62 research outputs found
Optimization of Green Pickup and Delivery Operations in Multi-depot Distribution Problems
In this work, the Multi-Depot Green VRP with Pickups and Deliveries (MDGVRP-PD) is studied. It is a routing optimization problem in which the objective is to construct a set of vehicle routes considering multiple depots and one-to-one pickup and delivery operations that minimize emissions through fuel consumption, which depends on weight and travel distance. In one-to-one problems, goods must be transported between a single origin and its single associated destination. Practical considerations imply addressing the pickup and delivery of customers from multiple depots, where a logistics service company can efficiently combine its resources, thus reducing environmental pollution. To tackle this problem, we develop a mathematical programming formulation and matheuristic approach based on the POPMUSIC (Partial Optimization Metaheuristic under Special Intensification Conditions) framework. The results show that if the weight carried on the routes as part of the fitness measure is considered, our matheuristic approach provide an average percentage improvement in emissions of 30.79 %, compared to a fitness measure that only takes into account the distances of the routes.</p
POPMUSIC for the Travelling Salesman Problem
POPMUSIC— Partial OPtimization Metaheuristic Under Special Intensification Conditions — is a template for tackling large problem instances. This metaheuristic has been shown to be very efficient for various hard combinatorial problems such as p-median, sum of squares clustering, vehicle routing, map labelling and location routing. A key point for treating large Travelling Salesman Problem (TSP) instances is to consider only a subset of edges connecting the cities. The main goal of this article is to present how to build a list of good candidate edges with a complexity lower than quadratic in the context of TSP instances given by a general function. The candidate edges are found with a technique exploiting tour merging and the POPMUSIC metaheuristic. When these candidate edges are provided to a good local search engine, high quality solutions can be found quite efficiently. The method is tested on TSP instances of up to several million cities with different structures (Euclidean uniform, clustered, 2D to 5D, grids, toroidal distances). Numerical results show that solutions of excellent quality can be obtained with an empirical complexity lower than quadratic without exploiting the geometrical properties of the instances
Decomposition strategies for large scale multi depot vehicle routing problems
Das Umfeld in der heutigen Wirtschaft verlangt nach immer bessern Ansätzen, um
Transportprobleme möglichst effizient zu lösen. Die Klasse der ”Vehicle Routing Problems” (VRP) beschäftigt sich speziell mit der Optimierung von Tourenplanungsproblemen
in dem ein Service-Leister seine Kunden möglichst effizient beliefern muss. Eine der VRP-Varianten ist das ”Multi Depot Vehicle Routing Problem with Time Windows” (MDVRPTW), in dem Kunden von verschiedenen Depots
in einem fix vorgegebenen Zeitintervall beliefert beliefert werden mĂĽssen. Das
MDVRPTW ist im realen Leben dank seiner realitätsnahen Restriktionen sehr oft
vertreten. Typische Transportprobleme, wie sie in der Wirklichkeit auftreten, sind
jedoch oftmals so groß, dass sie von optimalen Lösungsansätzen nicht zufriedenstellend
gelöst werden können.
In der vorliegenden Dissertation werden zwei Lösungsansätze präsentiert, wie
diese riesigen, realitätsnahen Probleme zufriedenstellend bewältigt werden können.
Beide Ansätze benutzen die POPMUSIC Grundstruktur, um das Problem möglichst
intelligent zu dekomponieren. Die Dekomponierten und damit kleineren Subprobleme
können dann von speziell entwickelten Algorithmen effizienter bearbeitet
und letztendlich gelöst werden. Mit dem ersten Ansatz präsentieren wir
eine Möglichkeit Transportprobleme zu dekomponieren, wenn populationsbasierte
Algorithmen als Problemlöser eingesetzt werden. Dazu wurde ein maßgeschneiderter
Memetischer Algorithmus (MA) entwickelt und in das Dekompositionsgerüst eingebaut um ein reales Problem eines österreichischen Transportunternehmens
zu lösen. Wir zeigen, dass die Dekomponierung und Optimierung
der resultierenden Subprobleme, im Vergleich zu den Ergebnissen des MA ohne
Dekomposition, eine Verbesserung der Zielfunktion von rund 20% ermöglicht.
Der zweite Ansatz beschäftigt sich mit der Entwicklung einer Dekomponierungsmethode
für Lösungsalgorithmen, die nur an einer einzigen Lösung arbeiten. Es wurde ein ”Variable Neigborhood Search” (VNS) als Optimierer in das POPMUSIC
GrundgerĂĽst implementiert, um an das vorhandene Echtwelt-Problem heranzugehen.
Wir zeigen, dass dieser Ansatz rund 7% bessere Ergebnisse liefert als
der pure VNS Lösungsansatz. Außerdem präsentieren wir Ergebnisse des VNS
Dekompositionsansatzes die um rund 6% besser sind als die des MA Dekompositionsansatzes.
Ein weiterer Beitrag dieser Arbeit ist das Vorstellen von zwei komplett verschiedenen
Ansätzen um das Problem in kleinere Sub-Probleme zu zerteilen. Dazu
wurden acht verschiedene Nähe-Maße definiert und betrachtet. Es wurde der
2,3 und 4 Depot Fall getestet und im Detail analysiert. Die Ergebnisse werden
präsentiert und wir stellen einen eindeutigen Gewinner vor, der alle Testinstanzen
am Besten lösen konnte. Wir weisen auch darauf hin, wie einfach die POPMUSIC
Dekomponierung an reale Bedürfnisse, wie zum Beispiel eine möglichst
schnelle Ergebnisgenerierung, angepasst werden kann. Wir zeigen damit, dass
die vorgestellten Dekomponierungsstrategien sehr effizient und flexibel sind, wenn
Transportprobleme, wie sie in der realen Welt vorkommen gelöst werden müssen.The optimization of transportation activities is of high importance for companies
in today’s economy. The Vehicle Routing Problem (VRP) class is dealing with
the routing of vehicles so that the customer base of a company can be served
in the most efficient way. One of the many variants in the VRP class is the
Multi Depot Vehicle Routing Problem with Time Windows (MDVRPTW) which
extends the VRP by additional depots from which customers can be served, as
well as an individual time window for each customer in which he is allowed to
be served. Modern carrier fleet operators often encounter these MDVRPTW in
the real world, and usually they are of very large size so that exact approaches
cannot solve them efficiently. This thesis presents two different approaches how
this real world large scale MDVRPTWs can be solved. Both approaches are based
on the POPMUSIC framework, which intelligently tries to decompose the large
scale problem into much smaller sub-problems. The resulting sub-problems can
then be solved more efficiently by specialized optimizers. The first approach in
this thesis was developed for population based optimizers. A Memetic Algorithm
(MA) was developed and used as an optimizer in the framework to solve a real
world MDVPRTW from an Austrian carrier fleet operator. We show that decomposing
the complete problem and solving the resulting sub-problems improves the
solution quality by around 20% compared to using the MA without any decomposition.
The second approach specially focuses on decomposition strategies for
single solution methods. More precisely, a Variable Neighborhood Search (VNS)
was implemented in the POPMUSIC framework to solve the real world instances.
We show that decomposing the problem can yield improvements of around 7%
compared to using the pure VNS method. Compared to the POPMUSIC MA
approach the second approach can further improve the solution quality by around
6%. Another contribution in this thesis is the development of two generally different ways to measure proximity when creating sub-problems. In detail we tested
eight different proximity measures and analyzed how good they decompose the
problem in different environments. We tested the two, three and four depot case
and present a clear winner that can outperform all other measures. Further we
demonstrate that the POPMUSIC approach can flexibly be adjusted to real world
demands, like a faster solution finding process, while at the same time maintaining
high quality solutions. We show that a decomposition strategies combined with
state of the art metaheuristic solvers are a very efficient and flexible tool to tackle
real world problems with regards to solution quality as well as runtime
An Integrated Strategy for a Production Planning and Warehouse Layout Problem: Modeling and Solution Approaches
We study a real-world production warehousing case, where the company always faces the challenge to find available space for their products and to manage the items in the warehouse. To resolve the problem, an integrated strategy that combines warehouse layout with the capacitated lot-sizing problem is presented, which have been traditionally treated separately in the existing literature. We develop a mixed integer linear programming model to formulate the integrated optimization problem with the objective of minimizing the total cost of production and warehouse operations. The problem with real data is a large-scale instance that is beyond the capability of optimization solvers. A novel Lagrangian relax-and-fix heuristic approach and its variants are proposed to solve the large-scale problem. The preliminary numerical results from the heuristic approaches are reported
Design of Heuristic Algorithms for Hard Optimization
This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content
A Periodic Location Routing Problem for Collaborative Recycling
Motivated by collaborative recycling efforts for non-profit agencies, we study a variant of the periodic location routing problem, in which one decides the set of open depots from the customer set, the capacity of open depots, and the visit frequency to nodes, in an effort to design networks for collaborative pickup activities. We formulate this problem, highlighting the challenges introduced by these decisions. We examine the relative dfficulty introduced with each decision through exact solutions and a heuristic approach which can incorporate extensions of model constraints and solve larger instances. The work is motivated by a project with a network of hunger relief agencies (e.g., food pantries, soup kitchens and shelters) focusing on collaborative approaches to address their cardboard recycling challenges collectively. We present a case study based on data from the network. In this novel setting, we evaluate collaboration in terms of participation levels and cost impact. These insights can be generalized to other networks of organizations that may consider pooling resources
Travelling Santa Problem: Optimization of a Million-Households Tour Within One Hour
Finding the shortest tour visiting all given points at least ones belongs to the most
famous optimization problems until today [travelling salesman problem (TSP)]. Optimal
solutions exist formany problems up to several ten thousand points. Themajor difficulty in
solving larger problems is the required computational complexity. This shifts the research
from finding the optimum with no time limitation to approaches that find good but
sub-optimal solutions in pre-defined limited time. This paper proposes a new approach
for two-dimensional symmetric problems with more than a million coordinates that is able
to create good initial tours within few minutes. It is based on a hierarchical clustering
strategy and supports parallel processing. In addition, a method is proposed that can
correct unfavorable paths with moderate computational complexity. The new approach
is superior to state-of-the-artmethods when applied to TSP instances with non-uniformly
distributed coordinates
A novel mathematical formulation for solving the dynamic and discrete berth allocation problem by using the Bee Colony Optimisation algorithm
AbstractBerth allocation is one of the crucial points for efficient management of ports. This problem is complex due to all possible combinations for assigning ships to available compatible berths. This paper focuses on solving the Berth Allocation Problem (BAP) by optimising port operations using an innovative model. The problem analysed in this work deals with the Discrete and Dynamic Berth Allocation Problem (DDBAP). We propose a novel mathematical formulation expressed as a Mixed Integer Linear Programming (MILP) for solving the DDBAP. Furthermore, we adapted a metaheuristic solution approach based on the Bee Colony Optimisation (BCO) for solving large-sized combinatorial BAPs. In order to assess the solution performance and efficiency of the proposed model, we introduce a new set of instances based on real data of the Livorno port (Italy), and a comparison between the BCO algorithm and CPLEX in solving the DDBAP is performed. Additionally, the application of the proposed model to a real berth scheduling (Livorno port data) and a comparison with the Ant Colony Optimisation (ACO) metaheuristic are carried out. Results highlight the feasibility of the proposed model and the effectiveness of BCO when compared to both CPLEX and ACO, achieving computation times that ensure a real-time application of the method
Internet of Things in urban waste collection
Nowadays, the waste collection management has an important role in urban areas. This paper faces this issue and proposes the application of a metaheuristic for the optimization of a weekly schedule and routing of the waste collection activities in an urban area. Differently to several contributions in literature, fixed periodic routes are not imposed. The results significantly improve the performance of the company involved, both in terms of resources used and costs saving
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