Application of genetic algorithms to the travelling salesperson problem.

Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1996.Genetic Algorithms (GAs) can be easily applied to many different problems since they make few assumptions about the application domain and perform relatively well. They can also be modified with some success for handling a particular problem. The travelling salesperson problem (TSP) is a famous NP-hard problem in combinatorial optimization. As a result it has no known polynomial time solution. The aim of this dissertation will be to investigate the application of a number of GAs to the TSP. These results will be compared with those of traditional solutions to the TSP and with the results of other applications of the GA to the TSP

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

Modelo de computación evolutivo para redes sostenibles, eficientes y resistentes.

We present a new approach to adapt the differential evolution (DE) algorithm so that it can be applied in combinatorial optimization problems. The differential evolution algorithm has been proposed as an optimization algorithm for the continuous domain, using real numbers to encode the solutions, and its main operator, the mutation, uses a arithmetic operations to create a mutant using three different random solutions. This mutation operator cannot be used in combinatorial optimization problems, which have a domain of a discrete and finite set of objects. Based on this concept, we present an idea of representing each solution as a set, and replace the arithmetic operators in the classic DE genetic operators by set operators. Using a well known NP-hard problem, the traveling salesman problem (TSP), as an example of a combinatorial optimization problem, we study different possibilities for the mutation operator, presenting the advantages and disadvantages of each, before setting with the best one. We also explain the modifications made to adapt the algorithm for a multiobjective optimization algorithm. Some of these modifications are inherent to the different type of problems, other modification are proposed to improve the algorithm. Amongst the later modification are using more than one population in the evolution process. We also present a new self-adaptive variation of the multiobjective optimization algorithm, although this is not limited to the multi-objective case, and can be used also in the single-objective

Hybrid metaheuristics for solving multi-depot pickup and delivery problems

In today's logistics businesses, increasing petrol prices, fierce competition, dynamic business environments and volume volatility put pressure on logistics service providers (LSPs) or third party logistics providers (3PLs) to be efficient, differentiated, adaptive, and horizontally collaborative in order to survive and remain competitive. In this climate, efficient computerised-decision support tools play an essential role. Especially, for freight transportation, e efficiently solving a Pickup and Delivery Problem (PDP) and its variants by an optimisation engine is the core capability required in making operational planning and decisions. For PDPs, it is required to determine minimum-cost routes to serve a number of requests, each associated with paired pickup and delivery points. A robust solution method for solving PDPs is crucial to the success of implementing decision support tools, which are integrated with Geographic Information System (GIS) and Fleet Telematics so that the flexibility, agility, visibility and transparency are fulfilled. If these tools are effectively implemented, competitive advantage can be gained in the area of cost leadership and service differentiation. In this research, variants of PDPs, which multiple depots or providers are considered, are investigated. These are so called Multi-depot Pickup and Delivery Problems (MDPDPs). To increase geographical coverage, continue growth and encourage horizontal collaboration, efficiently solving the MDPDPs is vital to operational planning and its total costs. This research deals with designing optimisation algorithms for solving a variety of real-world applications. Mixed Integer Linear Programming (MILP) formulations of the MDPDPs are presented. Due to being NP-hard, the computational time for solving by exact methods becomes prohibitive. Several metaheuristics and hybrid metaheuristics are investigated in this thesis. The extensive computational experiments are carried out to demonstrate their speed, preciseness and robustness.Open Acces

Phenotype Operators for Improved Performance of Heuristic Encoding Within Genetic Algorithms

Many approaches to applying Genetic Algorithms (GAs) to Nondeterministic Polynomial time Complete (NPC) problems involve population members encoded directly from the problem solution space. While this technique enables trivial mapping of the population members to solutions, it can cause complex problems for GA operators as they attempt to direct the evolution of the population toward more promising areas of the solution space. These operators, using inspiration from genetics and evolution in the biological world, combine and manipulate the current population to produce a new population that, it is hoped, will eventually converge toward better solutions to the original problem. However, many problems, especially graph-space problems, cannot be so easily manipulated when GA members consist of direct encodings. In such cases, GA operators must perform awkward transformations to convert the progeny into viable solutions. Here is where heuristic encoding comes into play, in that any combination of genes will produce a viable solution. However, this additional level of abstraction does cause other problems and tends to weaken the guiding effects of traditional GA operators. Thus, I have designed custom GA operators that mitigate these problems by using the solutions produced by the heuristic encoded members to better guide the manipulation when producing the next generation. This dissertation shows that heuristic encoding is an effective technique for the representation of solutions to graph-space problems. It also shows that, when using heuristic encoding, GAs with traditional operators perform well compared to more direct encoding techniques. Finally it shows the combination of heuristic encoding and GA operators designed to work with them increases GA performance and can be competitive with other techniques. I believe that these techniques will also work well for other types of problems for which GAs are commonly applied

Evolutionary Computation

This book presents several recent advances on Evolutionary Computation, specially evolution-based optimization methods and hybrid algorithms for several applications, from optimization and learning to pattern recognition and bioinformatics. This book also presents new algorithms based on several analogies and metafores, where one of them is based on philosophy, specifically on the philosophy of praxis and dialectics. In this book it is also presented interesting applications on bioinformatics, specially the use of particle swarms to discover gene expression patterns in DNA microarrays. Therefore, this book features representative work on the field of evolutionary computation and applied sciences. The intended audience is graduate, undergraduate, researchers, and anyone who wishes to become familiar with the latest research work on this field

A new three phase method (SDP method) for the multi-objective vehicle routing problem with simultaneous delivery and pickup (VRPSDP)

Transportation service operators are witnessing a growing demand for bi-directional movement of goods. Given this, the following thesis considers an extension to the vehicle routing problem (VRP) known as the delivery and pickup transportation problem (DPP), where delivery and pickup demands may occupy the same route. The problem is formulated here as the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), which requires the concurrent service of the demands at the customer location. This formulation provides the greatest opportunity for cost savings for both the service provider and recipient. The aims of this research are to propose a new theoretical design to solve the multi-objective VRPSDP, provide software support for the suggested design and validate the method through a set of experiments. A new real-life based multi-objective VRPSDP is studied here, which requires the minimisation of the often conflicting objectives: operated vehicle fleet size, total routing distance and the maximum variation between route distances (workload variation). The former two objectives are commonly encountered in the domain and the latter is introduced here because it is essential for real-life routing problems. The VRPSDP is defined as a hard combinatorial optimisation problem, therefore an approximation method, Simultaneous Delivery and Pickup method (SDPmethod) is proposed to solve it. The SDPmethod consists of three phases. The first phase constructs a set of diverse partial solutions, where one is expected to form part of the near-optimal solution. The second phase determines assignment possibilities for each sub-problem. The third phase solves the sub-problems using a parallel genetic algorithm. The suggested genetic algorithm is improved by the introduction of a set of tools: genetic operator switching mechanism via diversity thresholds, accuracy analysis tool and a new fitness evaluation mechanism. This three phase method is proposed to address the shortcoming that exists in the domain, where an initial solution is built only then to be completely dismantled and redesigned in the optimisation phase. In addition, a new routing heuristic, RouteAlg, is proposed to solve the VRPSDP sub-problem, the travelling salesman problem with simultaneous delivery and pickup (TSPSDP). The experimental studies are conducted using the well known benchmark Salhi and Nagy (1999) test problems, where the SDPmethod and RouteAlg solutions are compared with the prominent works in the VRPSDP domain. The SDPmethod has demonstrated to be an effective method for solving the multi-objective VRPSDP and the RouteAlg for the TSPSDP

Evolving comprehensible and scalable solvers using CGP for solving some real-world inspired problems

My original contribution to knowledge is the application of Cartesian Genetic Programming to design some scalable and human-understandable metaheuristics automatically; those find some suitable solutions for real-world NP-hard and discrete problems. This technique is thought to possess the ability to raise the generality of a problem-solving process, allowing some supervised machine learning tasks and being able to evolve non-deterministic algorithms. \\ Two extensions of Cartesian Genetic Programming are presented. Iterative My original contribution to knowledge is the application of Cartesian Genetic Programming to design some scalable and human-understandable metaheuristics automatically; those find some suitable solutions for real-world NP-hard and discrete problems. This technique is thought to possess the ability to raise the generality of a problem-solving process, allowing some supervised machine learning tasks and being able to evolve non-deterministic algorithms. \\ Two extensions of Cartesian Genetic Programming are presented. Iterative Cartesian Genetic Programming can encode loops and nested loop with their termination criteria, making susceptible to evolutionary modification the whole programming construct. This newly developed extension and its application to metaheuristics are demonstrated to discover effective solvers for NP-hard and discrete problems. This thesis also extends Cartesian Genetic Programming and Iterative Cartesian Genetic Programming to adapt a hyper-heuristic reproductive operator at the same time of exploring the automatic design space. It is demonstrated the exploration of an automated design space can be improved when specific types of active and non-active genes are mutated. \\ A series of rigorous empirical investigations demonstrate that lowering the comprehension barrier of automatically designed algorithms can help communicating and identifying an effective and ineffective pattern of primitives. The complete evolution of loops and nested loops without imposing a hard limit on the number of recursive calls is shown to broaden the automatic design space. Finally, it is argued the capability of a learning objective function to assess the scalable potential of a generated algorithm can be beneficial to a generative hyper-heuristic

Evolutionary Algorithms Based on Effective Search Space Reduction for Financial Optimization Problems

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 8. 문병로.This thesis presents evolutionary algorithms incorporated with effective search space reduction for financial optimization problems. Typical evolutionary algorithms try to find optimal solutions in the original, or unrestricted search space. However, they can be unsuccessful if the optimal solutions are too complex to be discovered from scratch. This can be relieved by restricting the forms of meaningful solutions or providing the initial population with some promising solutions. To this end, we propose three evolution approaches including modular, grammatical, and seeded evolutions for financial optimization problems. We also adopt local optimizations for fine-tuning the solutions, resulting in hybrid evolutionary algorithms. First, the thesis proposes a modular evolution. In the modular evolution, the possible forms of solutions are statically restricted to certain combinations of module solutions, which reflect more domain knowledge. To preserve the module solutions, we devise modular genetic operators which work on modular search space. The modular genetic operators and statically defined modules help genetic programming focus on highly promising search space. Second, the thesis introduces a grammatical evolution. We restrict the possible forms of solutions in genetic programming by a context-free grammar. In the grammatical evolution, genetic programming works on more extended search space than modular one. Grammatically typed genetic operators are introduced for the grammatical evolution. Compared with the modular evolution, grammatical evolution requires less domain knowledge. Finally, the thesis presents a seeded evolution. Our seeded evolution provides the initial population with partially optimized solutions. The set of genes for the partial optimization is selected in terms of encoding complexity. The partially optimized solutions help genetic algorithm find more promising solutions efficiently. Since they are not too excessively optimized, genetic algorithm is still able to search better solutions. Extensive empirical results are provided using three real-world financial optimization problems: attractive technical pattern discovery, extended attractive technical pattern discovery, and large-scale stock selection. They show that our search space reductions are fairly effective for the problems. By combining the search space reductions with systematic evolutionary algorithm frameworks, we show that evolutionary algorithms can be exploited for realistic profitable trading.1. Introduction 1 1.1 Search Methods 3 1.2 Search Space Reduction 4 1.3 Main Contributions 5 1.4 Organization 7 2. Preliminaries 8 2.1 Evolutionary Algorithms 8 2.1.1 Genetic Algorithm 10 2.1.2 Genetic Programing 11 2.2 Evolutionary Algorithms in Finance 12 2.3 Search Space Reduction 12 2.3.1 Modular Evolution 12 2.3.2 Grammatical Evolution 13 2.3.3 Seeded Evolution 14 2.3.4 Summary 14 2.4 Terminology 15 2.4.1 Technical Pattern and Technical Trading Rule 15 2.4.2 Forecasting Model and Trading Model 16 2.4.3 Portfolio and Rebalancing 17 2.4.4 Data Snooping Bias 17 2.5 Financial Optimization Problems 19 2.5.1 Attractive Technical Pattern Discovery and Its Extension 19 2.5.2 Stock Selection 20 2.6 Issues 21 2.6.1 General Assumptions 21 2.6.2 Performance Measure 22 3. Modular Evolution 23 3.1 Modular Genetic Programming 24 3.2 Hybrid Genetic Programming 28 3.3 Attractive Technical Pattern Discovery 29 3.3.1 Introduction 29 3.3.2 Problem Formulation 31 3.3.3 Modular Search Space 33 3.3.4 Experimental Results 35 3.3.5 Summary 41 4. Grammatical Evolution 44 4.1 Grammatical Type System 45 4.2 Hybrid Genetic Programming 47 4.3 Extended Attractive Technical Pattern Discovery 51 4.3.1 Introduction 51 4.3.2 Problem Formulation 54 4.3.3 Experimental Results 56 4.3.4 Summary 73 5. Seeded Evolution 76 5.1 Heuristic Seeding 77 5.2 Hybrid Genetic Algorithm 78 5.3 Large-Scale Stock Selection 81 5.3.1 Introduction 81 5.3.2 Problem Formulation 83 5.3.3 Ranking with Partitions 85 5.3.4 Experimental Results 87 5.3.5 Summary 96 6. Conclusions 104Docto