Fujitsu Computing as a Service Digital Annealer User’s Guide

Preface

This manual describes how to use Digital Annealer service and operation management procedures.

Intended Audience

This manual is intended for users who develop programs and applications to solve combinatorial optimization problems on Digital Annealer and who execute those programs and applications.
To fully benefit from this manual, the following knowledge is required:

Basic knowledge related to combinatorial optimization problems
Basic knowledge related to algorithms for combinatorial optimization problems such as quantum annealing and simulated annealing
Basic knowledge of Web APIs

Conventions

This manual uses abbreviations and symbols.

Product/Technology Name Abbreviations

Product/Technology Name	Abbreviation
Google Chrome™ browser	Google Chrome

Product/Technology Name

Abbreviation

Google Chrome™ browser

Google Chrome

About Symbols

Symbol	Meaning
" "	If the reference destination is another manual, the manual name is enclosed in " "

In addition, the following markings are used.

CAUTION

NOTE

Glossary

Explanation of terms used in this manual.

Term	Description
Digital Annealer	The quantum-inspired digital technology architecture, capable of performing parallel, real-time optimization calculations at speed, with precision and on a scale classical computing cannot.
Problem scale	The number of variables that make up a combinatorial optimization problem.
FujitsuDA3Solver	The 3rd generation and 4th generation Digital Annealer solver which can handle large scale problem. The maximum problem scale can be solved is 100K (100,000) bits.
FujitsuDA2PTSolver	The 2nd generation Digital Annealer solver with the parallel tempering feature. The maximum problem scale can be solved is 8192 bits.
FujitsuDA2Solver	The 2nd generation Digital Annealer solver. The maximum problem scale can be solved is 8192 bits.
FujitsuDA2MixedModeSolver	The 2nd generation Digital Annealer solver. The maximum problem scale can be solved is 8192 bits.
Higher Order Binary Optimization (HOBO)	An expression of combinatorial optimization problems with high-order monomials or high-order polynomials.
Quadratic Unconstrained Binary Optimization (QUBO)	An expression of combinatorial optimization problems with quadratic polynomials.
Web API	An interface used between applications and between systems for calling over a network using the HTTP protocol.
Azure Blob Storage	Object storage provided by Microsoft. FujitsuDA3Solver can calclulate the problem data (QUBO) uploaded to the Azure BLob Storage. The maximum size of the problem data (QUBO) is 20GB. You have to make the contract for Micorsoft Azure to use Azure Blob Storage.
Type ID	The Type ID is the "type" + "four-digit number" ID that is notified when the Premium-3c or Premium-4c service starts. (e.g. type1234)

Term

Description

Digital Annealer

The quantum-inspired digital technology architecture, capable of performing parallel, real-time optimization calculations at speed, with precision and on a scale classical computing cannot.

Problem scale

The number of variables that make up a combinatorial optimization problem.

FujitsuDA3Solver

The 3rd generation and 4th generation Digital Annealer solver which can handle large scale problem. The maximum problem scale can be solved is 100K (100,000) bits.

FujitsuDA2PTSolver

The 2nd generation Digital Annealer solver with the parallel tempering feature. The maximum problem scale can be solved is 8192 bits.

FujitsuDA2Solver

The 2nd generation Digital Annealer solver. The maximum problem scale can be solved is 8192 bits.

FujitsuDA2MixedModeSolver

The 2nd generation Digital Annealer solver. The maximum problem scale can be solved is 8192 bits.

Higher Order Binary Optimization (HOBO)

An expression of combinatorial optimization problems with high-order monomials or high-order polynomials.

Quadratic Unconstrained Binary Optimization (QUBO)

An expression of combinatorial optimization problems with quadratic polynomials.

Web API

An interface used between applications and between systems for calling over a network using the HTTP protocol.

Azure Blob Storage

Object storage provided by Microsoft. FujitsuDA3Solver can calclulate the problem data (QUBO) uploaded to the Azure BLob Storage. The maximum size of the problem data (QUBO) is 20GB. You have to make the contract for Micorsoft Azure to use Azure Blob Storage.

Type ID

The Type ID is the "type" + "four-digit number" ID that is notified when the Premium-3c or Premium-4c service starts. (e.g. type1234)

Export Control Regulations

Exportation/release of this document may require necessary procedures in accordance with the regulations of your resident country and/or US export control laws.

High Risk Activity

The Customer acknowledges and agrees that the Service is designed, developed and manufactured as contemplated for general use, including without limitation, general office use, personal use, household use, and ordinary industrial use, but is not designed, developed and manufactured as contemplated for use accompanying fatal risks or dangers that, unless extremely high safety is secured, could lead directly to death, personal injury, severe physical damage or other loss (hereinafter "High Safety Required Use"), including without limitation, nuclear reaction control in nuclear facility, aircraft flight control, air traffic control, mass transport control, medical life support system, missile launch control in weapon system.
The Customer, shall not use the Service without securing the sufficient safety required for the High Safety Required Use. In addition, Fujitsu (or other affiliate’s name) shall not be liable against the Customer and/or any third party for any claims or damages arising in connection with the High Safety Required Use of the Service.

Trademarks

Google is a trademark or registered trademark of Google Inc.
Microsoft, Azure are trademarks or registered trademarks of Microsft Corporation.
Other company names and product names are trade names, registered trademarks, or trademarks of their respective companies.
Trademark symbols are not always added to names such as company names, system names, and product names.

1. Overview

This chapter describes an overview of Digital Annealer.

1.1. What Is Digital Annealer?

Digital Annealer is a digital circuit designed with inspiration from a computation method that uses quantum phenomena. Using annealing methods enables it to solve large-scale combinatorial optimization problems rapidly. Unlike conventional computers, programming is not required, and computation is enabled only by setting parameters. In addition, adoption of a fully connected architecture enabling any element to freely exchange signals has enabled calculation of computationally intensive and complicated problems that have been difficult to solve with classical computers or quantum annealing machines.

Digital Annealer has Quadratic Unconstrained Binary Optimization (QUBO) as its input data and searches for combinations to minimize the following evaluation function (energy).

\(\displaystyle{E(x) = \sum_{i} \sum_{j>i} J_{ij}x_{i}x_{j} + \sum_{i}h_{i}x_{i} + c}\)

The condition of the combination is represented by a binary variable \(x \; (x \in \{0, 1\})\).

1.1.1. Digital Annealer Service

Digital Annealer service is a cloud service used to rapidly solve combinatorial optimization problems using software for quantum computers and the hardware equipped with the optimization circuit Digital Annealer.

Figure 1. Web API Service

2. Starting the Use of Services

This chapter describes how to start the use of Digital Annealer service.

2.1. Account Registration

To use the Digital Annealer service, access the Digital Annealer account creation page at the following URL in the Digital Annealer portal and register an account.

For users in Japan region:

https://portal.aispf.global.fujitsu.com/#/digitalannealer?lang=ja

For users in other regions:

https://portal.aispf.global.fujitsu.com/#/digitalannealer?lang=en

To access the Digital Annealer portal, use Google Chrome.
It is recommended that the screen resolution is 1366 \(\times\) 768 pixels or higher.

3. Using Services

This chapter describes how to use Digital Annealer service and other points to be noted.

3.1. Provided APIs

The APIs provided in the Web API service are as follows:

3.1.1. QUBO APIs

ContractType	API	Type	Description
Academic-2	qubo/hobo2qubo	Synchronous (sync)	Converts Higher Order Binary Optimization (HOBO) to Quadratic Unconstrained Binary Optimization (QUBO)
qubo/solve	Finds optimal solution for QUBO using FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver. The problem scale that can be calculated is 2048 bits or less.
async/qubo/solve	Asynchronous (async)	Registers a job to find optimal solution for QUBO using FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver. The problem scale that can be calculated is 8192 bits or less.
async/jobs	Retrieves a list of jobs
async/jobs/result/{Job_ID}	Retrieves or deletes the result of a job. Specify the Job D in {Job_ID}.
async/jobs/cancel	Cancels a job
Developer-4c Developer-3c Developer-4 Trial-3 Academic-3	qubo/hobo2qubo	Synchronous (sync)	Converts Higher Order Binary Optimization (HOBO) to Quadratic Unconstrained Binary Optimization (QUBO)
async/qubo/solve	Asynchronous (async)	Registers a job to find optimal solution for QUBO using FujitsuDA3Solver. The problem scale that can be calculated is 100K (100,000) bits or less.
async/jobs	Retrieves a list of jobs
async/jobs/result/{Job_ID}	Retrieves or deletes the result of a job. Specify the Job D in {Job_ID}.
async/jobs/cancel	Cancels a job
Premium-4c Premium-3c	{Type_ID}/hobo2qubo	Synchronous (sync)	Converts Higher Order Binary Optimization (HOBO) to Quadratic Unconstrained Binary Optimization (QUBO). Specify the Type ID in {Type_ID}.
{Type_ID}/async/solve	Asynchronous (async)	Registers a job to find optimal solution for QUBO using FujitsuDA3Solver. The problem scale that can be calculated is 100K (100,000) bits or less. Specify the Type ID in {Type_ID}.
{Type_ID}/async/jobs	Retrieves a list of jobs. Specify the Type ID in {Type_ID}.
{Type_ID}/async/jobs/result/{Job_ID}	Retrieves or deletes the result of a job. Specify the Type ID in {Type_ID}. Specify the Job D in {Job_ID}.
{Type_ID}/async/jobs/cancel	Cancels a job. Specify the Type ID in {Type_ID}.

ContractType

API

Type

Description

Academic-2

qubo/hobo2qubo

Synchronous (sync)

Converts Higher Order Binary Optimization (HOBO) to Quadratic Unconstrained Binary Optimization (QUBO)

qubo/solve

Finds optimal solution for QUBO using FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver. The problem scale that can be calculated is 2048 bits or less.

async/qubo/solve

Asynchronous (async)

Registers a job to find optimal solution for QUBO using FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver. The problem scale that can be calculated is 8192 bits or less.

async/jobs

Retrieves a list of jobs

async/jobs/result/{Job_ID}

Retrieves or deletes the result of a job. Specify the Job D in {Job_ID}.

async/jobs/cancel

Cancels a job

Developer-4c
Developer-3c
Developer-4
Trial-3
Academic-3

qubo/hobo2qubo

Synchronous (sync)

Converts Higher Order Binary Optimization (HOBO) to Quadratic Unconstrained Binary Optimization (QUBO)

async/qubo/solve

Asynchronous (async)

Registers a job to find optimal solution for QUBO using FujitsuDA3Solver. The problem scale that can be calculated is 100K (100,000) bits or less.

async/jobs

Retrieves a list of jobs

async/jobs/result/{Job_ID}

Retrieves or deletes the result of a job. Specify the Job D in {Job_ID}.

async/jobs/cancel

Cancels a job

Premium-4c
Premium-3c

{Type_ID}/hobo2qubo

Synchronous (sync)

Converts Higher Order Binary Optimization (HOBO) to Quadratic Unconstrained Binary Optimization (QUBO). Specify the Type ID in {Type_ID}.

{Type_ID}/async/solve

Asynchronous (async)

Registers a job to find optimal solution for QUBO using FujitsuDA3Solver. The problem scale that can be calculated is 100K (100,000) bits or less. Specify the Type ID in {Type_ID}.

{Type_ID}/async/jobs

Retrieves a list of jobs. Specify the Type ID in {Type_ID}.

{Type_ID}/async/jobs/result/{Job_ID}

Retrieves or deletes the result of a job. Specify the Type ID in {Type_ID}. Specify the Job D in {Job_ID}.

{Type_ID}/async/jobs/cancel

Cancels a job. Specify the Type ID in {Type_ID}.

QUBO size
- The maximum size of the QUBO API request body is 2GB. It is possible to calculate QUBO up to 2GB.
- If you made the contract for QUBO API V4 or QUBO API V3c (Premium-4c, Premium-3c, Developer-4c, Developer-3c, or Developer-4), it is possible to calculate QUBO up to 20GB by using Azure Blob Storage Storage. You have to make the contract for Micorsoft Azure to use Azure Blob Storage.
Problem scale
- If you made the contract for Premium-4c, Premium-3c, Developer-4c, Developer-3c, Developer-4, Trial-3, or Academic-3, the problem scale that can be calculated is as follows.
  Asynchronous (async): 100K (100,000) bits or less
- If you made the contract for Academic-2, the problem scale that can be calculated depends on the type of API.
  Synchronous (sync): 2048 bits or less
  Asynchronous (async): 8192 bits or less
Monthly fixed contract
- If you made the monthly fixed contract for Developer-4c, Developer-3c, Developer-4, Trial-3, Academic-3, or Academic-2, upper limits are set for the amount of usage time.
  Upper limits are set for both synchronous and asynchronous services, and you cannot exceed the limits.
- If you made the monthly fixed contract for Developer-4c, you can not use both QUBO API V3c and QUBO API V4 if the sum of QUBO API V3c and QUBO API V4 usage time exceeds the monthly usage time limit.
- If you made the monthly fixed contract for Developer-4, you can not use both QUBO API V3 and QUBO API V4 if the sum of QUBO API V3 and QUBO API V4 usage time exceeds the monthly usage time limit.
Asynchronous service
- If you made the contract for Academic-2 and you want to use an asynchronous (async) type API, you must make the contract for asynchronous services.
Multiple requests
- You can issue up to 2 requests using a synchronous qubo/hobo2qubo and qubo/solve request from the same account at the same time.
- You can issue up to 16 requests using an asynchronous async/qubo/solve request from the same account.
- Note that this limitation also applies to the quantity of async/qubo/solve processing results. So, please delete unnecessary processing results.
- If you made the contract for Developer-4c, you can issu up to 16 concurrent QUBO API V3c and QUBO API V4 requests.
- If you made the contract for Developer-4, you can issu up to 16 concurrent QUBO API V3 and QUBO API V4 requests.
List of asynchronous jobs
- When using async/jobs to retrieve a list of jobs, you can view up to 16 job information.
- If you made the contract for Developer-4c, when using async/jobs to retrieve a list of jobs, you can see job information for both QUBO API V3c and QUBO API V4, with a maximum total of 16 jobs for QUBO API V3c and QUBO API V4.
- If you made the contract for Developer-4, when using async/jobs to retrieve a list of jobs, you can see job information for both QUBO API V3 and QUBO API V4, with a maximum total of 16 jobs for QUBO API V3 and QUBO API V4.
API Reference
- For details about the QUBO API, refer to "Digital Annealer API Reference (QUBO API V3c/V4 for Premium)", "Digital Annealer API Reference (QUBO API V4)", "Digital Annealer API Reference (QUBO API V3c)", "Digital Annealer API Reference (QUBO API V3)", or "Digital Annealer API Reference (QUBO API V2)."
- If you made the contract for QUBO API V3c/V4 for Premium (Premium-4c or Premium-3c), please refer to "Digital Annealer API Reference (QUBO API V3c/V4 for Premium)."
- If you made the contract for QUBO API V4 (Developer-4c, or Developer-4), please refer to "Digital Annealer API Reference (QUBO API V4)."
- If you made the contract for QUBO API V3c (Developer-4c or Developer-3c), please refer to "Digital Annealer API Reference (QUBO API V3c)."
- If you made the contract for QUBO API V3 (Developer-4, Trial-3, or Academic-3), please refer to "Digital Annealer API Reference (QUBO API V3)."
- If you made the contract for QUBO API V2 (Academic-2), please refer to "Digital Annealer API Reference (QUBO API V2)."

3.1.2. Optimization Solutions APIs

Contract Type	API	Description
Warehouse Pickup Optimization API	picking/mapfile	Uploads (POST) or downloads (GET) a map file (a list of the shelves and aisles in the warehouse)
picking/showroute	Finds the shortest pickup route with its total distance

Contract Type

API

Description

Warehouse Pickup Optimization API

picking/mapfile

Uploads (POST) or downloads (GET) a map file (a list of the shelves and aisles in the warehouse)

picking/showroute

Finds the shortest pickup route with its total distance

The Optimization Solutions APIs can only be used in Japan region.

The number of shelves that can be specified for picking/showroute is within the following range.
  \(\sum x^2 \leq 1024\)
  \(x\): The number of shelves with the same priority. Except the selves that have no other shelves with the same priority.
Example 1: In the case of that 1 shelf is level of priority 0, 30 shelves are level of priority 1, 5 shelves are
  level of priority 2, and 2 shelves are level of priority 3
  \(30^2 + 5^2 + 2^2 = 900 + 25 + 4 = 929\)
  (Level of priority 0 is only 1 shelf, therefore this value is omitted)
  ⇒ The number (929) is less than 1024, therefore the route can be optimized.
Example 2: In the case of that 30 shelves are level of priority 1, 10 shelves are level of priority 2, 1 shelf is
  level of priority 3, and 5 shelves are level of priority 4
  \(30^2 + 10^2 + 5^2 = 900 + 100 + 25 = 1025\)
  (Level of priority 3 is only 1 shelf, therefore this value is omitted)
  ⇒ The number (1025) is more than 1024, therefore the route cannot be optimized.
Even though the above conditions are met, if the number of shelves (nodes) specified in the request body is more than 200, the processing time becomes long and a timeout error (HTTP 504 Gateway Time-out) may occur.
Only one map file can be registered to Digital Annealer server with picking/mapfile. The most recently uploaded file is registered to Digital Annealer server. A previously registered map file will be overwritten, therefore please back up the map files if necessary.

4. How to Use the QUBO APIs

This chapter describes the procedure to solve combinatorial optimization problems using mathematical models.

4.1. Calculation Precision of Digital Annealer

Digital Annealer encodes the coefficient of a binary quadratic polynomial as an integer.
Calculation precision of Digital Annealer is as follows. To find the optimal solution, it is recommended to specify coefficients in a QUBO expression within the range of calculation precision of Digital Annealer.

Solver	Scale of the Problem	Quadratic Term	Linear Term
FujitsuDA3Solver	Up to 100,000 bits	64 bits signed integer (*1)	76 bits signed integer
FujitsuDA2PTSolver FujitsuDA2Solver FujitsuDA2MixedModeSolver	Up to 4096 bits	64 bits signed integer (*1)	76 bits signed integer
From over 4096 bits to 8192 bits	16 bits signed integer	76 bits signed integer

Solver

Scale of the Problem

Quadratic Term

Linear Term

FujitsuDA3Solver

Up to 100,000 bits

64 bits signed integer (*1)

76 bits signed integer

FujitsuDA2PTSolver
FujitsuDA2Solver
FujitsuDA2MixedModeSolver

Up to 4096 bits

64 bits signed integer (*1)

76 bits signed integer

From over 4096 bits to 8192 bits

16 bits signed integer

76 bits signed integer

*1: The available range is \(-2^{63} + 1\) to \(2^{63} - 1\)

4.1.1. Scaling and Rounding

This is a feature that automatically converts a QUBO that has one or more terms whose coefficient is out of the calculation precision range of Digital Annealer or not an integer into a QUBO that has only terms whose coefficient is integers in the calculation precision range of Digital Annealer.
If one of the following solvers is used, this function is enabled for annealing.

FujitsuDA3Solver
FujitsuDA2PTSolver
FujitsuDA2Solver (with "false" specified for the expert_mode parameter)
FujitsuDA2MixedModeSolver

For the range of coefficients in a QUBO expression that can be specified for qubo/solve and async/qubo/solve, refer to "Digital Annealer API Reference (QUBO API V3c/V4 for Premium)", "Digital Annealer API Reference (QUBO API V4)", "Digital Annealer API Reference (QUBO API V3c)", "Digital Annealer API Reference (QUBO API V3)", or "Digital Annealer API Reference (QUBO API V2)."

4.2. API Usage

For details about the specification and usage of the provided APIs, refer to "Digital Annealer API Reference (QUBO API V3c/V4 for Premium)", "Digital Annealer API Reference (QUBO API V4)", "Digital Annealer API Reference (QUBO API V3c)", "Digital Annealer API Reference (QUBO API V3)", or "Digital Annealer API Reference (QUBO API V2)."

If you use FujitsuDA3Solver, please refer to "Digital Annealer API Reference (QUBO API V3c/V4 for Premium)", "Digital Annealer API Reference (QUBO API V4)", "Digital Annealer API Reference (QUBO API V3c)" or "Digital Annealer API Reference (QUBO API V3)."
If you use FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver, please refer to "Digital Annealer API Reference (QUBO API V2)."

4.2.1. Azure Blob Storage

If you made the contract for QUBO API V4 or QUBO API V3c (Premium-4c, Premium-3c, Developer-4c, Developer-3c, or Developer-4), it is possible to calculate QUBO up to 20GB by using Azure Blob Storage Storage. You have to make the contract for Micorsoft Azure to use Azure Blob Storage. If you use the Azure Blob Storage with Digital Annnealer, the following specification is recommended.

item	value
Performance/Access tires	Standard/Hot or more higher
Redundancy(replication)	Locally redundant storage(LRS) or higher
Region	Japan East

item

value

Performance/Access tires

Standard/Hot or more higher

Redundancy(replication)

Locally redundant storage(LRS) or higher

Region

Japan East

Overview of how to use Azure Blob Storage is as shown below

Upload problem data (QUBO) to Azure Blob Storage

Send a reqauest with specifying Azure Blob Storage storage account and SAS token

Example: Register a job to solve the uploaded problem with QUBO API V4
    Specify the storage account name in X-Storage-Account-Name of the request header.
    Specify the container name in bucket_name of the request body.
    Specify the BLOB SAS token in X-Blob-Sas-Token of the request header.

Storage Account Name: samplestorage
Bucket Name (Container Name): sample
BLOB SAS Token: sp=racwdl&st=2021-07-20T11:58:45Z&se=2021-07-20T19:58:45Z&spr=https&sv=2020-08-04&sr=c&sig=Gf3coiBWO0Y8FrGnw82OI0zBB1jpDTRJF8o%2FdGYNEM0%3D

$ cat sample-qubo.json
{
  "fujitsuDA3": {
    "time_limit_sec": 10
  },
  "object_format": "json",
  "bucket_name": "sample",
  "binary_polynomial_object_name": "sample-binary-polynomial",
  "penalty_binary_polynomial_object_name": "sample-penalty-binary-polynomial"
}

$ curl -v -k -X POST https://api.aispf.global.fujitsu.com/da/v4/async/qubo/solve \
-H 'Content-Type: application/json' \
-H 'X-Access-Token: 6470a9c268cfbe17cd7ad744c12cbc9f0129462aae818156b5224826f4ef0591' \
-H 'X-Storage-Account-Name: samplestorage' \
-H 'X-Blob-Sas-Token: sp=racwdl&st=2021-07-20T11:58:45Z&se=2021-07-20T19:58:45Z&spr=https&sv=2020-08-04&sr=c&sig=Gf3coiBWO0Y8FrGnw82OI0zBB1jpDTRJF8o%2FdGYNEM0%3D' \
-d @sample-qubo.json
{"job_id":"b2374563-3e80-425c-bffb-c6eeeff3c4df-212012224838091"}

Access control using Azure Blob Storage storage account and SAS token
Download problem data (QUBO) from Azure Blob Storage
Send result

Figure 2. Overview of how to use Azure Blob Storage

4.3. Notes

This section describes the points to be noted to use the QUBO APIs.

When a request is issued, even though the wrong parameter name (key) is specified (including spelling errors), the specified parameter is ignored and the process may continue. For this reason, an unexpected processing result may be obtained. Be careful to specify parameters.
A running job cannot be stopped after a synchronous qubo/solve request is issued.
Even though a request is issued by mistake or a process takes a long time, please wait until the process ends.
However, if you use an asynchronous async/qubo/solve request, then you can cancel the job before it is executed (by using async/jobs/cancel).
When a new qubo/solve request is issued during the annealing process performed by Digital Annealer, it waits for the completion of any running annealing processes.
The new request process starts after the completion of the running annealing processes.
When using FujitsuDA3Solver, the calculation time (solve_time) is determined by the value (in seconds) specified in the following parameter that specifies the upper limit of execution time.
- time_limit_sec parameter
When using FujitsuDA2PTSolver, FujitsuDA2Solver, or FujitsuDA2MixedModeSolver, the time required for annealing (anneal_time) is determined by the values specified for the following parameters.
- number_iterations parameter
- number_replicas parameter (for FujitsuDA2PTSolver)
- number_runs parameter (for FujitsuDA2Solver or FujitsuDA2MixedModeSolver)
  Example: In the case of number_iterations = 10000000 and number_runs = 100 Using FujitsuDA2Solver or FujitsuDA2MixedModeSolver: Approximately 5 seconds
  If a value is multiplied by 10, 100, …, anneal_time is also multiplied by 10, 100, … in direct proportion, therefore be careful to specify these values.
If the problem scale (the number of bits) is large, the scaling process, recalculation of energy, and other calculations that use CPU may take some time. The amount of time depends on the setting values that you specified for the solver and parameter.

The following parameters have lower and upper limit values.

Solver	Parameter	Lower Limit	Upper Limit
Solver	Parameter	Lower Limit	Synchronous	Asynchronous
FujitsuDA3Solver	time_limit_sec	1	-	1800
FujitsuDA2PTSolver	number_replicas	26	128	128
	number_iterations	1	2000000000	2000000000
	number_replicas \(\times\)number_iterations	100000	25600000000	256000000000
FujitsuDA2Solver FujitsuDA2MixedModeSolver	number_runs	16	128	128
	number_iterations	1	2000000000	2000000000
	number_runs \(\times\)number_iterations	100000	25600000000	256000000000

The annealing temperature schedule for the FujitsuDA2Solver or FujitsuDA2MixedModeSolver is defined by the following parameters: temperature_decay, temperature_interval, temperature_mode, and temperature_start.
For example, with "number_iterations = 100000" and "temperature_interval = 100" as shown below, the temperature is changed to the temperature calculated in the mode specified with the temperature_mode parameter every 100 searches.
If the number of searches per anneal (number_iterations) is 100000, the temperature is changed 1000 times (the result of \(100000 \div 100\)).
In a cycle of annealing with FujitsuDA2Solver or FujitsuDA2MixedModeSolver, searches are performed the number of times specified with the number_iterations parameter at each temperature specified with the annealing temperature schedule as mentioned above, and the annealing is repeated the number of times specified with the number_runs parameter.
For both parameters, specifying a larger value takes a longer time.
The offset_increase_rate parameter for FujitsuDA2PTSolver, FujitsuDA2Solver or FujitsuDA2MixedModeSolver is used to accelerate searches. If a state transition does not occur due to being trapped by a local solution, this parameter enables the process to increase the energy using the rate specified in offset_increase_rate for each search to improve the probability of a state transition. The energy that is accumulated according to offset_increase_rate is reset if a state transition occurs. To disable the offset_increase_rate parameter, specify 0 (zero).
With the FujitsuDA2Solver or FujitsuDA2MixedModeSolver, to specify at least one of the following parameters, be sure to specify all of the following five parameters and the number_iterations parameter:
- offset_increase_rate
- temperature_decay
- temperature_interval
- temperature_mode
- temperature_start
With the FujitsuDA2Solver or FujitsuDA2MixedModeSolver, the temperature_decay, temperature_interval, and temperature_start parameters are related to the temperature schedule, and optimal solutions can be obtained only if appropriate values are specified, especially for those parameters.
There are countless combinations of parameter values, requiring a tuning operation to search for an appropriate value to obtain an optimal solution.
With the FujitsuDA2PTSolver (using the parallel tempering function), specifying the following parameters is not required, which considerably reduces the time required for tuning.
- noise_model
- temperature_decay
- temperature_interval
- temperature_mode
- temperature_start

5. How to Use the Optimization Solutions APIs

This chapter describes the procedure used to solve combinatorial optimization problems specialized for business.

The Optimization Solutions APIs can only be used in Japan region.

5.1. Warehouse Pickup Optimization API

Warehouse Pickup Optimization API is a Web API service for finding "the shortest route (pickup route: closed circuit)" to retrieve (pick up) specified products from multiple shelves or other areas in a warehouse.

5.1.1. Procedure for Using the API

The following section describes the procedure for finding the pickup route with the shortest distance.

Create a map file
Upload and download a map file
Optimize the pickup route

1. Create a map file

To use the Warehouse Pickup Optimization API, you must create a map file on a client that includes information about the position of shelves and aisles in the warehouse where the pickup is performed (the pickup area).

Things to prepare before creating a map file
- Ground plan of the pickup area (scaled map)
- Position of the shelves on which the products targeted for pickup are located
How to create a map file

Step(1)

In the ground plan (scaled map) of the pickup area, record shelves on which the products targeted for pickup are located, and aisles it is possible to pass through for performing a pickup. (refer to "Example of ground plan of pickup area" in "Figure 2: Map File Creation Examples")

Step(2)

Place a plot point (a unique identification name in each area) on each shelf and point passed through along the aisles recorded in Step(1), and find the coordinates (absolute coordinates) of each plot point.
Plot points are also placed at the intersections of aisles, corners, and other places where the shelves and aisles connect.

Step(3)

Create a map file (.json) based on the coordinates found in Step(2).
The sets of coordinates for each plot point in the area defined as nodes, and the routes between the plot points defined as nodes that it is possible to pass through for performing a pickup are defined as edges. (refer to "Map file creation example 1" in "Figure 2: Map File Creation Examples")
If there are multiple areas, the nodes and edges are defined for each area, and the distances and routes between the areas are defined as cedges. (refer to "Map file creation example 2" in "Figure 2: Map File Creation Examples")
The direction of traffic for the routes defined as edges and cedges (two-way traffic (false) or one-way traffic (true)) is defined with directed.
For details about the data format of the map file, refer to "Digital Annealer API Reference (Warehouse Picup Optimization API)."

Do not use the same name or coordinate more than once for the plot points of shelves and aisles to define the "nodes" and "edges" within each area.
The values of the coordinates defined in the map file is not required to represent the actual distance. It is also possible to use the values of coordinates from a scaled ground plan.

Map file creation is also available for order through Digital Annealer technical service (paid service).

2. Upload and download a map file

Upload a map file created using "POST picking/mapfile." Then download (display) the uploaded map file using "GET picking/mapfile" and check that the map file is registered correctly.
For details about the specification of the API, refer to "Digital Annealer API Reference (Warehouse Picup Optimization API)."

3. Optimize the pickup route

Find the shortest pickup route using "POST picking/showroute."
For details about the specification of the API, refer to "Digital Annealer API Reference (Warehouse Picup Optimization API)."

If shelves (node) that does not exist in the map file are specified int the request, these shelves are excluded from being a target of optimization.
Specifying of the priority ("priority") cannot be omitted. If the prioritize is not required, specify 0 for the priority ("priority").

The total distance ("distance") is expressed in the unit defined for the coordinates of the plot points of the shelves and aisles recorded in the map file.
For example, if the unit of the coordinates is defined as 50 cm, the actual total distance in the response example shown above is \(1672 \times 0.5m = 836m\).

Response example：
{
   "distance": 1672.0,
   "route": [
       {"area": "A1F", "node": "DEPOT"},
       {"area": "A1F", "node": "F52"},
       {"area": "A1F", "node": "F32"},
       {"area": "A1F", "node": "R-4"},
       {"area": "A2F", "node": "R-1"},
       {"area": "A2F", "node": "B46"},
       {"area": "A2F", "node": "A10"},
       {"area": "A2F", "node": "B45"
   ]
}

Figure 3. Map File Creation Examples

Document History

Edition	Date	Modified location	Description
First	January 2020	Whole document	Newly created
Second	January 2021	Whole document	Added descriptions about FujitsuDA3Solver
Third	August 2021	Whole document	Updated descriptions about QUBO API V3
Forth	May 2022	Whole document	Added descriptions about QUBO API V4
Fifth	December 2022	Whole document	Added descriptions about QUBO API V3c
Sixth	June 2023	Whole document	Added descriptions about Premium-3c and Premium-4c
Seventh	July 2023	Whole document	Added descriptions about Developer-3c

Edition

Date

Modified location

Description

First

January 2020

Whole document

Newly created

Second

January 2021

Whole document

Added descriptions about FujitsuDA3Solver

Third

August 2021

Whole document

Updated descriptions about QUBO API V3

Forth

May 2022

Whole document

Added descriptions about QUBO API V4

Fifth

December 2022

Whole document

Added descriptions about QUBO API V3c

Sixth

June 2023

Whole document

Added descriptions about Premium-3c and Premium-4c

Seventh

July 2023

Whole document

Added descriptions about Developer-3c