Differential Evolution Algorithm for Multilevel Assignment Problem: A Case Study in Chicken Transportation

Abstract

This study aims to solve the real-world multistage assignment problem. The proposed problem is composed of two stages of assignment: (1) different types of trucks are assigned to chicken farms to transport young chickens to egg farms, and (2) chicken farms are assigned to egg farms. Assigning different trucks to the egg farms and different egg farms to the chicken farms generates different costs and consumes different resources. The distance and the idle space in the truck have to be minimized, while constraints such as the minimum number of chickens needed for all egg farms and the longest time that chickens can be in the truck remain. This makes the problem a special case of the multistage assignment (S-MSA) problem. A mathematical model representing the problem was developed and solved to optimality using Lingo v.11 optimization software. Lingo v.11 can solve to optimality only small- and medium-sized test instances. To solve large-sized test instances, the differential evolution (DE) algorithm was designed. An excellent decoding method was developed to increase the search performance of DE. The proposed algorithm was tested with three randomly generated datasets (small, medium, and large test instances) and one real case study. Each dataset is composed of 12 problems, therefore we tested with 37 instances, including the case study. The results show that for small- and medium-sized test instances, DE has 0.03% and 0.05% higher cost than Lingo v.11. For large test instances, DE has 3.52% lower cost than Lingo v.11. Lingo v.11 uses an average computation time of 5.8, 103, and 4320 s for small, medium and large test instances, while DE uses 0.86, 1.68, and 8.79 s, which is, at most, 491 times less than Lingo v.11. Therefore, the proposed heuristics are an effective algorithm that can find a good solution while using less computation time.

Solving a Special Case of the Generalized Assignment Problem Using the Modified Differential Evolution Algorithms: A Case Study in Sugarcane Harvesting

“…One of these five methods is the differential evolution algorithm and the other four are modified differential evolution algorithms MDE-1, MDE-2, MDE-3, and MDE-4. MDE-1 uses Equations (12)- (14) to generate the mutation vector, which is the product of BV-vectors, RV-vectors, and TV-vectors, instead of using only TV-vector, like the original DE. The probability of using the best vector (BV), the random vector (RV), and the target vector (TV) in the mutation process employs the idea of the attractiveness of each group of vectors.…”

“…In this paper, Equation 12is modified so that, instead of randomly selected vectors from the set of target vectors as stated in the proposed heuristic, the random vectors can come from three sets of vectors, which are (1) the set of target vectors (TV-vectors), (2) the set of best vectors (BV-vectors), and (3) the set of random vectors (RV-vectors). Equations (13) and (14) are both used to calculate the probability of selecting the set of vectors.…”

“…Comparing our problem to Kaewman et al [14], this article proposes the multi-level assignment problem. The young chicken farm has been assigned to deliver the chicken to the egg farm (to feed the young chicken and collect the eggs from it to sell).…”

Modified Differential Evolution Algorithm for U-Shaped Assembly Line Balancing Type 2

“…Many researchers have been engaged in solving problems for different purposes by using different methods like SA, CTM, GA, ACO and DE. However, the differential evolution algorithm (DE), which is considered as the optimal metaheuristic method because of its speed and accuracy [21,22], has attracted our attention.…”

“…The DE algorithm was first described by Storn and Price [23] in 1997. It has been used to solve a wide variety of problems and objectives in, for example, assignment problem to minimize cost [22], transportation problem to maximize profit and minimize cost of transport [24][25][26], location routing problem to minimize the fuel usage [27], simple assembly line balancing problem-type 1 (SALBP-1) to minimize number of workstation [28,29] and Ushaped assembly line balancing problem-type 1 (UALBP-1) to minimize number of workstation [13]. Ramadas, Abraham and Kumar [30] proposed a new revised mutation strategy in DE algorithm to improve the optimal solution.…”