The trade off between diversity and quality for multi-objective workforce scheduling

In this paper we investigate and compare multi-objective and weighted single objective approaches to a real world workforce scheduling problem. For this difficult problem we consider the trade off in solution quality versus population diversity, for different sets of fixed objective weights. Our real-world workforce scheduling problem consists of assigning resources with the appropriate skills to geographically dispersed task locations while satisfying time window constraints. The problem is NP-Hard and contains the Resource Constrained Project Scheduling Problem (RCPSP) as a sub problem. We investigate a genetic algorithm and serial schedule generation scheme together with various multi-objective approaches. We show that multi-objective genetic algorithms can create solutions whose fitness is within 2% of genetic algorithms using weighted sum objectives even though the multi-objective approaches know nothing of the weights. The result is highly significant for complex real-world problems where objective weights are seldom known in advance since it suggests that a multi-objective approach can generate a solution close to the user preferred one without having knowledge of user preferences

Assembly sequence planning using hybrid binary particle swarm optimization

Assembly Sequence Planning (ASP) is known as a large-scale, timeconsuming combinatorial problem. Therefore time is the main factor in production planning. Recently, ASP in production planning had been studied widely especially to minimize the time and consequently reduce the cost. The first objective of this research is to formulate and analyse a mathematical model of the ASP problem. The second objective is to minimize the time of the ASP problem and hence reduce the product cost. A case study of a product consists of 19 components have been used in this research, and the fitness function of the problem had been calculated using Binary Particle Swarm Optimization (BPSO), and hybrid algorithm of BPSO and Differential Evolution (DE). The novel algorithm of BPSODE has been assessed with performance-evaluated criteria (performance measure). The algorithm has been validated using 8 comprehensive benchmark problems from the literature. The results show that the BPSO algorithm has an improved performance and can reduce further the time of assembly of the 19 parts of the ASP compared to the Simulated Annealing and Genetic Algorithm. The novel hybrid BPSODE algorithm shows a superior performance when assessed via performance-evaluated criteria compared to BPSO. The BPSODE algorithm also demonstrated a good generation of the recorded optimal value for the 8 standard benchmark problems

A Field Guide to Genetic Programming

xiv, 233 p. : il. ; 23 cm.Libro ElectrónicoA Field Guide to Genetic Programming (ISBN 978-1-4092-0073-4) is an introduction to genetic programming (GP). GP is a systematic, domain-independent method for getting computers to solve problems automatically starting from a high-level statement of what needs to be done. Using ideas from natural evolution, GP starts from an ooze of random computer programs, and progressively refines them through processes of mutation and sexual recombination, until solutions emerge. All this without the user having to know or specify the form or structure of solutions in advance. GP has generated a plethora of human-competitive results and applications, including novel scientific discoveries and patentable inventions. The authorsIntroduction -- Representation, initialisation and operators in Tree-based GP -- Getting ready to run genetic programming -- Example genetic programming run -- Alternative initialisations and operators in Tree-based GP -- Modular, grammatical and developmental Tree-based GP -- Linear and graph genetic programming -- Probalistic genetic programming -- Multi-objective genetic programming -- Fast and distributed genetic programming -- GP theory and its applications -- Applications -- Troubleshooting GP -- Conclusions.Contents xi 1 Introduction 1.1 Genetic Programming in a Nutshell 1.2 Getting Started 1.3 Prerequisites 1.4 Overview of this Field Guide I Basics 2 Representation, Initialisation and GP 2.1 Representation 2.2 Initialising the Population 2.3 Selection 2.4 Recombination and Mutation Operators in Tree-based 3 Getting Ready to Run Genetic Programming 19 3.1 Step 1: Terminal Set 19 3.2 Step 2: Function Set 20 3.2.1 Closure 21 3.2.2 Sufficiency 23 3.2.3 Evolving Structures other than Programs 23 3.3 Step 3: Fitness Function 24 3.4 Step 4: GP Parameters 26 3.5 Step 5: Termination and solution designation 27 4 Example Genetic Programming Run 4.1 Preparatory Steps 29 4.2 Step-by-Step Sample Run 31 4.2.1 Initialisation 31 4.2.2 Fitness Evaluation Selection, Crossover and Mutation Termination and Solution Designation Advanced Genetic Programming 5 Alternative Initialisations and Operators in 5.1 Constructing the Initial Population 5.1.1 Uniform Initialisation 5.1.2 Initialisation may Affect Bloat 5.1.3 Seeding 5.2 GP Mutation 5.2.1 Is Mutation Necessary? 5.2.2 Mutation Cookbook 5.3 GP Crossover 5.4 Other Techniques 32 5.5 Tree-based GP 39 6 Modular, Grammatical and Developmental Tree-based GP 47 6.1 Evolving Modular and Hierarchical Structures 47 6.1.1 Automatically Defined Functions 48 6.1.2 Program Architecture and Architecture-Altering 50 6.2 Constraining Structures 51 6.2.1 Enforcing Particular Structures 52 6.2.2 Strongly Typed GP 52 6.2.3 Grammar-based Constraints 53 6.2.4 Constraints and Bias 55 6.3 Developmental Genetic Programming 57 6.4 Strongly Typed Autoconstructive GP with PushGP 59 7 Linear and Graph Genetic Programming 61 7.1 Linear Genetic Programming 61 7.1.1 Motivations 61 7.1.2 Linear GP Representations 62 7.1.3 Linear GP Operators 64 7.2 Graph-Based Genetic Programming 65 7.2.1 Parallel Distributed GP (PDGP) 65 7.2.2 PADO 67 7.2.3 Cartesian GP 67 7.2.4 Evolving Parallel Programs using Indirect Encodings 68 8 Probabilistic Genetic Programming 8.1 Estimation of Distribution Algorithms 69 8.2 Pure EDA GP 71 8.3 Mixing Grammars and Probabilities 74 9 Multi-objective Genetic Programming 75 9.1 Combining Multiple Objectives into a Scalar Fitness Function 75 9.2 Keeping the Objectives Separate 76 9.2.1 Multi-objective Bloat and Complexity Control 77 9.2.2 Other Objectives 78 9.2.3 Non-Pareto Criteria 80 9.3 Multiple Objectives via Dynamic and Staged Fitness Functions 80 9.4 Multi-objective Optimisation via Operator Bias 81 10 Fast and Distributed Genetic Programming 83 10.1 Reducing Fitness Evaluations/Increasing their Effectiveness 83 10.2 Reducing Cost of Fitness with Caches 86 10.3 Parallel and Distributed GP are Not Equivalent 88 10.4 Running GP on Parallel Hardware 89 10.4.1 Master–slave GP 89 10.4.2 GP Running on GPUs 90 10.4.3 GP on FPGAs 92 10.4.4 Sub-machine-code GP 93 10.5 Geographically Distributed GP 93 11 GP Theory and its Applications 97 11.1 Mathematical Models 98 11.2 Search Spaces 99 11.3 Bloat 101 11.3.1 Bloat in Theory 101 11.3.2 Bloat Control in Practice 104 III Practical Genetic Programming 12 Applications 12.1 Where GP has Done Well 12.2 Curve Fitting, Data Modelling and Symbolic Regression 12.3 Human Competitive Results – the Humies 12.4 Image and Signal Processing 12.5 Financial Trading, Time Series, and Economic Modelling 12.6 Industrial Process Control 12.7 Medicine, Biology and Bioinformatics 12.8 GP to Create Searchers and Solvers – Hyper-heuristics xiii 12.9 Entertainment and Computer Games 127 12.10The Arts 127 12.11Compression 128 13 Troubleshooting GP 13.1 Is there a Bug in the Code? 13.2 Can you Trust your Results? 13.3 There are No Silver Bullets 13.4 Small Changes can have Big Effects 13.5 Big Changes can have No Effect 13.6 Study your Populations 13.7 Encourage Diversity 13.8 Embrace Approximation 13.9 Control Bloat 13.10 Checkpoint Results 13.11 Report Well 13.12 Convince your Customers 14 Conclusions Tricks of the Trade A Resources A.1 Key Books A.2 Key Journals A.3 Key International Meetings A.4 GP Implementations A.5 On-Line Resources 145 B TinyGP 151 B.1 Overview of TinyGP 151 B.2 Input Data Files for TinyGP 153 B.3 Source Code 154 B.4 Compiling and Running TinyGP 162 Bibliography 167 Inde

Um algoritmo de otimização por nuvem de partículas para resolução de problemas combinatórios

Resumo: O Particle Swarm Optimization (PSO) pertence a uma classe de algoritmos inspirados em comportamentos sociais naturais inteligentes, chamada Swarm Intelligence (SI). O algoritmo PSO tem sido aplicado com sucesso na resolução de problemas de otimização contínua, no entanto, o seu potencial em problemas discretos não foi suficientemente explorado. Trabalhos recentes têm proposto a implementação de PSO usando algoritmos de busca local e Path relinking com resultados promissores. Este trabalho tem como objetivo apresentar um algoritmo PSO como um meta-modelo que utiliza internamente busca local e Path relinking, mas diferentemente das abordagens anteriores, o algoritmo proposto mantém o conceito principal de PSO para a atualização da velocidade da partícula. O trabalho descreve o algoritmo proposto como uma plataforma geral para problemas combinatórios. Tal proposta é validada em duas implementações: uma aplicada ao Problema do Caixeiro Viajante e outra ao Problema da Mochila. As peculiaridades e uma série de experimentos de calibragem de ambos os algoritmos são relatados. Finalmente, a qualidade do algoritmo proposto é testada na comparação com outros PSO discretos da literatura recente e também com outro conhecido algoritmo de metaheurística: o Ant Colony Optimization (ACO). Os resultados são encorajadores e reforçam a idéia de que o algoritmo PSO também pode ser competitivo em espaço de busca discreto, assim como levam a crer que a utilização de métodos dependentes do problema pode ser uma excelente alternativa na aplicação de PSO a este tipo de problema

Traveling Salesman Problem

The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance

Solving the vehicle routing problem using hybrid cellular evolutionary algorithm

Problem usmjeravanja vozila (VRP) kompleksan je kombinatorički problem s kojim se svakodnevno susreću tvrtke koje obavljaju dostavu robe. Njegovim učinkovitim rješavanjem moguće je značajno smanjiti troškove dostave. Metaheurističkim metodama moguće je relativno brzo pronaći visoko kvalitetna rješenja. Stanični evolucijski algoritam metaheuristički je algoritam kod kojeg su jedinke iz populacije raspoređene unutar toroidalne mreže i mogu biti u interakciji samo sa obližnjim jedinkama. Podešavanjem selekcijskog pritiska moguće je postići odgovarajući omjer diverzifikacije i intenzifikacije koji je ključan za uspješnost algoritma. Hibridizacija postupkom pretraživanja velikog susjedstva ubrzava pronalazak visoko kvalitetnih rješenja. Razvijeni algoritam testiran je na nekoliko skupova ispitnih zadataka te na problemima dostave hrvatskih tvrtki. Rezultati ostvareni na ispitnim zadacima pokazuju da učinkovitost algoritma ne odstupa mnogo od najboljih poznatih algoritama za ovu vrstu problema, dok rezultati ostvareni na problemima hrvatskih tvrtki pokazuju da je primjenom algoritma moguće postići značajne uštede.Vehicle Routing Problem (VRP) is a complex combinatorial problem encountered daily by companies that are dealing with goods delivery. With its ecient solving it is possible to signicantly reduce the cost of delivery. Metaheuristic methods are capable of nding high-quality solutions in reasonable amount of time. The cellular evolutionary algorithm is a metaheuristic algorithm in which the individuals from the population are distributed within the toroidal grid and can interact only with nearby entities. By adjusting the selection pressure, it is possible to achieve the appropriate ratio of diversication and intensication that is crucial to the success of the algorithm. Hybridization by a large neighborhood search accelerates the nding of high quality solutions. The developed algorithm has been tested on several sets of benchmarks and on the delivery problems of Croatian companies. The results obtained on the benchmarks show that the eciency of the algorithm does not dier much from the best-known algorithms for this type of problem, while the results achieved on the problems of Croatian companies show that it is possible to achieve signicant savings by algorithm application

Solving the vehicle routing problem using hybrid cellular evolutionary algorithm

Problem usmjeravanja vozila (VRP) kompleksan je kombinatorički problem s kojim se svakodnevno susreću tvrtke koje obavljaju dostavu robe. Njegovim učinkovitim rješavanjem moguće je značajno smanjiti troškove dostave. Metaheurističkim metodama moguće je relativno brzo pronaći visoko kvalitetna rješenja. Stanični evolucijski algoritam metaheuristički je algoritam kod kojeg su jedinke iz populacije raspoređene unutar toroidalne mreže i mogu biti u interakciji samo sa obližnjim jedinkama. Podešavanjem selekcijskog pritiska moguće je postići odgovarajući omjer diverzifikacije i intenzifikacije koji je ključan za uspješnost algoritma. Hibridizacija postupkom pretraživanja velikog susjedstva ubrzava pronalazak visoko kvalitetnih rješenja. Razvijeni algoritam testiran je na nekoliko skupova ispitnih zadataka te na problemima dostave hrvatskih tvrtki. Rezultati ostvareni na ispitnim zadacima pokazuju da učinkovitost algoritma ne odstupa mnogo od najboljih poznatih algoritama za ovu vrstu problema, dok rezultati ostvareni na problemima hrvatskih tvrtki pokazuju da je primjenom algoritma moguće postići značajne uštede.Vehicle Routing Problem (VRP) is a complex combinatorial problem encountered daily by companies that are dealing with goods delivery. With its ecient solving it is possible to signicantly reduce the cost of delivery. Metaheuristic methods are capable of nding high-quality solutions in reasonable amount of time. The cellular evolutionary algorithm is a metaheuristic algorithm in which the individuals from the population are distributed within the toroidal grid and can interact only with nearby entities. By adjusting the selection pressure, it is possible to achieve the appropriate ratio of diversication and intensication that is crucial to the success of the algorithm. Hybridization by a large neighborhood search accelerates the nding of high quality solutions. The developed algorithm has been tested on several sets of benchmarks and on the delivery problems of Croatian companies. The results obtained on the benchmarks show that the eciency of the algorithm does not dier much from the best-known algorithms for this type of problem, while the results achieved on the problems of Croatian companies show that it is possible to achieve signicant savings by algorithm application

Solving the vehicle routing problem using hybrid cellular evolutionary algorithm

Problem usmjeravanja vozila (VRP) kompleksan je kombinatorički problem s kojim se svakodnevno susreću tvrtke koje obavljaju dostavu robe. Njegovim učinkovitim rješavanjem moguće je značajno smanjiti troškove dostave. Metaheurističkim metodama moguće je relativno brzo pronaći visoko kvalitetna rješenja. Stanični evolucijski algoritam metaheuristički je algoritam kod kojeg su jedinke iz populacije raspoređene unutar toroidalne mreže i mogu biti u interakciji samo sa obližnjim jedinkama. Podešavanjem selekcijskog pritiska moguće je postići odgovarajući omjer diverzifikacije i intenzifikacije koji je ključan za uspješnost algoritma. Hibridizacija postupkom pretraživanja velikog susjedstva ubrzava pronalazak visoko kvalitetnih rješenja. Razvijeni algoritam testiran je na nekoliko skupova ispitnih zadataka te na problemima dostave hrvatskih tvrtki. Rezultati ostvareni na ispitnim zadacima pokazuju da učinkovitost algoritma ne odstupa mnogo od najboljih poznatih algoritama za ovu vrstu problema, dok rezultati ostvareni na problemima hrvatskih tvrtki pokazuju da je primjenom algoritma moguće postići značajne uštede.Vehicle Routing Problem (VRP) is a complex combinatorial problem encountered daily by companies that are dealing with goods delivery. With its ecient solving it is possible to signicantly reduce the cost of delivery. Metaheuristic methods are capable of nding high-quality solutions in reasonable amount of time. The cellular evolutionary algorithm is a metaheuristic algorithm in which the individuals from the population are distributed within the toroidal grid and can interact only with nearby entities. By adjusting the selection pressure, it is possible to achieve the appropriate ratio of diversication and intensication that is crucial to the success of the algorithm. Hybridization by a large neighborhood search accelerates the nding of high quality solutions. The developed algorithm has been tested on several sets of benchmarks and on the delivery problems of Croatian companies. The results obtained on the benchmarks show that the eciency of the algorithm does not dier much from the best-known algorithms for this type of problem, while the results achieved on the problems of Croatian companies show that it is possible to achieve signicant savings by algorithm application