Abstract
Ising model-based computation has attracted attention as it can obtain better solutions of various combinatorial optimization problems at high speed by mapping the problems to natural phenomena. A slot placement problem is one of the combinatorial optimization problems which plays an important role in the optimal logic-block placement as well as optimal delivery decisions but it is known as an NP-hard problem. Solving it efficiently is one of the largest challenges. In this paper, we propose an efficient Ising model mapping to solve the slot placement problem and an interpretation method for the obtained Ising solutions to satisfy the slot-placement constraints. First, we propose slot-placement constraint terms that minimize the energy function or Hamiltonian of the Ising model when satisfying the slot-placement constraints. Secondly, we propose an objective function term in the energy function that minimizes the total weighted wiring length between items to be placed to the slots. In Ising model-based computations, the final spin states cannot necessarily satisfy the slot-placement constraints, which gives one of the largest differences from the conventional computations. Hence we newly propose an interpretation method for the obtained Ising solutions to satisfy the slot-placement constraints. On a fully-connected annealing machine, we could obtain feasible solutions with almost the same accuracy as the simulated annealing for slot placement problem with two orders of magnitude faster.
| Original language | English |
|---|---|
| Title of host publication | 2019 IEEE International Conference on Consumer Electronics, ICCE 2019 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| ISBN (Electronic) | 9781538679104 |
| DOIs | |
| Publication status | Published - 2019 Mar 6 |
| Event | 2019 IEEE International Conference on Consumer Electronics, ICCE 2019 - Las Vegas, United States Duration: 2019 Jan 11 → 2019 Jan 13 |
Publication series
| Name | 2019 IEEE International Conference on Consumer Electronics, ICCE 2019 |
|---|
Conference
| Conference | 2019 IEEE International Conference on Consumer Electronics, ICCE 2019 |
|---|---|
| Country | United States |
| City | Las Vegas |
| Period | 19/1/11 → 19/1/13 |
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Keywords
- annealing machine
- Ising model
- Ising model-based computers
- slot placement problem
ASJC Scopus subject areas
- Industrial and Manufacturing Engineering
- Media Technology
- Electrical and Electronic Engineering
Cite this
Efficient Ising Model Mapping to Solving Slot Placement Problem. / Kanamaru, Sho; Oku, Daisuke; Tawada, Masashi; Tanaka, Shu; Hayashi, Masato; Yamaoka, Masanao; Yanagisawa, Masao; Togawa, Nozomu.
2019 IEEE International Conference on Consumer Electronics, ICCE 2019. Institute of Electrical and Electronics Engineers Inc., 2019. 8661947 (2019 IEEE International Conference on Consumer Electronics, ICCE 2019).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Efficient Ising Model Mapping to Solving Slot Placement Problem
AU - Kanamaru, Sho
AU - Oku, Daisuke
AU - Tawada, Masashi
AU - Tanaka, Shu
AU - Hayashi, Masato
AU - Yamaoka, Masanao
AU - Yanagisawa, Masao
AU - Togawa, Nozomu
PY - 2019/3/6
Y1 - 2019/3/6
N2 - Ising model-based computation has attracted attention as it can obtain better solutions of various combinatorial optimization problems at high speed by mapping the problems to natural phenomena. A slot placement problem is one of the combinatorial optimization problems which plays an important role in the optimal logic-block placement as well as optimal delivery decisions but it is known as an NP-hard problem. Solving it efficiently is one of the largest challenges. In this paper, we propose an efficient Ising model mapping to solve the slot placement problem and an interpretation method for the obtained Ising solutions to satisfy the slot-placement constraints. First, we propose slot-placement constraint terms that minimize the energy function or Hamiltonian of the Ising model when satisfying the slot-placement constraints. Secondly, we propose an objective function term in the energy function that minimizes the total weighted wiring length between items to be placed to the slots. In Ising model-based computations, the final spin states cannot necessarily satisfy the slot-placement constraints, which gives one of the largest differences from the conventional computations. Hence we newly propose an interpretation method for the obtained Ising solutions to satisfy the slot-placement constraints. On a fully-connected annealing machine, we could obtain feasible solutions with almost the same accuracy as the simulated annealing for slot placement problem with two orders of magnitude faster.
AB - Ising model-based computation has attracted attention as it can obtain better solutions of various combinatorial optimization problems at high speed by mapping the problems to natural phenomena. A slot placement problem is one of the combinatorial optimization problems which plays an important role in the optimal logic-block placement as well as optimal delivery decisions but it is known as an NP-hard problem. Solving it efficiently is one of the largest challenges. In this paper, we propose an efficient Ising model mapping to solve the slot placement problem and an interpretation method for the obtained Ising solutions to satisfy the slot-placement constraints. First, we propose slot-placement constraint terms that minimize the energy function or Hamiltonian of the Ising model when satisfying the slot-placement constraints. Secondly, we propose an objective function term in the energy function that minimizes the total weighted wiring length between items to be placed to the slots. In Ising model-based computations, the final spin states cannot necessarily satisfy the slot-placement constraints, which gives one of the largest differences from the conventional computations. Hence we newly propose an interpretation method for the obtained Ising solutions to satisfy the slot-placement constraints. On a fully-connected annealing machine, we could obtain feasible solutions with almost the same accuracy as the simulated annealing for slot placement problem with two orders of magnitude faster.
KW - annealing machine
KW - Ising model
KW - Ising model-based computers
KW - slot placement problem
UR - http://www.scopus.com/inward/record.url?scp=85063795425&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85063795425&partnerID=8YFLogxK
U2 - 10.1109/ICCE.2019.8661947
DO - 10.1109/ICCE.2019.8661947
M3 - Conference contribution
T3 - 2019 IEEE International Conference on Consumer Electronics, ICCE 2019
BT - 2019 IEEE International Conference on Consumer Electronics, ICCE 2019
PB - Institute of Electrical and Electronics Engineers Inc.
ER -