A new class of hard problem instances for the 0–1 knapsack problem

The 0–1 knapsack problem is an important optimization problem, because it arises as a special case of wide variety problems and has been generalized in several ways. Decades research have resulted very powerful algorithms that can solve large instances involving thousands decision variables short amount time. Current the literature no longer challenge these algorithms. However, hard are to demonstrate strengths weaknesses this knowledge turn be used create better performing In paper, we propose new class for provide theoretical support helps explain why optimality. A dataset 3240 was generated subsequently solved on supercomputer, using approximately 810 CPU-hours. analysis obtained results shows which extent different parameters influence hardness instances. This also demonstrates proposed lot harder than previously known hardest instances, despite being much smaller.