My assignment is to use local search heuristics to solve the Multidimensional multiple-choice knapsack problem, but to do so I first need to find a feasible solution to start with. Here is an example problem with what I tried so far. Problem R1 R2 R3 RESOUCES : 8 8 8 GROUPS: G1: 11.0 3 2 2 12.0 1 1 3 G2: 20.0 1 1 3 5.0 2 3 2 G3: 10.0 2 2 3 30.0 1 1 3 Sorting strategies To find a starting feasible solution for my local search I decided to ignore maximization of gains and just try to fit the resources requirements. I decided to sort the choices (strategies) in each group by comparing their "distance" from the multidimensional space origin, thus calculating SQRT(R1^2 + R2^2 + ... + RN^2). I felt like this was a keen solution as it somehow privileged those choices with resouce usages closer to each other (e.g. R1:2 R2:2 R3:2 < R1:1 R2:2 R3:3) even if the total sum is the same. Doing so and selecting the best choice from each group proved sufficent to find a feasible solution for many[30] different benchmark problems, but of course I knew it was just luck. So I came up with the problem presented above which sorts like this: R1 R2 R3 RESOUCES : 8 8 8 GROUPS: G1: 12.0 1 1 3 < select this 11.0 3 2 2 G2: 20.0 1 1 3 < select this 5.0 2 3 2 G3: 30.0 1 1 3 < select this 10.0 2 2 3 And it is not feasible because the resources consmption is R1:3, R2:3, R3:9. The easy solution is to pick one of the second best choices in group 1 or 2, so I'll need some kind of iteration (local search[?]) to find the starting feasible solution for my local search solution. Here are the options I came up with Option 1: iterate choices I tried to find a way to iterate all the choices with a specific order, something like G1 G2 G3 1 1 1 2 1 1 1 2 1 1 1 2 2 2 1 ... believeng that feasible solutions won't be that far away from the unfeasible one I start with and thus the number of iterations will keep quite low. Does this make any sense? If yes, how can I iterate the choices (grouped combinations) of each group keeping "as near as possibile" to the previous iteration? Option 2: Change the comparation term I tried to think how to find a better variable to sort the choices on. I thought at a measure of how "precious" a resource is based on supply and demand, so that an higer demand of a more precious resource will push you down the list, but this didn't help at all. Also I thought there probably isn't gonna be such a comparsion variable which assures me a feasible solution at first strike. I there such a variable? If not, is there a better sorting criteria anyways? Option 3: implement any known sub-optimal fast solving algorithm Unfortunately I could not find any of such algorithms online. Any suggestion?