Two-phase strategies for the bi-objective minimum spanning tree problem

This paper presents a new two-phase algorithm for the bi-objective minimum spanning tree (BMST) prob-lem. In the first phase, it computes the extreme supported efficient solutions resorting to both mathematicalprogramming and algorithmic approaches, while the second phase is devoted to obtaining the remaining ef-ficient solutions (non-extreme supported and non-supported). This latter phase is based on a new recursiveprocedure capable of generating all the spanning trees of a connected graph through edge interchanges basedon increasing evaluation of non-zero reduced costs of associated weighted linear programs. Such a procedureexploits a common property of a wider class of problems to which the minimum spanning tree (MST) prob-lem belongs, that is the spanning tree structure of its basic feasible solutions. Computational experimentsare conducted on different families of graphs and with different types of cost. These results show that thisnew two-phase algorithm is correct, very easy to implement and it allows one to extract conclusions on thedifficulty of finding the entire set of Pareto solutions of the BMST problem depending on the graph topologyand the possible correlation of the edge cost

PaMILO: A Solver for Multi-Objective Mixed Integer Linear Optimization and Beyond

In multi-objective optimization, several potentially conflicting objective functions need to be optimized. Instead of one optimal solution, we look for the set of so called non-dominated solutions. An important subset is the set of non-dominated extreme points. Finding it is a computationally hard problem in general. While solvers for similar problems exist, there are none known for multi-objective mixed integer linear programs (MOMILPs) or multi-objective mixed integer quadratically constrained quadratic programs (MOMIQCQPs). We present PaMILO, the first solver for finding non-dominated extreme points of MOMILPs and MOMIQCQPs. PaMILO provides an easy to use interface and is implemented in C++17. It solves occurring subproblems employing either CPLEX or Gurobi. PaMILO adapts the dual-benson algorithm for multi-objective linear programming (MOLP). As it was previously only defined for MOLPs, we describe how it can be adapted for MOMILPs, MOMIQCQPs and even more problem classes in the future

Graph-based Algorithms for Smart Mobility Planning and Large-scale Network Discovery

Graph theory has become a hot topic in the past two decades as evidenced by the increasing number of citations in research. Its applications are found in many fields, e.g. database, clustering, routing, etc. In this thesis, two novel graph-based algorithms are presented. The first algorithm finds itself in the thriving carsharing service, while the second algorithm is about large graph discovery to unearth the unknown graph before any analyses can be performed. In the first scenario, the automatisation of the fleet planning process in carsharing is proposed. The proposed work enhances the accuracy of the planning to the next level by taking an advantage of the open data movement such as street networks, building footprints, and demographic data. By using the street network (based on graph), it solves the questionable aspect in many previous works, feasibility as they tended to use rasterisation to simplify the map, but that comes with the price of accuracy and feasibility. A benchmark suite for further research in this problem is also provided. Along with it, two optimisation models with different sets of objectives and contexts are proposed. Through a series of experiment, a novel hybrid metaheuristic algorithm is proposed. The algorithm is called NGAP, which is based on Reference Point based Non-dominated Sorting genetic Algorithm (NSGA-III) and Pareto Local Search (PLS) and a novel problem specific local search operator designed for the fleet placement problem in carsharing called Extensible Neighbourhood Search (ENS). The designed local search operator exploits the graph structure of the street network and utilises the local knowledge to improve the exploration capability. The results show that the proposed hybrid algorithm outperforms the original NSGA-III in convergence under the same execution time. The work in smart mobility is done on city scale graphs which are considered to be medium size. However, the scale of the graphs in other fields in the real-world can be much larger than that which is why the large graph discovery algorithm is proposed as the second algorithm. To elaborate on the definition of large, some examples are required. The internet graph has over 30 billion nodes. Another one is a human brain network contains around 1011 nodes. Apart of the size, there is another aspect in real-world graph and that is the unknown. With the dynamic nature of the real-world graphs, it is almost impossible to have a complete knowledge of the graph to perform an analysis that is why graph traversal is crucial as the preparation process. I propose a novel memoryless chaos-based graph traversal algorithm called Chaotic Traversal (CHAT). CHAT is the first graph traversal algorithm that utilises the chaotic attractor directly. An experiment with two well-known chaotic attractors, Lozi map and Rössler system is conducted. The proposed algorithm is compared against the memoryless state-of-the-art algorithm, Random Walk. The results demonstrate the superior performance in coverage rate over Random Walk on five tested topologies; ring, small world, random, grid and power-law. In summary, the contribution of this research is twofold. Firstly, it contributes to the research society by introducing new study problems and novel approaches to propel the advance of the current state-of-the-art. And Secondly, it demonstrates a strong case for the conversion of research to the industrial sector to solve a real-world problem

MOMO - multi-objective metabolic mixed integer optimization : application to yeast strain engineering

BACKGROUND: In this paper, we explore the concept of multi-objective optimization in the field of metabolic engineering when both continuous and integer decision variables are involved in the model. In particular, we propose a multi-objective model that may be used to suggest reaction deletions that maximize and/or minimize several functions simultaneously. The applications may include, among others, the concurrent maximization of a bioproduct and of biomass, or maximization of a bioproduct while minimizing the formation of a given by-product, two common requirements in microbial metabolic engineering. RESULTS: Production of ethanol by the widely used cell factory Saccharomyces cerevisiae was adopted as a case study to demonstrate the usefulness of the proposed approach in identifying genetic manipulations that improve productivity and yield of this economically highly relevant bioproduct. We did an in vivo validation and we could show that some of the predicted deletions exhibit increased ethanol levels in comparison with the wild-type strain. CONCLUSIONS: The multi-objective programming framework we developed, called MOMO, is open-source and uses POLYSCIP (Available at http://polyscip.zib.de/). as underlying multi-objective solver. MOMO is available at http://momo-sysbio.gforge.inria.fr

MOMO - multi-objective metabolic mixed integer optimization : application to yeast strain engineering

In this paper, we explore the concept of multi-objective optimization in the field of metabolic engineering when both continuous and integer decision variables are involved in the model. In particular, we propose a multi-objective model that may be used to suggest reaction deletions that maximize and/or minimize several functions simultaneously. The applications may include, among others, the concurrent maximization of a bioproduct and of biomass, or maximization of a bioproduct while minimizing the formation of a given by-product, two common requirements in microbial metabolic engineering. Production of ethanol by the widely used cell factory Saccharomyces cerevisiae was adopted as a case study to demonstrate the usefulness of the proposed approach in identifying genetic manipulations that improve productivity and yield of this economically highly relevant bioproduct. We did an in vivo validation and we could show that some of the predicted deletions exhibit increased ethanol levels in comparison with the wild-type strain. The multi-objective programming framework we developed, called Momo, is open-source and uses PolySCIP‡ as underlying multi-objective solver. Momo is available at http://momo-sysbio.gforge.inria.f

El problema paramétrico del emparejamiento en grafos y problema de emparejamiento con dos objetivos

The minimum (maximum) matching problem is a fundamental problem in combinatorial optimization. The special structure of matching found by Edmonds allows to use different approximations. The idea of this work is to present a general insight of the matching problem, different sorts of algorithms for solving its original and the bi-objective formulations and a computational approach. In section 1 we describe the problem, its applications and the Grötschel-Holland algorithm (for solving using linear programming). In section 2 we introduce the theoretical background necessary for understanding the SAP algorithm and the sensitive analysis. In section 3 we implement some methods in Python 3.7 with Gurobi to study their computational properties and sensitive analysis. In section 4 we present our conclusions.El problema del emparejamiento es una de las cuestiones clásicas de la Programación Matemática. En este trabajo desarrollamos un extenso análisis sobre el trasfondo teórico de ciertos métodos para resolverlo, tanto en su formulación original, como en la formulación biobjetivo. Tras una presentación inicial del problema, presentamos una primera aproximación a la resolución del problema mediante la Programación Lineal conocida como el algoritmo de Grötschel-Holland. Seguidamente, veremos numerosas aplicaciones que motivan el interés del problema. En el segundo capítulo nos centramos en los conceptos y la estructura intrínseca del problema del emparejamiento, la cuál nos permite finalmente detallar el algoritmo del SAP. Además, presentamos el método de reoptimización propuesto por Derigs para este algoritmo. El tercer epígrame lo dedicamos a realizar un análisis computacional. Implementamos en Python 3.7 distintos métodos de resolución del problema del emparejamiento con el fin de reportar una comparativa entre ellos. Finalmente, llevamos a cabo un análisis de sensibilidad del problema original y la versión biobjetivo. Finalmente, en el cuarto capítulo presentamos las conclusiones.Universidad de Sevilla. Máster Universitario en Matemática

Applied Metaheuristic Computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC

Applied Methuerstic computing

For decades, Applied Metaheuristic Computing (AMC) has been a prevailing optimization technique for tackling perplexing engineering and business problems, such as scheduling, routing, ordering, bin packing, assignment, facility layout planning, among others. This is partly because the classic exact methods are constrained with prior assumptions, and partly due to the heuristics being problem-dependent and lacking generalization. AMC, on the contrary, guides the course of low-level heuristics to search beyond the local optimality, which impairs the capability of traditional computation methods. This topic series has collected quality papers proposing cutting-edge methodology and innovative applications which drive the advances of AMC