Methodology to Solve the Combination of the Generalized Assignment Problem and the Vehicle Routing Problem: A Case Study in Drug and Medical Instrument Sales and Service

Abstract

This article presents algorithms for solving a special case of the vehicle routing problem (VRP). We define our proposed problem of a special VRP case as a combination of two hard problems: the generalized assignment and the vehicle routing problem. The different evolution (DE) algorithm is used to solve the problem. The recombination process of the original DE is modified by adding two more sets of vectors—best vector and random vector—and using two other sets—target vector and trial vector. The linear probability formula is proposed to potentially use one out of the four sets of vectors. This is called the modified DE (MDE) algorithm. Two local searches are integrated into the MDE algorithm: exchange and insert. These procedures create a DE and MDE that use (1) no local search techniques, (2) two local search techniques, (3) only the exchange procedure, and (4) only the insert procedure. This generates four DE algorithms and four MDE algorithms. The proposed methods are tested with 15 tested instances and one case study. The current procedure is compared with all proposed heuristics. The computational result shows that, in the case study, the best DE algorithm (DE-4) has a 1.6% better solution than that of the current practice, whereas the MDE algorithm is 8.2% better. The MDE algorithm that uses the same local search as the DE algorithms generates a maximum 5.814% better solution than that of the DE algorithms.

A dual model node based optimization algorithm for simultaneous escape routing in PCBs

“…The application of optimization theory is not only limited to the fields of communication and networking but it is also been used in the vehicle routing problem (Thongkham & Kaewman, 2019), network reconfiguration for Distribution Systems (Guo et al, 2020), microgrid systems (Wu et al, 2019), distributed energy resource allocation in virtual power plants (Ko & Joo, 2020), control of humanoid robots Tedrake (2017), smart grid ecosystem (Koutsopoulos, Papaioannou & Hatzi, 2016) and Computation of the Centroidal Voronoi Tessellations (CVT) that is widely used in the computer graphics (Liu et al, 2016). Ozdal & Wong (2004) and Ozdal & Wong (2006) can be regarded as the initial work on SER as they consider two pin arrays simultaneously and minimize the net ordering mismatch.…”

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

“…The metaheuristics and heuristics are used to find the promising solution. Metaheuristics have been successfully developed to solve various problem types both in discrete and continuous optimization such as disease detection from medical images [15], fruit peel defects detection [16], develop the intelligent simulation and control model of electric drive engine [17], and use to solve the GAP problem [18]. Solving GAP, some effective exact methods have been proposed to solve classical GAP, such as branch and bound [6], branch and price [19], etc.…”