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| Original file line number | Diff line number | Diff line change |
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| #' Clique partitioning algorithms | ||
| #' | ||
| #' @description | ||
| #' These functions create a vector of nodes' memberships in | ||
| #' cliques: | ||
| #' | ||
| #' - `node_roulette()` assigns nodes to maximally diverse groups. | ||
| #' | ||
| #' @section Maximally diverse grouping problem: | ||
| #' This well known computational problem is a NP-hard problem | ||
| #' with a number of relevant applications, | ||
| #' including the formation of groups of students that have encountered | ||
| #' each other least or least recently. | ||
| #' Essentially, the aim is to return a membership of nodes in cliques | ||
| #' that minimises the sum of their previous (weighted) ties: | ||
| #' | ||
| #' \deqn{\sum_{g=1}^{m} \sum_{i=1}^{n-1} \sum_{j=i+1}^{n} x_{ij} y_{ig} y_{jg}} | ||
| #' | ||
| #' where \eqn{y_{ig} = 1} if node \eqn{i} is in group \eqn{g}, and 0 otherwise. | ||
| #' | ||
| #' \eqn{x_{ij}} is the existing network data. | ||
| #' If this is an empty network, the function will just return cliques. | ||
| #' To run this repeatedly, one can join a clique network of the membership result | ||
| #' with the original network, using this as the network data for the next round. | ||
| #' | ||
| #' A form of the Lai and Hao (2016) iterated maxima search (IMS) is used here. | ||
| #' This performs well for small and moderately sized networks. | ||
| #' It includes both weak and strong perturbations to an initial solution | ||
| #' to ensure that a robust solution from the broader state space is identified. | ||
| #' The user is referred to Lai and Hao (2016) and Lai et al (2021) for more details. | ||
| #' @inheritParams cohesion | ||
| #' @name cliques | ||
| #' @family memberships | ||
| NULL | ||
|
|
||
| #' @rdname cliques | ||
| #' @param num_groups An integer indicating the number of groups desired. | ||
| #' @param group_size An integer indicating the desired size of most of the groups. | ||
| #' Note that if the number of nodes is not divisible into groups of equal size, | ||
| #' there may be some larger or smaller groups. | ||
| #' @param times An integer of the number of search iterations the algorithm should complete. | ||
| #' By default this is the number of nodes in the network multiplied by the number of groups. | ||
| #' This heuristic may be insufficient for small networks and numbers of groups, | ||
| #' and burdensome for large networks and numbers of groups, but can be overwritten. | ||
| #' At every 10th iteration, a stronger perturbation of a number of successive changes, | ||
| #' approximately the number of nodes divided by the number of groups, | ||
| #' will take place irrespective of whether it improves the objective function. | ||
| #' @references | ||
| #' Lai, Xiangjing, and Jin-Kao Hao. 2016. | ||
| #' “Iterated Maxima Search for the Maximally Diverse Grouping Problem.” | ||
| #' _European Journal of Operational Research_ 254(3):780–800. | ||
| #' \doi{10.1016/j.ejor.2016.05.018}. | ||
| #' | ||
| #' Lai, Xiangjing, Jin-Kao Hao, Zhang-Hua Fu, and Dong Yue. 2021. | ||
| #' “Neighborhood Decomposition Based Variable Neighborhood Search and Tabu Search for Maximally Diverse Grouping.” | ||
| #' _European Journal of Operational Research_ 289(3):1067–86. | ||
| #' \doi{10.1016/j.ejor.2020.07.048}. | ||
| #' @export | ||
| node_roulette <- function(.data, num_groups, group_size, times = NULL){ | ||
| if(missing(num_groups) & missing(group_size)){ | ||
| stop(paste("Either `num_groups` must indicate number of groups desired", | ||
| "or `group_size` must indicate the desired average size of groups.")) | ||
| } | ||
| n <- manynet::network_nodes(.data) | ||
| my_vec <- sample(seq.int(n)) | ||
| # Initial partition | ||
| if(!missing(num_groups)){ | ||
| out <- cut(seq_along(my_vec), num_groups, labels = FALSE)[my_vec] | ||
| } else { | ||
| out <- ceiling(seq_along(my_vec) / group_size)[my_vec] | ||
| } | ||
| if(is.null(times)) times <- n * max(out) | ||
| # Get fitness | ||
| mat <- manynet::as_matrix(.data) | ||
| fit <- sum(.to_cliques(out) * mat) | ||
| soln <- out | ||
| for(t in seq.int(times)){ | ||
| soln <- .weakPerturb(soln) | ||
| new_fit <- sum(.to_cliques(soln) * mat) | ||
| if(new_fit < fit){ | ||
| out <- soln | ||
| fit <- new_fit | ||
| } | ||
| if(t %% 10) soln <- .strongPerturb(soln) | ||
| } | ||
| make_node_member(out, .data) | ||
| } | ||
|
|
||
| .to_cliques <- function(member){ | ||
| (member == t(matrix(member, length(member), length(member))))*1 | ||
| } | ||
|
|
||
| .weakPerturb <- function(soln){ | ||
| gsizes <- table(soln) | ||
| evens <- all(gsizes == max(gsizes)) | ||
| if(evens){ | ||
| soln <- .swapMove(soln) | ||
| } else { | ||
| if(stats::runif(1)<0.5) soln <- .swapMove(soln) else | ||
| soln <- .oneMove(soln) | ||
| } | ||
| soln | ||
| } | ||
|
|
||
| .swapMove <- function(soln){ | ||
| from <- sample(seq.int(length(soln)), 1) | ||
| to <- sample(which(soln != soln[from]), 1) | ||
| soln[c(to,from)] <- soln[c(from,to)] | ||
| soln | ||
| } | ||
|
|
||
| .oneMove <- function(soln){ | ||
| gsizes <- table(soln) | ||
| maxg <- which(gsizes == max(gsizes)) | ||
| from <- sample(which(soln %in% maxg), 1) | ||
| soln[from] <- sample(which(gsizes != max(gsizes)), 1) | ||
| soln | ||
| } | ||
|
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| .strongPerturb <- function(soln, strength = 1){ | ||
| times <- ceiling(strength * length(soln)/max(soln)) | ||
| for (t in seq.int(times)){ | ||
| soln <- .weakPerturb(soln) | ||
| } | ||
| soln | ||
| } | ||
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