Has anyone used the mmKnapsack function from the FLSSS R package, and received sub-optimal solutions?

Question

I've just tried using the mmKnapsack function to solve a multi-dimensional knapsack problem in R. I noticed that the solution seemed a bit suspect, so I tried a very simple 2-d problem:the 2-d problem. It returned an optimal profit of 720, which I can easily see is not the optimal profit of the 2-d problem(the optimal profit is 740). It returns a solution of items 2 and 1 as shown here, but the optimal solution is items 1, 4 and 6. Here is the code I ran

Answer 1

Probably it just depends on the argument len of the function. For example, if I run the following code

# packages
library(FLSSS)

# data
prof <- c(400, 320, 230, 210, 190, 130)
costs <- cbind(
  c(6, 3, 2, 2, 2, 1), 
  c(8, 8, 7, 6, 5, 4)
)

capac <- c(9, 18)

then I get your current optimal sack

mmKnapsack(
  maxCore = 3, 
  len = 2, 
  itemsProfits = prof, 
  itemsCosts = costs, 
  capacities = capac
)
#> Updated profit = 720
#> $solution
#> [1] 2 1
#> 
#> $selectionCosts
#> [1]  9 16
#> 
#> $budgets
#> [1]  9 18
#> 
#> $selectionProfit
#> [1] 720
#> 
#> $unconstrainedMaxProfit
#> [1] 720

but if I increase the maximum subsize size (i.e. please note that I set len = 3), the I get another optimal solution.

mmKnapsack(
  maxCore = 3, 
  len = 3, 
  itemsProfits = prof, 
  itemsCosts = costs, 
  capacities = capac
)
#> Updated profit = 630
#> Updated profit = 660
#> Updated profit = 720
#> Updated profit = 740
#> $solution
#> [1] 6 4 1
#> 
#> $selectionCosts
#> [1]  9 18
#> 
#> $budgets
#> [1]  9 18
#> 
#> $selectionProfit
#> [1] 740
#> 
#> $unconstrainedMaxProfit
#> [1] 950

^{Created on 2020-03-19 by the reprex package (v0.3.0)}

From the package docs you can read that if you set len = 0, then FLSSS function tries to look for the optimal solution for all subset sizes, i.e.

mmKnapsack(
  maxCore = 3, 
  len = 0, 
  itemsProfits = prof, 
  itemsCosts = costs, 
  capacities = capac
)
#> Updated profit = 630
#> Updated profit = 740
#> $solution
#> [1] 1 4 6
#> 
#> $selectionCosts
#> [1]  9 18
#> 
#> $budgets
#> [1]  9 18
#> 
#> $selectionProfit
#> [1] 740
#> 
#> $unconstrainedMaxProfit
#> [1] NA

^{Created on 2020-03-19 by the reprex package (v0.3.0)}