Optimizing a Tri-objective Fuzzy Agricultural Food Load Planning Problem for Point-to-point Short-haul Road Transportation with a Pareto-based Discrete Firefly Algorithm

In this paper, we define the mathematical model of a tri-objective fuzzy agricultural food load planning problem, which is a blend of the multi-objective optimization, the multidimensional knapsack problem, and the multiple knapsack problem under fuzziness. For the imprecise model, profit and shelf life for each agricultural food product are fuzzified and represented by triangular fuzzy numbers, and then defuzzified by the graded mean integration representation method. To solve this problem, we develop a pareto-based discrete firefly algorithm. In this algorithm, both the initial configuration and movements of fireflies are redefined. Meanwhile, a two-phase repair operator is proposed to guarantee the feasibility and quality of solutions. The (μ+λ)-PAES (Pareto Archived Evolution Strategy) with a 3-dimensional adaptive grid algorithm is adopted to optimize the population of fireflies. Finally, the effectiveness of the proposed algorithm is evaluated based on 14 problem instances.