A 0-1 knapsack problem-based approach for solving open-pit mining problem with type-2 fuzzy parameters

Open-pit mining has several non-deterministic polynomial-time hard (NP-hard) 0-1 knapsack problems. The complexities of these problems are also increased due to some uncertain input parameters. This paper proposed an innovative hybrid fuzzy logic and genetic algorithm-based approach for solving a critical open-pit mining problem. First, the uncertainty of this problem is incorporated within the type-2 fuzzy environment, where the critical value reduction method was used to defuzzify the objective value. Next, genetic algorithm was used to solve the optimisation problem iteratively using a special initial solution generator, unique mutation, refinement, and immigration operations. Some benchmark instances from KPLIB were solved to show the effectiveness of the proposed hybrid fuzzy type-2 and genetic algorithm approach. The benchmark results show the proposed method can generate optimum solutions. Finally, a few OPMP instances from MineLib were solved using the proposed technique to demonstrate the applicability of this research to actual cases under fuzziness. The case study results indicated that the proposed approach can effectively solve the open-pit optimisation problem and similar NP-hard knapsack problems.