Easy Solver Usage

The Easy Solver is a heuristic solver for QUBO/HUBO expressions.

Solving a problem with the Easy Solver consists of the following three steps:

  1. Create an EasySolver object.
  2. Set search options by calling methods of the solver object.
  3. Search for solutions by calling the search() method, which returns a Sol object.

Creating Easy Solver object

To use the Easy Solver, an EasySolver object is constructed with an expression as follows:

  • EasySolver(f)

Here, f is the expression to be solved. It must be simplified as a binary expression in advance by calling simplify_as_binary().

Setting Easy Solver Options

  • time_limit(time): Specifies the time limit in seconds. The default value is 10.0 seconds. If the time limit is set to 0, the solver never terminates due to the time limit.
  • target_energy(energy): Specifies the target energy. The solver terminates when a solution with energy less than or equal to the target is found.
  • callback(func): Sets a callback function that is called when a new best solution is found. The callback receives two arguments: energy (int) and tts (float, time to solution in seconds).
  • thread_count(n): Sets the number of threads.

Searching Solutions

The Easy Solver searches for solutions by calling the search() method.

Program Example

The following program searches for a solution to the Low Autocorrelation Binary Sequences (LABS) problem using the Easy Solver:

from pyqbpp import var, expr, sqr, EasySolver

size = 100
x = var("x", size)
f = expr()
for d in range(1, size):
    temp = expr()
    for i in range(size - d):
        temp += (2 * x[i] - 1) * (2 * x[i + d] - 1)
    f += sqr(temp)
f.simplify_as_binary()

solver = EasySolver(f)
solver.time_limit(5.0)
solver.target_energy(900)
solver.callback(lambda energy, tts: print(f"TTS = {tts:.3f}s Energy = {energy}"))
sol = solver.search()
bits = "".join("-" if sol.get(i) == 0 else "+" for i in range(size))
print(f"{sol.energy()}: {bits}")

In this example, the following options are set:

  • a 5.0-second time limit,
  • a target energy of 900, and
  • a callback that prints the energy and TTS whenever a new best solution is found.

Therefore, the solver terminates either when the elapsed time reaches 5.0 seconds or when a solution with energy 900 or less is found.

For example, this program produces the following output:

TTS = 0.000s Energy = 300162
TTS = 0.000s Energy = 273350
...
TTS = 2.691s Energy = 898
898: ++-++-----+--+--++++++---++-+-+--++-------++-++-+-+-+-+-++-++++-++-+++++-+-+--++++++---+++--+++---++

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