Building Better Nurse Scheduling Algorithms

The aim of this research is twofold: Firstly, to model and solve a complex nurse scheduling problem with an integer programming formulation and evolutionary algorithms. Secondly, to detail a novel statistical method of comparing and hence building better scheduling algorithms by identifying successful algorithm modifications. The comparison method captures the results of algorithms in a single figure that can then be compared using traditional statistical techniques. Thus, the proposed method of comparing algorithms is an objective procedure designed to assist in the process of improving an algorithm. This is achieved even when some results are non-numeric or missing due to infeasibility. The final algorithm outperforms all previous evolutionary algorithms, which relied on human expertise for modification

The congested multicommodity network design problem

This paper studies a version of the fixed-charge multicommodity network design problem where in addition to the traditional costs of flow and design, congestion at nodes is explicitly considered. The problem is initially modeled as a nonlinear integer programming formulation and two solution approaches are proposed: (i) a reformulation of the problem as a mixed integer second order cone program to optimally solve the problem for small to medium scale problem instances, and (ii) an evolutionary algorithm using elements of iterated local search and scatter search to provide upper bounds. Extensive computational results on new benchmark problem instances and on real case data are presented

Incorporating Road Networks into Territory Design

Given a set of basic areas, the territory design problem asks to create a predefined number of territories, each containing at least one basic area, such that an objective function is optimized. Desired properties of territories often include a reasonable balance, compact form, contiguity and small average journey times which are usually encoded in the objective function or formulated as constraints. We address the territory design problem by developing graph theoretic models that also consider the underlying road network. The derived graph models enable us to tackle the territory design problem by modifying graph partitioning algorithms and mixed integer programming formulations so that the objective of the planning problem is taken into account. We test and compare the algorithms on several real world instances

Bus driver rostering by hybrid methods based on column generation

Tese de doutoramento, Informática (Engenharia Informática), Universidade de Lisboa, Faculdade de Ciências, 2018Rostering problems arise in a diversity of areas where, according to the business and labor rules, distinct variants of the problem are obtained with different constraints and objectives considered. The diversity of existing rostering problems, allied with their complexity, justifies the activity of the research community addressing them. The current research on rostering problems is mainly devoted to achieving near-optimal solutions since, most of the times, the time needed to obtain optimal solutions is very high. In this thesis, a Bus Driver Rostering Problem is addressed, to which an integer programming model is adapted from the literature, and a new decomposition model with three distinct subproblems representations is proposed. The main objective of this research is to develop and evaluate a new approach to obtain solutions to the problem in study. The new approach follows the concept of search based on column generation, which consists in using the column generation method to solve problems represented by decomposition models and, after, applying metaheuristics to search for the best combination of subproblem solutions that, when combined, result in a feasible integer solution to the complete problem. Besides the new decomposition models proposed for the Bus Driver Rostering Problem, this thesis proposes the extension of the concept of search by column generation to allow using population-based metaheuristics and presents the implementation of the first metaheuristic using populations, based on the extension, which is an evolutionary algorithm. There are two additional contributions of this thesis. The first is an heuristic allowing to obtain solutions for the subproblems in an individual or aggregated way and the second is a repair operator which can be used by the metaheuristics to repair infeasible solutions and, eventually, generate missing subproblem solutions needed. The thesis includes the description and results from an extensive set of computational tests. Multiple configurations of the column generation with three decomposition models are tested to assess the best configuration to use in the generation of the search space for the metaheuristic. Additional tests compare distinct single-solution metaheuristics and our basic evolutionary algorithm in the search for integer solutions in the search space obtained by the column generation. A final set of tests compares the results of our final algorithm (with the best column generation configuration and the evolutionary algorithm using the repair operator) and the solutions obtained by solving the problem represented by the integer programming model with a commercial solver.Programa de Apoio à Formação Avançada de Docentes do Ensino Superior Politécnico (PROTEC), SFRH/PROTEC/67405/201

Ortalama-varyans portföy optimizasyonunda genetik algoritma uygulamaları üzerine bir literatür araştırması

Mean-variance portfolio optimization model, introduced by Markowitz, provides a fundamental answer to the problem of portfolio management. This model seeks an efficient frontier with the best trade-offs between two conflicting objectives of maximizing return and minimizing risk. The problem of determining an efficient frontier is known to be NP-hard. Due to the complexity of the problem, genetic algorithms have been widely employed by a growing number of researchers to solve this problem. In this study, a literature review of genetic algorithms implementations on mean-variance portfolio optimization is examined from the recent published literature. Main specifications of the problems studied and the specifications of suggested genetic algorithms have been summarized

PonyGE2: Grammatical Evolution in Python

Grammatical Evolution (GE) is a population-based evolutionary algorithm, where a formal grammar is used in the genotype to phenotype mapping process. PonyGE2 is an open source implementation of GE in Python, developed at UCD's Natural Computing Research and Applications group. It is intended as an advertisement and a starting-point for those new to GE, a reference for students and researchers, a rapid-prototyping medium for our own experiments, and a Python workout. As well as providing the characteristic genotype to phenotype mapping of GE, a search algorithm engine is also provided. A number of sample problems and tutorials on how to use and adapt PonyGE2 have been developed.Comment: 8 pages, 4 figures, submitted to the 2017 GECCO Workshop on Evolutionary Computation Software Systems (EvoSoft

A mixed integer quadratic programming formulation for the economic dispatch of generators with prohibited operating zones

In this paper, an optimisation-based approach is proposed using a mixed integer quadratic programming model for the economic dispatch of electrical power generators with prohibited zones of operation. The main advantage of the proposed approach is its capability to solve case studies from the literature to global optimality quickly and without any targeting of solution procedures. (c) 2006 Elsevier B.V. All rights reserved