# SCIP

Solving Constraint Integer Programs

nodesel_uct.c File Reference

## Detailed Description

uct node selector which balances exploration and exploitation by considering node visits

the UCT node selection rule selects the next leaf according to a mixed score of the node's actual lower bound and the number of times it has been visited so far compared to its parent node.

The idea of UCT node selection for MIP appeared in: Ashish Sabharwal and Horst Samulowitz Guiding Combinatorial Optimization with UCT (2011)

The authors adapted a game-tree exploration scheme called UCB to MIP trees. Starting from the root node as current node, the algorithm selects the current node's child $$N_i$$ which maximizes the UCT score

$$\mbox{score}(N_i) := -\mbox{estimate}_{N_i} + \mbox{weight} \cdot \frac{\mbox{visits}(\mbox{parent}(N_i))}{\mbox{visits}(N_i)}$$

where $$\mbox{estimate}$$ is the node's lower bound normalized by the root lower bound, and $$\mbox{visits}$$ denotes the number of times a leaf in the subtree rooted at this node has been explored so far.

The selected node in the sense of the SCIP node selection is the leaf reached by the above criterion.

The authors suggest that this node selection rule is particularly useful at the beginning of the solving process, but to switch to a different node selection after a number of nodes has been explored to reduce computational overhead. Our implementation uses only information available from the original SCIP tree which does not support the forward path mechanism needed for the most efficient node selection. Instead, the algorithm selects the next leaf by looping over all leaves and comparing the best leaf found so far with the next one. Two leaves l_1, l_2 are compared by following their paths back upwards until their deepest common ancestor $$a$$ is reached, together with the two children of $$a$$ representing the two paths to l_1, l_2. The leaf represented by the child of $$a$$ with higher UCT score is a candidate for the next selected leaf.

The node selector features several parameters:

the nodelimit delimits the number of explored nodes before UCT selection is turned off the weight parameter changes the relevance of the visits quotient in the UCT score (see above score formula) useestimate determines whether the node's estimate or lower bound is taken as estimate

Note
It should be avoided to switch to uct node selection after the branch and bound process has begun because the central UCT score information how often a path was taken is not collected if UCT is inactive. A safe use of UCT is to switch it on before SCIP starts optimization.

Definition in file nodesel_uct.c.

#include "blockmemshell/memory.h"
#include "scip/nodesel_uct.h"
#include "scip/pub_message.h"
#include "scip/pub_nodesel.h"
#include "scip/pub_tree.h"
#include "scip/scip_mem.h"
#include "scip/scip_message.h"
#include "scip/scip_nodesel.h"
#include "scip/scip_numerics.h"
#include "scip/scip_param.h"
#include "scip/scip_solvingstats.h"
#include "scip/scip_tree.h"
#include <string.h>

Go to the source code of this file.

## Macros

#define NODESEL_NAME   "uct"

#define NODESEL_DESC   "node selector which balances exploration and exploitation "

#define NODESEL_STDPRIORITY   10

#define NODESEL_MEMSAVEPRIORITY   0

#define DEFAULT_WEIGHT   0.1

#define DEFAULT_NODELIMIT   31

#define DEFAULT_USEESTIMATE   FALSE

#define INITIALSIZE   1024

#define MAXNODELIMIT   1000000

## Functions

static int nodeGetVisits (SCIP_NODESELDATA *nodeseldata, SCIP_NODE *node)

static void updateVisits (SCIP_NODESELDATA *nodeseldata, SCIP_NODE *node)

static SCIP_RETCODE turnoffNodeSelector (SCIP *scip, SCIP_NODESEL *nodesel)

static SCIP_Real nodeGetUctScore (SCIP *scip, SCIP_NODE *node, SCIP_NODESELDATA *nodeseldata)

static int compareNodes (SCIP *scip, SCIP_NODESELDATA *nodeseldata, SCIP_NODE *node1, SCIP_NODE *node2)

static void selectBestNode (SCIP *scip, SCIP_NODE **selnode, SCIP_NODESELDATA *nodeseldata, SCIP_NODE **nodes, int nnodes)

static SCIP_RETCODE ensureMemorySize (SCIP *scip, SCIP_NODESELDATA *nodeseldata)

static SCIP_DECL_NODESELCOPY (nodeselCopyUct)

static SCIP_DECL_NODESELINITSOL (nodeselInitsolUct)

static SCIP_DECL_NODESELEXITSOL (nodeselExitsolUct)

static SCIP_DECL_NODESELFREE (nodeselFreeUct)

static SCIP_DECL_NODESELSELECT (nodeselSelectUct)

static SCIP_DECL_NODESELCOMP (nodeselCompUct)

SCIP_RETCODE SCIPincludeNodeselUct (SCIP *scip)

## ◆ NODESEL_NAME

 #define NODESEL_NAME   "uct"

Definition at line 74 of file nodesel_uct.c.

Referenced by SCIP_DECL_NODESELSELECT(), and SCIPincludeNodeselUct().

## ◆ NODESEL_DESC

 #define NODESEL_DESC   "node selector which balances exploration and exploitation "

Definition at line 75 of file nodesel_uct.c.

Referenced by SCIPincludeNodeselUct().

## ◆ NODESEL_STDPRIORITY

 #define NODESEL_STDPRIORITY   10

Definition at line 76 of file nodesel_uct.c.

Referenced by SCIPincludeNodeselUct().

## ◆ NODESEL_MEMSAVEPRIORITY

 #define NODESEL_MEMSAVEPRIORITY   0

Definition at line 77 of file nodesel_uct.c.

Referenced by SCIPincludeNodeselUct().

## ◆ DEFAULT_WEIGHT

 #define DEFAULT_WEIGHT   0.1

default values for user parameters weight of node visits in UCT score

Definition at line 80 of file nodesel_uct.c.

Referenced by SCIPincludeNodeselUct().

## ◆ DEFAULT_NODELIMIT

 #define DEFAULT_NODELIMIT   31

limit of node selections after which UCT node selection is turned off

Definition at line 81 of file nodesel_uct.c.

Referenced by SCIPincludeNodeselUct().

## ◆ DEFAULT_USEESTIMATE

 #define DEFAULT_USEESTIMATE   FALSE

should the estimate (TRUE) or the lower bound of a node be used for UCT score?

Definition at line 82 of file nodesel_uct.c.

Referenced by SCIPincludeNodeselUct().

## ◆ INITIALSIZE

 #define INITIALSIZE   1024

initial size of node visits array (increased dynamically if required)

Definition at line 83 of file nodesel_uct.c.

Referenced by ensureMemorySize().

## ◆ MAXNODELIMIT

 #define MAXNODELIMIT   1000000

the maximum value for user parameter nodelimit

Definition at line 84 of file nodesel_uct.c.

Referenced by SCIPincludeNodeselUct().

## ◆ nodeGetVisits()

 static int nodeGetVisits ( SCIP_NODESELDATA * nodeseldata, SCIP_NODE * node )
static

get the number times node has been visited so far

Parameters
 nodeseldata node selector data node the node in question

Definition at line 107 of file nodesel_uct.c.

References NULL, and SCIPnodeGetNumber().

Referenced by nodeGetUctScore().

## ◆ updateVisits()

 static void updateVisits ( SCIP_NODESELDATA * nodeseldata, SCIP_NODE * node )
static

increases the visits counter along the path from node to the root node

Parameters
 nodeseldata node selector data node leaf node of path along which the visits are backpropagated

Definition at line 129 of file nodesel_uct.c.

References NULL, SCIPnodeGetDepth(), SCIPnodeGetNumber(), and SCIPnodeGetParent().

Referenced by SCIP_DECL_NODESELSELECT().

## ◆ turnoffNodeSelector()

 static SCIP_RETCODE turnoffNodeSelector ( SCIP * scip, SCIP_NODESEL * nodesel )
static

switches to a different node selection rule by assigning the lowest priority of all node selectors to uct

Parameters
 scip SCIP data structure nodesel the node selector to be turned off

Definition at line 159 of file nodesel_uct.c.

Referenced by SCIP_DECL_NODESELSELECT().

## ◆ nodeGetUctScore()

 static SCIP_Real nodeGetUctScore ( SCIP * scip, SCIP_NODE * node, SCIP_NODESELDATA * nodeseldata )
static

returns UCT score of node; the UCT score is a mixture of the node's lower bound or estimate and the number of times it has been visited so far in relation with the number of times its parent has been visited so far

Parameters
 scip SCIP data structure node the node for which UCT score is requested nodeseldata node selector data

Definition at line 192 of file nodesel_uct.c.

Referenced by compareNodes().

## ◆ compareNodes()

 static int compareNodes ( SCIP * scip, SCIP_NODESELDATA * nodeseldata, SCIP_NODE * node1, SCIP_NODE * node2 )
static

compares two leaf nodes by comparing the UCT scores of the two children of their deepest common ancestor

Parameters
 scip SCIP data structure nodeseldata node selector data node1 first node for comparison node2 second node for comparisons

Definition at line 244 of file nodesel_uct.c.

Referenced by selectBestNode().

## ◆ selectBestNode()

 static void selectBestNode ( SCIP * scip, SCIP_NODE ** selnode, SCIP_NODESELDATA * nodeseldata, SCIP_NODE ** nodes, int nnodes )
static

selects the best node among nodes with respect to UCT score

Parameters
 scip SCIP data structure selnode pointer to store the selected node, needs not be empty nodeseldata node selector data nodes array of nodes to select from nnodes size of the nodes array

Definition at line 297 of file nodesel_uct.c.

References compareNodes(), nnodes, and NULL.

Referenced by SCIP_DECL_NODESELSELECT().

## ◆ ensureMemorySize()

 static SCIP_RETCODE ensureMemorySize ( SCIP * scip, SCIP_NODESELDATA * nodeseldata )
static

keeps visits array large enough to save visits for all nodes in the branch and bound tree

Parameters
 scip SCIP data structure nodeseldata node selector data

Definition at line 326 of file nodesel_uct.c.

Referenced by SCIP_DECL_NODESELSELECT().

## ◆ SCIP_DECL_NODESELCOPY()

 static SCIP_DECL_NODESELCOPY ( nodeselCopyUct )
static

copy method for node selector plugins (called when SCIP copies plugins)

Definition at line 366 of file nodesel_uct.c.

References NULL, SCIP_CALL, SCIP_OKAY, and SCIPincludeNodeselUct().

## ◆ SCIP_DECL_NODESELINITSOL()

 static SCIP_DECL_NODESELINITSOL ( nodeselInitsolUct )
static

solving process initialization method of node selector (called when branch and bound process is about to begin)

Definition at line 376 of file nodesel_uct.c.

References NULL, SCIP_OKAY, SCIPnodeselGetData(), and SCIPnodeselGetStdPriority().

## ◆ SCIP_DECL_NODESELEXITSOL()

 static SCIP_DECL_NODESELEXITSOL ( nodeselExitsolUct )
static

solving process deinitialization method of node selector (called when branch and bound process data gets freed)

Definition at line 394 of file nodesel_uct.c.

## ◆ SCIP_DECL_NODESELFREE()

 static SCIP_DECL_NODESELFREE ( nodeselFreeUct )
static

destructor of node selector to free user data (called when SCIP is exiting)

Definition at line 420 of file nodesel_uct.c.

## ◆ SCIP_DECL_NODESELSELECT()

 static SCIP_DECL_NODESELSELECT ( nodeselSelectUct )
static

node selection method of node selector

Definition at line 441 of file nodesel_uct.c.

## ◆ SCIP_DECL_NODESELCOMP()

 static SCIP_DECL_NODESELCOMP ( nodeselCompUct )
static

node comparison method of UCT node selector

Definition at line 508 of file nodesel_uct.c.

References SCIP_Real, SCIPisGT(), SCIPisLT(), and SCIPnodeGetLowerbound().