Genetic Algorithm applied to the Capacitated Vehicle Routing Problem: an analysis of the influence of different encoding schemes on the population behavior

Genetic Algorithm (GA) is an optimization method that has been widely used in the solution of NP-Hard (Non-deterministic Polynomial-time) problems, among which is the Vehicle Routing Problem (VRP), widely known in the literature due to its applications in the logistics and supply sectors, and which is considered in this work. However, finding solution for any optimization problem using GA presupposes the adoption of a solution encoding scheme that, according to the literature, impacts its performance. However, there is a lack of works in the literature exploring this theme. In this work we carry out an analysis of the main encoding schemes (binary and integer) employed in the GA for the solution of the capacitated VRP (CVRP), in order to evaluate the influence of each of them on the behavior of the GA population and, consequently, on the algorithm performance. To this end, we developed a computational tool that allows visualizing the GA individuals (solutions) mapped to a two-dimensional space. Based on the experiments conducted, we observed that, in general, integer vectors provide better conditions for GA individuals to explore the solution space, leading to better results. The results found, besides corroborating some assumptions in the literature, may justify the preference for integer encoding schemes to solve CVRP in recent literature works. In addition, this study can contribute to the choice and/or proposition of heuristics that allow GA to search for better quality solutions for the VRP with less computational effort

Genetic algorithm for the continuous location-routing problem

This paper focuses on the continuous location-routing problem that comprises of the location of multiple depots from a given region and determining the routes of vehicles assigned to these depots. The objective of the problem is to design the delivery system of depots and routes so that the total cost is minimal. The standard location-routing problem considers a finite number of possible locations. The continuous location-routing problem allows location to infinite number of locations in a given region and makes the problem much more complex. We present a genetic algorithm that tackles both location and routing subproblems simultaneously.Web of Science29318717

Quantum annealing for vehicle routing and scheduling problems

Metaheuristic approaches to solving combinatorial optimization problems have many attractions. They sidestep the issue of combinatorial explosion; they return good results; they are often conceptually simple and straight forward to implement. There are also shortcomings. Optimal solutions are not guaranteed; choosing the metaheuristic which best fits a problem is a matter of experimentation; and conceptual differences between metaheuristics make absolute comparisons of performance difficult. There is also the difficulty of configuration of the algorithm - the process of identifying precise values for the parameters which control the optimization process. Quantum annealing is a metaheuristic which is the quantum counterpart of the well known classical Simulated Annealing algorithm for combinatorial optimization problems. This research investigates the application of quantum annealing to the Vehicle Routing Problem, a difficult problem of practical significance within industries such as logistics and workforce scheduling. The work devises spin encoding schemes for routing and scheduling problem domains, enabling an effective quantum annealing algorithm which locates new solutions to widely used benchmarks. The performance of the metaheuristic is further improved by the development of an enhanced tuning approach using fitness clouds as behaviour models. The algorithm is shown to be further enhanced by taking advantage of multiprocessor environments, using threading techniques to parallelize the optimization workload. The work also shows quantum annealing applied successfully in an industrial setting to generate solutions to complex scheduling problems, results which created extra savings over an incumbent optimization technique. Components of the intellectual property rendered in this latter effort went on to secure a patent-protected status

Advanced Optimization Models in Waste Management

Diplomová práce se zabývá optimalizací svozu odpadu pro středně velká města. Model úlohy zohledňuje požadavky vzešlé z praxe. K jejímu řešení byl navržen původní memetický algoritmus, který byl implementován v jazyce C++.This thesis deals with an optimization of waste collection in a mid-sized town. The model is formulated based on requirements from a real process. To deal with this problem, the original memetic algorithm was developed and implemented in C++.

Modeling a four-layer location-routing problem

Distribution is an indispensable component of logistics and supply chain management. Location-Routing Problem (LRP) is an NP-hard problem that simultaneously takes into consideration location, allocation, and vehicle routing decisions to design an optimal distribution network. Multi-layer and multi-product LRP is even more complex as it deals with the decisions at multiple layers of a distribution network where multiple products are transported within and between layers of the network. This paper focuses on modeling a complicated four-layer and multi-product LRP which has not been tackled yet. The distribution network consists of plants, central depots, regional depots, and customers. In this study, the structure, assumptions, and limitations of the distribution network are defined and the mathematical optimization programming model that can be used to obtain the optimal solution is developed. Presented by a mixed-integer programming model, the LRP considers the location problem at two layers, the allocation problem at three layers, the vehicle routing problem at three layers, and a transshipment problem. The mathematical model locates central and regional depots, allocates customers to plants, central depots, and regional depots, constructs tours from each plant or open depot to customers, and constructs transshipment paths from plants to depots and from depots to other depots. Considering realistic assumptions and limitations such as producing multiple products, limited production capacity, limited depot and vehicle capacity, and limited traveling distances enables the user to capture the real world situations

Two-Echelon Vehicle and UAV Routing for Post-Disaster Humanitarian Operations with Uncertain Demand

Humanitarian logistics service providers have two major responsibilities immediately after a disaster: locating trapped people and routing aid to them. These difficult operations are further hindered by failures in the transportation and telecommunications networks, which are often rendered unusable by the disaster at hand. In this work, we propose two-echelon vehicle routing frameworks for performing these operations using aerial uncrewed autonomous vehicles (UAVs or drones) to address the issues associated with these failures. In our proposed frameworks, we assume that ground vehicles cannot reach the trapped population directly, but they can only transport drones from a depot to some intermediate locations. The drones launched from these locations serve to both identify demands for medical and other aids (e.g., epi-pens, medical supplies, dry food, water) and make deliveries to satisfy them. Specifically, we present two decision frameworks, in which the resulting optimization problem is formulated as a two-echelon vehicle routing problem. The first framework addresses the problem in two stages: providing telecommunications capabilities in the first stage and satisfying the resulting demands in the second. To that end, two types of drones are considered. Hotspot drones have the capability of providing cell phone and internet reception, and hence are used to capture demands. Delivery drones are subsequently employed to satisfy the observed demand. The second framework, on the other hand, addresses the problem as a stochastic emergency aid delivery problem, which uses a two-stage robust optimization model to handle demand uncertainty. To solve the resulting models, we propose efficient and novel solution approaches

Solving Capacitated Vehicle Routing Problem Using Football Game Algorithm

The Capacitated Vehicle Routing Problem (CVRP) plays an important role in the logistics transportation sector. Determining the proper route will reduce the company's operational costs. In CVRP, a number of vehicles have a capacity limit that can serve all customers. This research completes a real case study on a bottled drinking water company where the company still uses the subjective method of the driver to determine the transportation route. Based on the conditions in the company, the selection of the best route will consider vehicle capacity and demand to determine the shortest route. The execution of this case study uses the Football Game Algorithm (FGA) which was first initiated by Fadakar Ebrahimi which proved promising and had the strongest performance in all cases. FGA is expected to be able to determine the shortest distribution route from the existing cases to reduce the distribution costs incurred. This study takes data from 4 days of delivery that served 78 customers. The average daily transportation cost savings result is 42%. This amount indicates that the FGA algorithm is effective for completing a real case study in CVRP

A social vulnerability-based genetic algorithm to locate-allocate transit bus stops for disaster evacuation in New Orleans, Louisiana

In the face of severe disasters, some or all of the endangered residents must be evacuated to a safe place. A portion of people, due to various reasons (e.g., no available vehicle, too old to drive), will need to take public transit buses to be evacuated. However, to optimize the operation efficiency, the location of these transit pick-up stops and the allocation of the available buses to these stops should be considered seriously by the decision-makers. In the case of a large number of alternative bus stops, it is sometimes impractical to use the exhaustive (brute-force) search to solve this kind of optimization problem because the enumeration and comparison of the effectiveness of a huge number of alternative combinations would take too much model running time. A genetic algorithm (GA) is an efficient and robust method to solve the location/allocation problem. This thesis utilizes GA to discover accurately and efficiently the optimal combination of locations of the transit bus stop for a regional evacuation of the New Orleans metropolitan area, Louisiana. When considering people’s demand for transit buses in the face of disaster evacuation, this research assumes that residents of high social vulnerability should be evacuated with high priority and those with low social vulnerability can be put into low priority. Factor analysis, specifically principal components analysis, was used to identify the social vulnerability from multiple variables input over the study area. The social vulnerability was at the census block group level and the overall social vulnerability index was used to weight the travel time between the centroid of each census block to the nearest transit pick-up location. The simulation results revealed that the pick-up locations obtained from this study can greatly improve the efficiency over the ones currently used by the New Orleans government. The new solution led to a 26,397.6 (total weighted travel time for the entire system measured in hours) fitness value, which is much better than the fitness value 62,736.3 rendered from the currently used evacuation solution

A Study on the Optimization of Chain Supermarkets’ Distribution Route Based on the Quantum-Inspired Evolutionary Algorithm

The chain supermarket has become a major part of China’s retail industry, and the optimization of chain supermarkets’ distribution route is an important issue that needs to be considered for the distribution center, because for a chain supermarket it affects the logistics cost and the competition in the market directly. In this paper, analyzing the current distribution situation of chain supermarkets both at home and abroad and studying the quantum-inspired evolutionary algorithm (QEA), we set up the mathematical model of chain supermarkets’ distribution route and solve the optimized distribution route throughout QEA. At last, we take Hongqi Chain Supermarket in Chengdu as an example to perform the experiment and compare QEA with the genetic algorithm (GA) in the fields of the convergence, the optimal solution, the search ability, and so on. The experiment results show that the distribution route optimized by QEA behaves better than that by GA, and QEA has stronger global search ability for both a small-scale chain supermarket and a large-scale chain supermarket. Moreover, the success rate of QEA in searching routes is higher than that of GA