A genetic algorithm with exact dynamic programming for the green vehicle routing &amp; scheduling problem

Xiao, Yiyong; Konak, Abdullah

doi:10.1016/j.jclepro.2016.11.115

Cited by 127 publications

(65 citation statements)

References 44 publications

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“…In each generation, the fitness of the whole population will be evaluated. Based on their fitness, a part of individuals will be randomly selected from the current population, and new populations will be generated through selection, crossover, and mutation [36][37][38][39][40]. The main feature of GA is to operate the object directly, adopt the probabilistic optimization method, automatically obtain the optimized search space, adaptively adjust the search and evolution, without the limitation of derivation and function continuity, with the inherent implicit parallelism and better overall optimization ability [38].…”

Section: Genetic Algorithm (Ga) For Path Optimizationmentioning

confidence: 99%

Modeling Method for Cost and Carbon Emission of Sheep Transportation Based on Path Optimization

et al. 2020

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Energy conservation, cost, and emission reduction are the research topics of most concern today. The aim of this paper is to reduce the cost and carbon emissions and improve the sustainable development of sheep transportation. Under the typical case of the “farmers–middlemen–slaughterhouses” (FMS) supply model, this paper comprehensively analyzed the factors, sources, and types of cost and carbon emissions in the process of sheep transportation, and a quantitative evaluation model was established. The genetic algorithm (GA) was proposed to search for the optimal path of sheep transportation, and then the model solving algorithm was designed based on the basic GA. The results of path optimization indicated that the optimal solution can be obtained effectively when the range of basic parameters of GA was set reasonably. The optimal solution is the optimal path and the shortest distance under the supply mode of FMS, and the route distance of the optimal path is 245.6 km less than that of random path. From the cost distribution, the fuel power cost of the vehicle, labor cost in transportation, and consumables cost account for a large proportion, while the operation and management cost of the vehicle and depreciation cost of the tires account for a small proportion. The total cost of the optimal path is 26.5% lower than that of the random path, and the total carbon emissions are 36.3% lower than that of random path. Path optimization can thus significantly reduce the cost of different types and significantly reduce the proportion of vehicle fuel power cost and consumables cost, but the degree of cost reduction of different types is different. The result of the optimal path is the key to be explored in this study, and it can be used as the best reference for sheep transportation. The quantitative evaluation model established in this paper can systematically measure the cost and carbon emissions generated in the sheep transportation, which can provide theoretical support for practical application.

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Section: Genetic Algorithm (Ga) For Path Optimizationmentioning

confidence: 99%

Modeling Method for Cost and Carbon Emission of Sheep Transportation Based on Path Optimization

et al. 2020

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“…Firstly, it was necessary to find a concentration set according to some rules, and secondly, the optimal solution in the concentration set could be solved every time by generating a concentration set. Based on Rosing and Hodgson's heuristic concentration procedure, the MILP-based neighborhood searching algorithms by Xiao et al [24,25] and You et al [27,28] were introduced, and the concept of the partial set was also presented. For this paper, we developed a heuristic algorithm for large-sized problems following the steps showed above.…”

Section: A Heuristic Partial Optimization Algorithmmentioning

confidence: 99%

“…Sustainability 2020, 12, x FOR PEER REVIEW 9 of 17 searching algorithms by Xiao et al [24,25] and You et al [27,28] were introduced, and the concept of the partial set was also presented. For this paper, we developed a heuristic algorithm for large-sized problems following the steps showed above.…”

Section: A Heuristic Partial Optimization Algorithmmentioning

confidence: 99%

“…Using the cyclic algorithm, the computer generate two decision packages for both the attacker and defender until the equilibrium was cyclically reached. For the large-sized problem, we developed a heuristic algorithm based on the partial optimization strategy [24,25] to efficiently solve the problem with near-optimal solutions. Contributions of the paper are outlined as follows.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Gaming Case of the R-Interdiction Median Problem with Fortification and an MILP-Based Solution Approach

et al. 2020

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This paper studies the cyclic dynamic gaming case of the r-interdiction median problem with fortification (CDGC-RIMF), which is important for strengthening a facility’s reliability and invulnerability under various possible attacks. We formulated the CDGC-RIMF as a bi-objective mixed-integer linear programming (MILP) model with two opposing goals to minimize/maximize the loss from both the designer (leader) and attacker (follower) sides. The first goal was to identify the most cost-effective plan to build and fortify the facility considering minimum loss, whereas the attacker followed the designer to seek the most destructive way of attacking to cause maximum loss. We found that the two sides could not reach a static equilibrium with a single pair of confrontational plans in an ordinary case, but were able to reach a dynamically cyclic equilibrium when the plan involved multiple pairs. The proposed bi-objective model aimed to discover the optimal cyclic plans for both sides to reach a dynamic equilibrium. To solve this problem, we first started from the designer’s side with a design and fortification plan, and then the attacker was able to generate their worst attack plan based on that design. After that, the designer changed their plan again based on the attacker’s plan in order to minimize loss, and the attacker correspondingly modified their plan to achieve maximum loss. This game looped until, finally, a cyclic equilibrium was reached. This equilibrium was deemed to be optimal for both sides because there was always more loss for either side if they left the equilibrium first. This game falls into the subgame of a perfect Nash equilibrium—a kind of complete game. The proposed bi-objective model was directly solved by the CPLEX solver to achieve optimal solutions for small-sized problems and near-optimal feasible solutions for larger-sized problems. Furthermore, for large-scale problems, we developed a heuristic algorithm that implemented dynamic iterative partial optimization alongside MILP (DIPO-MILP), which showed better performance compared with the CPLEX solver when solving large-scale problems.

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“…Some evaluation techniques were introduced to the GA to evaluate and prune neighborhoods, and to decompose large instances efficiently. Xiao and Konak [36] studied the green vehicle routing and the scheduling problem, in which a fleet of heterogeneous vehicles travel within a time-varying traffic environment to minimize the total CO 2 emissions. An MIP was first proposed for small-sized problems, and an exact dynamic programming algorithm was presented next for large-sized problems.…”

Section: Literature Reviewmentioning

confidence: 99%

An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

Kang

Lee

2018

Symmetry

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The vehicle routing problem (VRP) is a challenging combinatorial optimization problem. This research focuses on the problem under which a manufacturer needs to outsource materials from other suppliers and to ship the materials back to the company. Heterogeneous vehicles are available to ship the materials, and each vehicle has a limited loading capacity and a limited travelling distance. The purpose of this research is to study a multiple vehicle routing problem (MVRP) with soft time window and heterogeneous vehicles. Two models, using mixed integer programming (MIP) and genetic algorithm (GA), are developed to solve the problem. The MIP model is first constructed to minimize the total transportation cost, which includes the assignment cost, travelling cost, and the tardiness cost, for the manufacturer. The optimal solution can present multiple vehicle routing and the loading size of each vehicle in each period. The GA is next applied to solve the problem so that a near-optimal solution can be obtained when the problem is too difficult to be solved using the MIP. A case of a food manufacturing company is used to examine the practicality of the proposed MIP model and the GA model. The results show that the MIP model can obtain the optimal solution under a short computational time when the scale of the problem is small. When the problem becomes non-deterministic polynomial hard (NP-hard), the MIP model cannot find the optimal solution. On the other hand, the GA model can obtain a near-optimal solution within a reasonable amount of computational time. This paper is related to several important topics of the Symmetry journal in the areas of mathematics and computer science theory and methods. In the area of mathematics, the theories of linear and non-linear algebraic structures and information technology are adopted. In the area of computer science, theory and methods, and metaheuristics are applied.Unit of measure: min.Symmetry 2018, 10, 650 9 of 20 Table 6 lists the problem configurations for the three cases, including the number of periods, number of suppliers, number of vehicles, size of the transportation network, number of variables for the MIP, and number of constraints for the MIP. In the first case, there are five periods, the number of suppliers is five, the number of vehicles is three, the transportation network is 6 × 6, and the numbers of variables and constraints for the MIP model are 931 and 1171, respectively. In the second case, there are seven periods, the number of suppliers is nine, the number of vehicles is four, the transportation network is 10 × 10, and the numbers of variables and constraints for the MIP model are 3903 and 3977, respectively. In the third case, there are nine periods, the number of suppliers is 12, the number of vehicles is five, the transportation network is 13 × 13, and the numbers of variables and constraints for the MIP model are 9758 and 9919, respectively.

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A genetic algorithm with exact dynamic programming for the green vehicle routing & scheduling problem

Cited by 127 publications

References 44 publications

Modeling Method for Cost and Carbon Emission of Sheep Transportation Based on Path Optimization

Modeling Method for Cost and Carbon Emission of Sheep Transportation Based on Path Optimization

Dynamic Gaming Case of the R-Interdiction Median Problem with Fortification and an MILP-Based Solution Approach

An Enhanced Approach for the Multiple Vehicle Routing Problem with Heterogeneous Vehicles and a Soft Time Window

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