ABS3 Solver Usage

Solving an expression f using the ABS3 Solver involves the following three steps:

1. Create an ABS3 Solver (or qbpp::abs3::ABS3Solver) object for the expression f.
2. Create a parameter object (or qbpp::abs3::Params) and set the options for solution search.
3. Call the search() member function of the ABS3 Solver object, which returns the obtained solution.

Solving LABS problem using the ABS3 Solver

The following QUBO++ program solves the Low Autocorrelation Binary Sequence (LABS) problem using the ABS3 Solver:

#include "qbpp.hpp"
#include "qbpp_abs3_solver.hpp"

int main() {
  const size_t size = 100;
  auto x = qbpp::var("x", size);
  auto f = qbpp::expr();
  for (size_t d = 1; d < size; ++d) {
    auto temp = qbpp::expr();
    for (size_t i = 0; i < size - d; ++i) {
      temp += (2 * x[i] - 1) * (2 * x[i + d] - 1);
    }
    f += qbpp::sqr(temp);
  }
  f.simplify_as_binary();

  auto solver = qbpp::abs3::ABS3Solver(f);
  auto params = qbpp::abs3::Params();
  params("time_limit", "10.0");
  params("enable_callback", "1");

  auto sol = solver.search(params);
  std::cout << sol.energy() << ": ";
  for (auto val : sol(x)) {
    std::cout << (val == 0 ? "-" : "+");
  }
  std::cout << std::endl;
}

In this program, an ABS3 Solver object solver is first created for the expression f. Next, a parameter object params is created, and the options time_limit and enable_callback are set. The time_limit option specifies the maximum search time in seconds, while enable_callback enables a callback function that reports newly found best solutions during the search. The search() member function of the solver is then invoked with params as its argument. This function returns the best solution found within the given time limit, which is stored in sol.

The program prints the energy of the solution and the corresponding binary sequence, where “+” represents 1 and “-“ represents 0.

This program produces the following output:

TTS = 0.002s Energy = 1218
TTS = 0.002s Energy = 1170
TTS = 0.002s Energy = 994
TTS = 0.015s Energy = 958
TTS = 0.018s Energy = 922
TTS = 0.034s Energy = 874
TTS = 4.364s Energy = 834
834: -+--+---++-++-+---++-++--+++--+-+-+++++----+++-+-+---++-+--+-----+--+----++----+-+--++++++---+------

ABS3 Solver object

An ABS3 Solver (or qbpp::abs3::ABS3Solver) object is created for a given expression. When the solver object is constructed, the expression is converted into an internal data format and loaded into GPU memory. Therefore, the number of GPU devices to be used can be specified as a second argument:

• qbpp::abs3::ABS3Solver(expression, device_count) If device_count is omitted, all available GPUs are used by default.

A parameter object (or qbpp::abs3::Params) stores the options used by the ABS3 Solver during solution search. Each option is specified as a key–value pair of strings. In the example above:

• params("time_limit", "10.0") sets the time limit to 10.0 seconds.
• params("enable_callback", "1") enables the callback function, which reports the energy of newly obtained solutions.

ABS3 Parameters

A parameter (or qbpp::abs3::Param()) object stores parameter options used when the ABS3 Solver searches a solution. Options consists of the key and the value as strings. In the program above, params("time_limit", "10.0") set the time limit to 10.0 seconds and params("enable_callback", "1") enables the callback function, which displays the energy of newly obtained solution.

Basic Options

Advanced Options