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Bruteforce.php
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Bruteforce.php
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<?php
namespace Graphp\Algorithms\TravelingSalesmanProblem;
use Fhaculty\Graph\Exception\UnexpectedValueException;
use Fhaculty\Graph\Exception\UnderflowException;
use Fhaculty\Graph\Graph;
use Fhaculty\Graph\Vertex;
use Fhaculty\Graph\Set\Edges;
use Graphp\Algorithms\TravelingSalesmanProblem\MinimumSpanningTree as AlgorithmTspMst;
class Bruteforce extends Base
{
/**
*
* @var Graph
*/
private $graph;
/**
* best weight so for (used for branch-and-bound)
*
* @var number|NULL
*/
private $bestWeight;
/**
* reference to start vertex
*
* @var Vertex
*/
private $startVertex;
/**
* total number of edges needed
*
* @var int
*/
private $numEdges;
/**
* upper limit to use for branch-and-bound (BNB)
*
* @var float|NULL
* @see AlgorithmTspBruteforce::setUpperLimit()
*/
private $upperLimit = NULL;
/**
* whether to use branch-and-bound
*
* simply put, there's no valid reason why anybody would want to turn off this flag
*
* @var boolean
*/
private $branchAndBound = true;
/**
*
* @param Graph $graph
*/
public function __construct(Graph $graph)
{
$this->graph = $graph;
}
/**
* explicitly set upper limit to use for branch-and-bound
*
* this method can be used to optimize the algorithm by providing an upper
* bound of when to stop branching any further.
*
* @param double $limit
* @return AlgorithmTspBruteforce $this (chainable)
*/
public function setUpperLimit($limit)
{
$this->upperLimit = $limit;
return $this;
}
public function setUpperLimitMst()
{
$alg = new AlgorithmTspMst($this->graph);
$limit = $alg->createGraph()->getWeight();
return $this->setUpperLimit($limit);
}
protected function getVertexStart()
{
// actual start doesn't really matter as we're only considering complete graphs here
return $this->graph->getVertices()->getVertexFirst();
}
protected function getGraph()
{
return $this->graph;
}
/**
* get resulting (first) best circle of edges connecting all vertices
*
* @throws Exception on error
* @return Edges
*/
public function getEdges()
{
$this->numEdges = count($this->graph->getVertices());
if ($this->numEdges < 3) {
throw new UnderflowException('Needs at least 3 vertices');
}
// numEdges 3-12 should work
$this->bestWeight = $this->upperLimit;
$this->startVertex = $this->getVertexStart();
$result = $this->step($this->startVertex,
0,
array(),
array()
);
if ($result === NULL) {
throw new UnexpectedValueException('No resulting solution for TSP found');
}
return new Edges($result);
}
/**
*
* @param Vertex $vertex current point-of-view
* @param number $totalWeight total weight (so far)
* @param boolean[] $visitedVertices
* @param Edge[] $visitedEdges
* @return Edge[]
*/
private function step(Vertex $vertex, $totalWeight, array $visitedVertices, array $visitedEdges)
{
// stop recursion if best result is exceeded (branch and bound)
if ($this->branchAndBound && $this->bestWeight !== NULL && $totalWeight >= $this->bestWeight) {
return NULL;
}
// kreis geschlossen am Ende
if ($vertex === $this->startVertex && count($visitedEdges) === $this->numEdges) {
// new best result
$this->bestWeight = $totalWeight;
return $visitedEdges;
}
// only visit each vertex once
if (isset($visitedVertices[$vertex->getId()])) {
return NULL;
}
$visitedVertices[$vertex->getId()] = true;
$bestResult = NULL;
// weiter verzweigen in alle vertices
foreach ($vertex->getEdgesOut() as $edge) {
// get target vertex of this edge
$target = $edge->getVertexToFrom($vertex);
$weight = $edge->getWeight();
if ($weight < 0) {
throw new UnexpectedValueException('Edge with negative weight "' . $weight . '" not supported');
}
$result = $this->step($target,
$totalWeight + $weight,
$visitedVertices,
array_merge($visitedEdges, array($edge))
);
// new result found
if ($result !== NULL) {
// branch and bound enabled (default): returned result MUST be the new best result
if($this->branchAndBound ||
// this is the first result, just use it anyway
$bestResult === NULL ||
// this is the new best result
$this->sumEdges($result) < $this->sumEdges($bestResult)){
$bestResult = $result;
}
}
}
return $bestResult;
}
/**
* get sum of weight of given edges
*
* no need to optimize this further, as it's only evaluated if branchAndBound is disabled and
* there's no valid reason why anybody would want to do so.
*
* @param Edge[] $edges
* @return float
*/
private function sumEdges(array $edges)
{
$sum = 0;
foreach ($edges as $edge) {
$sum += $edge->getWeight();
}
return $sum;
}
}