1
1-23-20-13-33-9-31-1
Bab 1 Bab 2 Bab 3 Bab 4 Bab 5 Bab 6 LampiranDaftar
pustaka
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Pengujian algoritma
Metode roptwaktu
komputasisubtour T (i)
CE-CVRP1-3-2-11-44-34-16-28-43-8-39-36-19-32-26-7-6-
22-10-5-23-20-40-24-30-37-9-35-12-17-13-27-
18-4-38-33-31-15-21-42-25-41-29- 14-1
547,18725 1-3-2-11-44-34-16-28-43-8-39-36-19-1
577,26
1-32-26-7-6-22-10-5-23-1
20000 sampel rute
1-32-26-7-6-22-10-5-23-1
1-20-40-24-30-37-9-35-1
1-12-17-13-27-18-4-38-33-1
1-31-15-21-42-25-41-29- 14-1
Tabu Search
1-12-36-35-19-8-15-17-21-22-10-5-6-38-14-11-
37-43-42-18-32-2-3-29-26-27-25-4-41-16-30-24-
40-28-34-39-7-44-23-20-13-33-9-31-1
215,5631-12-36-35-19-8-15-17-21-22-10-5-6-
38-1363.71
1-14-11-37-43-42-18-32-2-3-29-26-1
1-27-25-4-41-16-30-24-1
1-40-28-34-39-7-44-1
1-23-20-13-33-9-31-1
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pustaka
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Pengujian algoritma
Metode roptwaktu
komputasisubtour T (i)
CE-CVRP 4.535,1406 1-35-15-21-10-14-39-41-18-38-31-6-1 574,73
1-23-28-40-30-33- 37-1
1-16-3-4-27-24-22-43-7-11-1
1-12-36-44-20-32-29-42-2-26-25-1
40000 sampel rute
1-35-15-21-10-14-39-41-18-38-31-6-23-28-40-
30-33- 37-16-3-4-27-24-22-43-7-11-12-36-44-20-
32-29-42-2-26-25-13-34-9-5-19-17-8-1
1-12-36-44-20-32-29-42-2-26-25-1
1-13-34-9-5-19-17-8-1
Tabu Search
1-12-36-35-19-8-15-17-21-22-10-5-6-38-14-11-
37-43-42-18-32-2-3-29-26-27-25-4-41-16-30-24-
40-28-34-39-7-44-23-20-13-33-9-31-1
215,5631-12-36-35-19-8-15-17-21-22-10-5-6-
38-1363.71
1-14-11-37-43-42-18-32-2-3-29-26-1
1-27-25-4-41-16-30-24-1
1-40-28-34-39-7-44-1
1-23-20-13-33-9-31-1
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Analisa dan Pembahasan
validasi
8 simpul10
simpul
20
simpul 44
simpul
Performansi Keseluruhan
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Tabu
SearchCE-CVRP
Analisa dan Pembahasan
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Kesimpulan dan Saran
Kesimpulan
� Metode optimasi Cross Entropny dapat diaplikasikan untuk
penyelesaian masalah Capacitated Vehicle Routing dengan
melakukan insialisasi matriks transisi sebagai parameter utama yang
berguna dalam pembangkitan sejumlah sampel rute sebagai
kandidat solusi.
� Metode CE-CVRP dalam penyelesaian permasalahan sangat
bergantung pada stopping criterion yang ditentukan dan banyaknya
sampel rute yang dibangkitkan pada setiap iterasinya.sampel rute yang dibangkitkan pada setiap iterasinya.
� Dibandingkan dengan tabu search, CE-CVRP dapat menunjukan
performansi yang lebih baik pada permasalahan-permasalahan
tertentu.
Saran
Penelitian selanjutnya bisa dilakukan dengan memodifikasi algoritma
sehinga dapat meminimalkan jumlah sampel yang perlu dibangkitkan
pada permasalahan yang melibatkan banyak simpul.
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lampiran
1. M-file tabu search
2. M-file CE-CVRP2. M-file CE-CVRP
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Daftar pustaka
De Boer, Pieter Tjerk, D.P. Kroese, Shie Mannor and Reuven Rubinstein, 2005, A Tutorial on the Cross-entropy method, Annals of
Operations Research, vol. 134, No. 1, pp. 19-67
D.P. Kroese and K.-P. Hui Applications of the Cross-Entropy Method in Reliability Computational Intelligence in Reliability Engineering
(SCI) 40, 37–82 (2007)
Rubinstein,R.Y., The Cross-Entropy Method for Combinatorial and Continuous Optimization, Methodology and Computing in Applied
Probability, vol 1, 127-190 Kluwer Academic Publishers, Boston, (1999).
Rubinstein, R., & Kroese., D., The cross-entropy method: A unified approach to combinatorial optimization, Monte-Carlo simulation,
and machine-learning, Springer-Verlag, (2004).
Rubinstein, R.Y. Stochastic Minimum Cross-Entropy Method for Combinatorial Optimization and Rare-Event, Estimation Methodology
and Computing in Applied Probability, 7, 5–50, (2005)
Sang Putu Eka Kesuma Putra, Analisis Dan Implementasi Vrp (Vehicle Routing Problem) Menggunakan Bfs (Breadth First Search) Dan
Branch And Bound, IT TELKOM
T.K. Ralphs, L. Kopman , W.R. Pulleyblank , L.E. Trotter, On the Capacitated Vehicle Routing Problem, Mathematical programming,
submitted
Lawjer, E., & Leastra, J. (1985). The Traveling Salesman Problem. England: SERC.Lawjer, E., & Leastra, J. (1985). The Traveling Salesman Problem. England: SERC.
Rubinstein, R. Y., & Kroese, D. P. (2008). Simulation and The MOnte Carlo Method. USA: A John Wiley and Sons.
Rubinstein, R. Y., & Kroese, D. P. (2004). The Cross Entropy; A Unified Approach to Combinatorial Optimiztion, Monte Carlo Simulation
and Machine Learning. USA: Springer.
Chepuri, K., & Homem, T. (2003). Solving The Vehicle Routing Problem with Stochastic Demands Using The Cross Entropy Method.
Elsevier-ScienceDirect .
Lagua, M., Abraham, D., & Marti, R. (2007). Hybridizing The Cross Entropy Method: An Application in The Max-Cut Poblem. Elsevier-
ScienceDirect .
Mohemmed, A. W., Sahoo, N. C., & Geok, T. K. (2008). Solving Shortest Path Problem Using Particle Swarm Optimiztion. Elsevier-
ScienceDirect .
Rubinstein, R. Y., & Kroese, D. P. (2004). The Cross Entropy; A Unified Approach to Combinatorial Optimiztion, Monte Carlo Simulation
and Machine Learning. USA: Springer.
Shi, X. H., Liang, Y., Lee, H., C.Lu, & Wang, Q. (2007). Particle Swarm Optimization Based Algorithms for TSP and Generalized TSP.
Elsevier-ScienceDirect.
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Terima Kasih
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300
400
500
600
700
tra
ve
rsin
g c
ost
CE-CVRP VS TABU SEARCH
CE-CVRP
Tabu Search
Analisa dan Pembahasan
0
100
200
300
10000 20000 40000
tra
ve
rsin
g c
ost
Tabu Search
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Pengujian algoritma
15 simpul
Metode
waktu
komputasi
(detik)
ropt subtour T (i)
CE-CVRP 73,511-12-7-5-6-11-2-3-4-13-14-8-
15-9-10-11-12-7-5-6-1 204,02CE-CVRP 73,51
15-9-10-11-12-7-5-6-1 204,02
1-11-2-3-4-1
1-13-14-8-15-9-10-1
Tabu Search
172,171-12-8-9-15-6-5-10-14-11-13-
2-3-4-7-11-12-8-9-15-1 224,49
1-6-5-10-14-11-1
1-13-2-3-1
1-4-7-1
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Pengujian algoritma
17 simpul
Metode
waktu
komputasi
(detik)
ropt subtour T (i)
CE-CVRP 150,151-12-8-9-15-17-6-5-10-14-
11-4-16-3-2-13-7-11-12-8-9-15-17-1 224,94
11-4-16-3-2-13-7-1
1-6-5-10-14-11-4-1
1-16-3-2-13-1
1-7-1
Tabu Search 272,9531-10-5-6-17-15-8-9-13-11-
2-3-16-4-14-7-12-1
1-10-5-6-17-15-8-1 227,62
1-9-13-11-2-1
1-3-16-4-14-7-1
1-7-1
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Pengujian algoritma
19 simpul
Metode
waktu
komputasi
(detik)
ropt subtour T (i)
CE-CVRP 169,981-16-4-3-2-13-18-14-11-7-6-
5-10-17-15-9-8-19-12-11-16-4-3-2-13-18-14-11-1 152,01
5-10-17-15-9-8-19-12-1
1-7-6-5-10-17-15-9-8-19-1
1-12-1
Tabu Search177,562
1-12-19-8-9-15-17-10-5-6-7-
11-14-18-13-2-3-4-16-1 1-12-19-8-9-15-17-10-5-6-1 198,74
1-7-11-14-18-13-2-3-4-1
1-16-1
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