DISCRETE PARTICLE SWARM OPTIMIZATION FOR THE ORIENTEERING PROBLEM

Discrete particle swarm optimization (DPSO) is gaining popularity in the area of combinatorial optimization in the recent past due to its simplicity in coding and consistency in performance.  A DPSO algorithm has been developed for orienteering problem (OP) which has been shown to have many practical applications.  It uses reduced variable neighborhood search as a local search tool.  The DPSO algorithm was compared with ten heuristic models from the literature using benchmark problems.  The results show that the DPSO algorithm is a robust algorithm that can optimally solve the well known OP test problems

Exact Algorithm for the Capacitated Team Orienteering Problem with Time Windows

The capacitated team orienteering problem with time windows (CTOPTW) is a problem to determine players' paths that have the maximum rewards while satisfying the constraints. In this paper, we present the exact solution approach for the CTOPTW which has not been done in previous literature. We show that the branch-and-price (B&P) scheme which was originally developed for the team orienteering problem can be applied to the CTOPTW. To solve pricing problems, we used implicit enumeration acceleration techniques, heuristic algorithms, and ng-route relaxations

Two-Stage Vehicle Routing Problems with Profits and Buffers: Analysis and Metaheuristic Optimization Algorithms

This thesis considers the Two-Stage Vehicle Routing Problem (VRP) with Profits and Buffers, which generalizes various optimization problems that are relevant for practical applications, such as the Two-Machine Flow Shop with Buffers and the Orienteering Problem. Two optimization problems are considered for the Two-Stage VRP with Profits and Buffers, namely the minimization of total time while respecting a profit constraint and the maximization of total profit under a budget constraint. The former generalizes the makespan minimization problem for the Two-Machine Flow Shop with Buffers, whereas the latter is comparable to the problem of maximizing score in the Orienteering Problem. For the three problems, a theoretical analysis is performed regarding computational complexity, existence of optimal permutation schedules (where all vehicles traverse the same nodes in the same order) and potential gaps in attainable solution quality between permutation schedules and non-permutation schedules. The obtained theoretical results are visualized in a table that gives an overview of various subproblems belonging to the Two-Stage VRP with Profits and Buffers, their theoretical properties and how they are connected. For the Two-Machine Flow Shop with Buffers and the Orienteering Problem, two metaheuristics 2BF-ILS and VNSOP are presented that obtain favorable results in computational experiments when compared to other state-of-the-art algorithms. For the Two-Stage VRP with Profits and Buffers, an algorithmic framework for Iterative Search Algorithms with Variable Neighborhoods (ISAVaN) is proposed that generalizes aspects from 2BF-ILS as well as VNSOP. Various algorithms derived from that framework are evaluated in an experimental study. The evaluation methodology used for all computational experiments in this thesis takes the performance during the run time into account and demonstrates that algorithms for structurally different problems, which are encompassed by the Two-Stage VRP with Profits and Buffers, can be evaluated with similar methods. The results show that the most suitable choice for the components in these algorithms is dependent on the properties of the problem and the considered evaluation criteria. However, a number of similarities to algorithms that perform well for the Two-Machine Flow Shop with Buffers and the Orienteering Problem can be identified. The framework unifies these characteristics, providing a spectrum of algorithms that can be adapted to the specifics of the considered Vehicle Routing Problem.:1 Introduction 2 Background 2.1 Problem Motivation 2.2 Formal Definition of the Two-Stage VRP with Profits and Buffers 2.3 Review of Literature on Related Vehicle Routing Problems 2.3.1 Two-Stage Vehicle Routing Problems 2.3.2 Vehicle Routing Problems with Profits 2.3.3 Vehicle Routing Problems with Capacity- or Resource-based Restrictions 2.4 Preliminary Remarks on Subsequent Chapters 3 The Two-Machine Flow Shop Problem with Buffers 3.1 Review of Literature on Flow Shop Problems with Buffers 3.1.1 Algorithms and Metaheuristics for Flow Shops with Buffers 3.1.2 Two-Machine Flow Shop Problems with Buffers 3.1.3 Blocking Flow Shops 3.1.4 Non-Permutation Schedules 3.1.5 Other Extensions and Variations of Flow Shop Problems 3.2 Theoretical Properties 3.2.1 Computational Complexity 3.2.2 The Existence of Optimal Permutation Schedules 3.2.3 The Gap Between Permutation Schedules an Non-Permutation 3.3 A Modification of the NEH Heuristic 3.4 An Iterated Local Search for the Two-Machine Flow Shop Problem with Buffers 3.5 Computational Evaluation 3.5.1 Algorithms for Comparison 3.5.2 Generation of Problem Instances 3.5.3 Parameter Values 3.5.4 Comparison of 2BF-ILS with other Metaheuristics 3.5.5 Comparison of 2BF-OPT with NEH 3.6 Summary 4 The Orienteering Problem 4.1 Review of Literature on Orienteering Problems 4.2 Theoretical Properties 4.3 A Variable Neighborhood Search for the Orienteering Problem 4.4 Computational Evaluation 4.4.1 Measurement of Algorithm Performance 4.4.2 Choice of Algorithms for Comparison 4.4.3 Problem Instances 4.4.4 Parameter Values 4.4.5 Experimental Setup 4.4.6 Comparison of VNSOP with other Metaheuristics 4.5 Summary 5 The Two-Stage Vehicle Routing Problem with Profits and Buffers 5.1 Theoretical Properties of the Two-Stage VRP with Profits and Buffers 5.1.1 Computational Complexity of the General Problem 5.1.2 Existence of Permutation Schedules in the Set of Optimal Solutions 5.1.3 The Gap Between Permutation Schedules an Non-Permutation Schedules 5.1.4 Remarks on Restricted Cases 5.1.5 Overview of Theoretical Results 5.2 A Metaheuristic Framework for the Two-Stage VRP with Profits and Buffers 5.3 Experimental Results 5.3.1 Problem Instances 5.3.2 Experimental Results for O_{max R, Cmax≤B} 5.3.3 Experimental Results for O_{min Cmax, R≥Q} 5.4 Summary Bibliography List of Figures List of Tables List of Algorithm

Advanced Traveller Information Systems: Optimasi Rencana Perjalanan dengan Model Orienteering Problem dan Great Deluge Iterative Local Search (Studi Kasus: Trayek Angkot Surabaya)

Kemacetan merupakan salah satu permasalahan terbesar untuk kota – kota besar di dunia, ini disebabkan oleh banyak hal mulai dari urbanisasi, peningkatan populasi dan permasalahan jumlah kendaraan pribadi yang lebih banyak digunakan dibandingkan dengan kendaraan umum yang disediakan. Metode yang digunakan untuk memodelkan permasalahan tersebut adalah Orientering Problem dengan pengambilan jarak dan waktu diambil menggunakan Google Maps dan penentuan skor dengan demand atau jumlah angkutan kota pada trayek tersebut, lalu formulasi permaslahaan akan dibuat sesuai dengan langkah – langkah metode tersebut. Orienteering problem diigunakan dikarenakan penelitian sebelumnya belum ada yang menggunakan terhadap studi kasus saat ini tetapi sudah teruji baik dalam permasalahan sejenis. Pencarian solusi dari model yang telah dibuat akan dilakukan dengan menggunakan Great Deluge Iterative Local Search untuk mencari solusi terbaik dari model dan bagaimana pencarian skor terbesar dapat dilakukan dengan menggunakan iterative local search yang disampaikan. Iteratice local search ini menyediakan kecepatan dan keefisienan dalam melakukan pencarian solusi. Dalam penelitian ini, didapati bahwa orienteering problem dapat memodelkan enam buah trayek angkot menjadi network model yang saling terhubung antara satu sama lain dan mendapatkn rute terpendeknya. Algoritma Great Deluge Iterative Local Search juga dapat meningkatkan hasil dari pencarian solusi awal yang layak dengan menggunakan cara random dengan waktu tempuh 81 menit dan skor 4010. ===================================================================== Congestion is one of the biggest problems for big cities in the world, this is caused by many things ranging from urbanization, population increase and the problem of the number of private vehicles that are more widely used than public transport provided. The method used to model the problem is Orientering Problem with distance taking and time taken using Google Maps and determining the score with the demand or the number of city transport on the route, then the formulation of the permaslahaan will be made in accordance with the steps of the method. Orienteering problem is used because previous research has not been applied to the current case study but it has been well tested in similar problems. The search for a solution of the model that has been created will be done using Great Deluge Iterative Local Search to find the best solution of the model and how the largest scoring search can be done using iterative local search submitted. Iteratice local search provides the speed and efficiency in searching for solutions. In this study, it was found that the orienteering problem can model six angkot routes into network models that are interconnected with each other and find the shortest route. The Great Deluge Iterative Local Search algorithm can also improve results from searching for a feasible initial solution using a random manner with an 81 minute travel time and a 4010 score

Metaheuristic approach for solving scheduling and financial derivative problems

This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe objective of this thesis is to implement metaheuristic approaches to solve di erent types of combinatorial problems. The thesis is focused on neighborhood heuristic optimisation techniques such as Variable Neighborhood Search (VNS) and Ant Colony Optimisation (ACO) algorithms. The thesis will focus on two diverse combinatorial problems. A job shop scheduling problem, and a nancial derivative matching problem. The rst is a NP-hard 2-stage assembly problem, where we will be focussing on the rst stage. It consists of sequencing a set of jobs having multiple components to be processed. Each job has to be worked on independently on a speci c machine. We consider these jobs to form a vector of tasks. Our objective is to schedule jobs on the particular machines in order to minimise the completion time before the second stage starts. In this thesis, we have constructed a new hybrid metaheuristic approach to solve this unique job shop scheduling problem. The second problem has arisen in the nancial sector, where the nancial regulators collects transaction data across regulated assets classes. Our focus is to identify any unhedged derivative, Contract for Di erence (CFD), with its corresponding underlying asset that has been reported to the corresponding component authorities. The underlying asset and CFD transaction contain di erent variables, like volume and price. Therefore, we are looking for a combination of underlying asset variables that may hedge the equivalent CFD variables. Our aim is to identify unhedged or unmatched CFD's with their corresponding underlying asset. This problem closely relates to the goal programming problem with variable parameters. We have developed two new local search methods and embedded the newly constructed local search methods with basic VNS, to attain a new modi ed variant of the VNS algorithm. We then used these newly constructed VNS variants to solve this nancial matching problem. In tackling the Vector Job Scheduling problem, we developed a new hybrid optimisation heuristic algorithm by combining VNS and ACO. We then compared the results of this hybrid algorithm with VNS and ACO on their own. We found that the hybrid algorithm performance is better than the other two independent heuristic algorithms. In tackling the nancial derivative problem, our objective is to match the CFD trades with their corresponding underlying equity trades. Our goal is to identify the mismatched CFD trades while optimising the search process. We have developed two new local search techniques and we have implemented a VNS algorithm with the newly developed local search techniques to attain better solutions

Mathematical formulations and optimization algorithms for solving rich vehicle routing problems.

Objectives and methods of study: The main objective of this work is to analyze and solve three different rich selective Vehicle Routing Problems (VRPs). The first problem is a bi-objective variant of the well-known Traveling Purchaser Problem (TPP) in which the purchased products are delivered to customers. This variant aims to find a route for which the total cost (transportation plus purchasing costs) and the sum of the customers’s waiting time are simultaneously minimized. A mixed integer bi-objective programming formulation of the problem is presented and tested with CPLEX 12.6 within an ǫ-constraint framework which fails to find non-dominated solutions for instances containing more than 10 nodes. Therefore, a heuristic based on relinked local search and Variable Neighborhood Search (VNS) is proposed to approximate the Pareto front for large instances. The proposed heuristic was tested over a large set of artificial instances of the problem. Computational results over small-sized instances show that the heuristic is competitive with the ǫ-constraint method. Also, computational tests over large-sized instances were carried out in order to study how the characteristics of the instances impact the algorithm performance. The second problem consists of planning a selective delivery schedule of multiple products. The problem is modeled as a multi-product split delivery capacitated team orienteering problem with incomplete services, and soft time windows. The problem is modeled through a mixed integer linear programming formulation and approximated by means of a multi-start Adaptive Large Neighborhood Search (ALNS) metaheuristic. Computational results show that the multi-start metaheuristic reaches better results than its classical implementation in which a single solution is build and then improved. Finally, an Orienteering Problem (OP) with mandatory visits and conflicts, is formulated through five mixed integer linear programming models. The main difference among them lies in the way they handle the subtour elimination constraints. The models were tested over a large set of instances of the problem. Computational experiments reveal that the model which subtour elimination constraints are based on a single-commodity flow formulation allows CPLEX 12.6 to obtain the optimal solution for more instances than the other formulations within a given computation time limit. Contributions: The main contributions of this thesis are: • The introduction of the bi-objective TPP with deliveries since few bi-objective versions of the TPP have been studied in the literature. Furthermore, to the best of our knowledge, there is only one more work that takes into account deliveries in a TPP. • The design and implementation of a hybrid heuristic based on relinked local search and VNS to solve the bi-objective TPP with deliveries. Additionally, we provide guidelines for the application of the heuristic when different characteristics of the instances are observed. • The design and implementation of a multi-start adaptive large neighborhood search to solve a selective delivery schedule problem. • The experimental comparison among different formulations for an OP with mandatory nodes and conflicts

Heuristics for New Problems Arising in the Transport of People and Goods

The Vehicle Routing Problem (VRP) and its numerous variants are amongst the most widely studied in the entire Operations Research literature, with applications in fields includ- ing supply chain management, journey planning and vehicle scheduling. In this thesis, we focus on three problems from two fields with a wide reach; the design of public trans- port systems and the robust routing of delivery vehicles. Each chapter investigates a new setting, formulates an optimization problem, introduces various solution methods and presents computational experiments highlighting salient points. The first problem involves commuters who use a flexible shuttle service to travel to a main transit hub, where they catch a fixed route public transport service to their true destina- tion. In our variant, passengers must forgo some of the choices they had in previous ver- sions; the service provider chooses the specific hub passengers are taken to (provided all relevant timing constraints are satisfied). This introduces both complexities and opportu- nities not seen in other VRP variants, so we present two solution methods tailored for this problem. An extensive computational study over a range of networks shows this flexibility allows significant cost savings with little impact on the quality of service received. The second problem involves dynamic ridesharing schemes and one of their most per- sistent drawbacks: the requirement to attract a large number of users during the start up phase. Although this is influenced by many factors, a significant consideration is the per- ceived uncertainty around finding a match. To address this, the service provider may wish to employ a small number of their own private drivers, to serve riders who would oth- erwise remain unmatched. We explore how this could be formulated as an optimization problem and discuss the objectives and constraints the service provider may have. We then describe a special structure inherent to the problem and present three different so- lution methods which exploit this. Finally, a broad computational study demonstrates the potential benefits of these dedicated drivers and identifies environments in which they are most useful. The third problem comes from the field of logistics and involves a large delivery firm serving an uncertain customer set. The firm wishes to build low cost delivery routes that remain efficient after the appearance and removal of some customers. We formulate this problem and present a heuristic which is both computationally cheaper and more versatile than comparative exact methods. A wide computational study illustrates our heuristic’s predictive power and its efficacy compared to natural alternative strategies

Two-Stage Vehicle Routing Problems with Profits and Buffers: Analysis and Metaheuristic Optimization Algorithms

This thesis considers the Two-Stage Vehicle Routing Problem (VRP) with Profits and Buffers, which generalizes various optimization problems that are relevant for practical applications, such as the Two-Machine Flow Shop with Buffers and the Orienteering Problem. Two optimization problems are considered for the Two-Stage VRP with Profits and Buffers, namely the minimization of total time while respecting a profit constraint and the maximization of total profit under a budget constraint. The former generalizes the makespan minimization problem for the Two-Machine Flow Shop with Buffers, whereas the latter is comparable to the problem of maximizing score in the Orienteering Problem. For the three problems, a theoretical analysis is performed regarding computational complexity, existence of optimal permutation schedules (where all vehicles traverse the same nodes in the same order) and potential gaps in attainable solution quality between permutation schedules and non-permutation schedules. The obtained theoretical results are visualized in a table that gives an overview of various subproblems belonging to the Two-Stage VRP with Profits and Buffers, their theoretical properties and how they are connected. For the Two-Machine Flow Shop with Buffers and the Orienteering Problem, two metaheuristics 2BF-ILS and VNSOP are presented that obtain favorable results in computational experiments when compared to other state-of-the-art algorithms. For the Two-Stage VRP with Profits and Buffers, an algorithmic framework for Iterative Search Algorithms with Variable Neighborhoods (ISAVaN) is proposed that generalizes aspects from 2BF-ILS as well as VNSOP. Various algorithms derived from that framework are evaluated in an experimental study. The evaluation methodology used for all computational experiments in this thesis takes the performance during the run time into account and demonstrates that algorithms for structurally different problems, which are encompassed by the Two-Stage VRP with Profits and Buffers, can be evaluated with similar methods. The results show that the most suitable choice for the components in these algorithms is dependent on the properties of the problem and the considered evaluation criteria. However, a number of similarities to algorithms that perform well for the Two-Machine Flow Shop with Buffers and the Orienteering Problem can be identified. The framework unifies these characteristics, providing a spectrum of algorithms that can be adapted to the specifics of the considered Vehicle Routing Problem.:1 Introduction 2 Background 2.1 Problem Motivation 2.2 Formal Definition of the Two-Stage VRP with Profits and Buffers 2.3 Review of Literature on Related Vehicle Routing Problems 2.3.1 Two-Stage Vehicle Routing Problems 2.3.2 Vehicle Routing Problems with Profits 2.3.3 Vehicle Routing Problems with Capacity- or Resource-based Restrictions 2.4 Preliminary Remarks on Subsequent Chapters 3 The Two-Machine Flow Shop Problem with Buffers 3.1 Review of Literature on Flow Shop Problems with Buffers 3.1.1 Algorithms and Metaheuristics for Flow Shops with Buffers 3.1.2 Two-Machine Flow Shop Problems with Buffers 3.1.3 Blocking Flow Shops 3.1.4 Non-Permutation Schedules 3.1.5 Other Extensions and Variations of Flow Shop Problems 3.2 Theoretical Properties 3.2.1 Computational Complexity 3.2.2 The Existence of Optimal Permutation Schedules 3.2.3 The Gap Between Permutation Schedules an Non-Permutation 3.3 A Modification of the NEH Heuristic 3.4 An Iterated Local Search for the Two-Machine Flow Shop Problem with Buffers 3.5 Computational Evaluation 3.5.1 Algorithms for Comparison 3.5.2 Generation of Problem Instances 3.5.3 Parameter Values 3.5.4 Comparison of 2BF-ILS with other Metaheuristics 3.5.5 Comparison of 2BF-OPT with NEH 3.6 Summary 4 The Orienteering Problem 4.1 Review of Literature on Orienteering Problems 4.2 Theoretical Properties 4.3 A Variable Neighborhood Search for the Orienteering Problem 4.4 Computational Evaluation 4.4.1 Measurement of Algorithm Performance 4.4.2 Choice of Algorithms for Comparison 4.4.3 Problem Instances 4.4.4 Parameter Values 4.4.5 Experimental Setup 4.4.6 Comparison of VNSOP with other Metaheuristics 4.5 Summary 5 The Two-Stage Vehicle Routing Problem with Profits and Buffers 5.1 Theoretical Properties of the Two-Stage VRP with Profits and Buffers 5.1.1 Computational Complexity of the General Problem 5.1.2 Existence of Permutation Schedules in the Set of Optimal Solutions 5.1.3 The Gap Between Permutation Schedules an Non-Permutation Schedules 5.1.4 Remarks on Restricted Cases 5.1.5 Overview of Theoretical Results 5.2 A Metaheuristic Framework for the Two-Stage VRP with Profits and Buffers 5.3 Experimental Results 5.3.1 Problem Instances 5.3.2 Experimental Results for O_{max R, Cmax≤B} 5.3.3 Experimental Results for O_{min Cmax, R≥Q} 5.4 Summary Bibliography List of Figures List of Tables List of Algorithm