Discrete Flower Pollination Algorithm for solving the symmetric Traveling Salesman Problem

A dissertation submitted in fulfilment of the requirements for the degree of Masters of Science in Engineering (Electrical) to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, 2017The Travelling Salesman Problem (TSP) is an important NP-hard combinatorial optimisation problem that forms the foundation of many modern-day, practical problems such as logistics or network route planning. It is often used to benchmark discrete optimisation algorithms since it is a fundamental problem that has been widely researched. The Flower Pollination Algorithm (FPA) is a continuous optimisation algorithm that demonstrates promising results in comparison to other well-known algorithms. This research proposes the design, implementation and testing of two new algorithms based on the FPA for solving discrete optimisation problems, more specifically the TSP, namely the Discrete Flower Pollination Algorithm (DFPA) and the iterative Discrete Flower Pollination Algorithm (iDFPA). The iDFPA uses two proposed update methods, namely the Best Tour Update (BTU) and the Rejection Update (RU), to perform the iterative update process. The two algorithms are compared to the Ant Colony Optimisation’s (ACO) MAX−MIN Ant System (MMAS) as well as the Genetic Algorithm (GA) since they are well studied and developed. The DFPA and iDFPA results are significantly better than the GA and the iDFPA is able to outperform the ACO in all tested instances. The iDFPA with 300 iterations was able to achieve the optimal solution in the Berlin52 benchmark TSP problem as well as have improvements of up to 4.56% and 41.87% compared to the ACO and GA respectively. An analysis of how the RU and the annealing schedule used in the RU impacts on the overall results of the iDFPA is given. The RU analysis demonstrates how the annealing schedule can be manipulated to achieve certain results from the iDFPA such as faster convergence or better overall results. A parameter analysis is performed on both the DFPA and iDFPA for different TSP problem sizes and the suggested initial parameters for these algorithms are outlined.XL201

JavaEvA : a Java based framework for Evolutionary Algorithms

Das Softwarepaket JavaEvA (eine Java Implementierung Evolutionärer Algorithmen) ist ein allgemeines modulares Framework für Optimierungsalgorithmen basierend auf einer Client-Server Architektur, das geeignet ist eine Vielzahl von Optimierungsproblemen zu lösen. Das Paket wurde mit dem Schwerpunkt entwickelt neue Verfahren im Bereich der Evolutionären Algorithmen einfach entwickeln und testen zu können und diese Verfahren letztlich in praktischen Anwendungen anzuwenden. JavaEvA beinhaltet Implementierungen der üblichen Evolutionären Verfahren wie zum Beispiel Genetische Algorithmen, die CHC Adaptive Search, Population Based Incremental Learning, Evolutionsstrategien, Modellunterstützte Evolutionsstrategien, Genetisches Programmieren und Grammatical Evolution. Zusätzlich erlaubt es das modulare Framework von JavaEvA eigene eventuell problemspezifische Optimierungsmodule zu ergänzen und mit den implementieren Verfahren zu vergleichen. Das JavaEvA Paket benutzt ein generisches Verfahren zur GUI Generierung und erlaubt so einen einfachen Objektorientierten Zugang zu allen relevanten Parametern eines Evolutionären Algorithmus. Das gleiche Verfahren generiert auch entsprechende GUI Elemente für neu entwickelte Methoden und vereinfacht so den Aufwand bei der Entwicklung neuer Methoden erheblich. Zusätzlich besteht die Möglichkeit spezialisiere GUI Elemente für einzelne Objekte zu entwickeln und in das bestehende System zu integrieren, um die Benutzerfreundlichkeit weiter zu erhöhen. Da es uns unmöglich ist jedwede potenzielle Anwendung oder Optimierungsproblem zu antizipieren, ist es aus praktischen Gründen fast immer nötig eigene Implementierungen des jeweiligen Anwendungsproblems zu erstellen. Um diesen Vorgang zu erleichtern bietet diese Anleitung zusätzliche Beispiele mit detaillierten Beschreibungen, wie man ein eigenes Problem implementieren kann und JavaEvA lediglich als Optimierungstoolbox integriert. Auf diese Weise behält ihre jeweilige Anwendung die vollständige Kontrolle über die verwendeten Verfahren und die anwendungsspezifische Darstellung der Optimierungsergebnisse.The package JavaEvA (a Java implementation of Evolutionary Algorithms) is a general modular framework with an inherent client server structure to solve practical optimization problems. This package was especially designed to test and develop new approaches for Evolutionary Algorithms and to utilize them in real-world applications. JavaEvA already provides implementations of the most common Evolutionary Algorithms, like Genetic Algorithms, CHC Adaptive Search, Population Based Incremental Learning, Evolution Strategies, Model-Assisted Evolution Strategies, Genetic Programming and Grammatical Evolution. In addition the modular framework of JavaEvA allows everyone to add their own optimization modules to meet their specific requirements. The JavaEvA package uses a generic GUI framework that allows GUI access to any member of a class if get and set methods are provided and an editor is defined for the given data type. This approach allows very fast development cycles, since hardly any additional effort is necessary for implementing GUI elements, while still at the same time user specific GUI elements can be developed and integrated to increase usability. Since we cannot anticipate specific optimization problem and requirements, it is necessary for users to define their optimization problem. Therefore, we provide an additional framework and explain how one can include JavaEvA in an existing Java project or how one can implement ones own optimization problem and optimize it by using JavaEvA. This gives users total control of the optimization algorithms used

Contribution to multi-domain network slicing : resource orchestration framework and algorithms

5G/6G services and applications, in the context of the eMBB, mMTC and uRLLC network slicing framework, whose network infrastructure requirements may span beyond the coverage area of a single Infrastructure Provider (InP), are envisaged to be supported by leasing resources from multiple InPs. A challenging aspect for a Service Provider (SP) is how to obtain an optimal set of InPs on which to provision the requests and the particular substrate nodes and links within each InP on which to map the different VNFs and virtual links of the service requests, respectively, for a seamless, reliable and cost-effective orchestration of service requests. Existing works in this area either perform service mapping in uncoordinated manner, do not incorporate service reliability or do so from the perspective of stateless VNFs. Also they assume full information disclosure, or are based on exact approaches, which considerations are not well suited for future network scenarios characterized by delay sensitive mission critical applications and resource constrained networks. This thesis contributes to the above challenge by breaking the multi-domain service orchestration problem into two interlinked sub-problems that are solved in a coordinated manner: (1) Request splitting/partitioning (sub-problem 1), involving obtaining a subset of InPs and the corresponding inter-domain links on which to provision the different VNFs and virtual links of the service request; (2) Intra-domain VNF orchestration (sub-problem 2), involving obtaining the intra-domain nodes and links to provision the VNFs and virtual links of the sub-SFC associated with each InP. In this way, the thesis sets out four key targets that are necessary to align with the mission critical and delay sensitive use-cases envisaged in 5G and future networks in terms of service deployment cost and QoS: (1) coordinated mapping of service requests, with a view of realizing better utilization of the substrate resources; (2) survivability and fault-tolerant orchestration of service requests, to tame both QoS violations and the penalties from such violations; (3) limited disclosure of InP internal information, in order adhere to the privacy requirements InPs, and (4) achieving all the above targets in polynomial time. In order to realize the above targets, the thesis sought for solution techniques that are: (1) able to incorporate information learned in the previous solutions search space and historical mapping decisions, hence, resulting in acceptable performance even in scenarios of limited information exposure and fuzzy environments; (2) robust and less problem specific, hence, can be tailored to different optimization objectives, network topologies and service request constraints, thus enabling to deal with requests with either chained topologies or with bifurcated paths; (3) capable of dealing with an optimization problem that is jointly affected by multiple attributes, since in practice, the service deployment cost is jointly affected by multiple conflicting costs; (4) able to realize near-optimal solutions in practical run-times, thus rendering well suited approaches for delay sensitive and resource constrained scenarios. Three different algorithms namely, an RL, Genetic Algorithm (GA) and a fully distributed multi-stage graph-based algorithms are proposed for sub-problem 1. In addition, five different algorithms based on GA, Harmony search, RL, and multi-stage graph approach are proposed for sub-problem 2. Finally, in order to guide the implementation and adherence of the thesis proposals to the four main targets of the thesis, an architectural framework is proposed, aligned with the ETSI NFV-MANO architectural framework. Overall, the simulations results proved that the thesis proposals are optimized in terms of request acceptance ratios, mapping cost and execution time, hence, rendering such proposals well suited for 5G and future scenarios.Els serveis que es poden presentar en el marc de la tecnologia de “slicing” de xarxa de 5G/6G, com ara eMBB, mMTC o uRLLC, es possible que no els pugui oferir un sol proveïdor d’infraestructura (InP) degut a les limitacions que pot tenir la seva xarxa, i per tant que faci necessària la cooperació de múltiples InPs. En aquest cas, el primer repte que afronta el Proveïdor de Servei (SP) que rep la sol·licitud de desplegament es determinar el conjunt òptim de InPs que hi han d’intervenir i en concret els nodes i enllaços de cada un d’ells que s’han d’utilitzar per al mapatge de les diferents VNFs i enllaços virtuals de la sol·licitud. Els treballs que existeixen en aquesta àrea duen a terme el mapatge del servei be sigui de manera no coordinada, o no incorporen la fiabilitat, o ho fan des de la perspectiva de VNFs sense estat. També, pressuposen la divulgació total de la informació, o estan basats en metodologies exactes que fa que no siguin idonis per a escenaris de xarxes del futur, caracteritzats per aplicacions de missió critica, sensibles al retard i sobre xarxes amb recursos limitats. Aquesta tesi contribueix a afrontar aquests reptes dividint el problema d’orquestració de serveis multi domini en dos subproblemes relacionats, que es resolen de manera coordinada. (1) Divisió / partició de la sol·licitud de servei (sub-problema 1), que implica l'obtenció d'un subconjunt d'InPs i els enllaços interdomini corresponents sobre els quals proporcionar les diferents VNF i enllaços virtuals de la sol·licitud de servei; (2) Orquestració VNF intradomini (sub-problema 2), que implica l'obtenció dels nodes i enllaços intradomini per aprovisionar les VNF i enllaços virtuals dels sub-SFC associats a cada InP. D'aquesta manera, la tesi estableix quatre objectius clau que són necessaris per alinear-se amb els casos d'ús de missió crítica i sensibles al retard previstos en 5G i xarxes futures en termes de cost de desplegament del servei i QoS: (1) mapatge coordinat de les sol·licituds de servei, amb l'objectiu de realitzar una millor utilització dels recursos del substrat; (2) orquestració de les sol·licituds de servei contemplant la supervivència del servei en situacions de fallides, minimitzant les violacions de la QoS i les sancions derivades d'aquestes violacions; (3) divulgació limitada de la informació interna de l’InP, per tal d'adherir-se als requisits de privadesa dels InPs, i (4) aconseguir tots els objectius anteriors en temps polinòmic. Per tal de realitzar els objectius anteriors, la tesi busca solucions que siguin: (1) capaces d'incorporar informació apresa en les solucions anteriors de l'espai de cerca i decisions de mapatge històric, donant lloc a un rendiment acceptable fins i tot en escenaris d'exposició limitada a la informació i entorns difusos; (2) robustes i menys dependents dels problemes específics, i per tant, que es poden adaptar a diferents objectius d'optimització, topologies de xarxa i restriccions de sol·licitud de servei, permetent així fer front a sol·licituds amb cadenes de funcions de topologies molt diverses; (3) capaces de fer front a un problema d'optimització de múltiples atributs, ja que a la pràctica, el cost de desplegament del servei depèn de múltiples costos; (4) capaces de trobar solucions gairebé òptimes en temps suficientment breus, resultant així adequades a escenaris sensibles al retard i amb limitació de recursos. La tesi proposa tres algorismes diferents per al sub-problema 1: un algorisme de RL, un algorisme genètic (GA) i un algorisme multi etapa basat en grafs i completament distribuït. A més, es proposen cinc algorismes diferents basats en l'enfocament de grafs, un algorisme GA, un algorisme de cerca d’harmonia, un algorisme de RL i un algorisme multi-etapa per al sub-problema 2. Finalment, per tal de guiar la implementació i l'adhesió de les propostes als quatre objectius principals de la tesi, es proposa...Postprint (published version

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set