A model for characterising the collective dynamic behaviour of evolutionary algorithms

Exploration and exploitation are considered essential notions in evolutionary algorithms. However, a precise interpretation of what constitutes exploration or exploitation is clearly lacking and so are specific measures for characterising such notions. In this paper, we start addressing this issue by presenting new measures that can be used as indicators of the exploitation behaviour of an algorithm. These work by characterising the extent to which available information guides the search. More precisely, they quantify the dependency of a population's activity on the observed fitness values and genetic material, utilising an empirical model that uses a coarse-grained representation of population dynamics and records information about it. The model uses the k-means clustering algorithm to identify the population's "basins of activity". The exploitation behaviour is then captured by an entropy-based measure based on the model that quantifies the strength of the association between a population's activity distribution and the observed fitness landscape information. In experiments, we analysed the effects of the search operators and their parameter settings on the collective dynamic behaviour of populations. We also analysed the effect of using different problems on algorithm behaviours.We define a behavioural landscape for each problem to identify the appropriate behaviour to achieve good results and point out possible applications for the proposed model

An Analysis Of The Robustness Of Genetic Algorithm (ga) Methodology In The Design Of Trading System

(WP24/02 Clave pdf) This paper analyzes the robustness of Genetic Algorithms (GAs) technique for its application in the field of trading systems design for the Stock Exchange. The functioning of the GA is driven by the control parameters: crossover and mutation probabilities, number of generations, and size of population. Whether the results generated by the application of GAs to a specific problem are conditioned by the value assess to these parameters, becomes a main research field. The purpose of this paper is to develop a sensibility analyses about the dependency of the GA to the value of these parameters....Control parameters, Genetic algorithms, Trading systems

A Model for Characterising the Collective Dynamic Behaviour of Evolutionary Algorithms

Abstract. Exploration and exploitation are considered essential notions in evolutionary algorithms. However, a precise interpretation of what constitutes exploration or exploitation is clearly lacking and so are specific measures for characterising such notions. In this paper, we start addressing this issue by presenting new measures that can be used as indicators of the exploitation behaviour of an algorithm. These work by characterising the extent to which available information guides the search. More precisely, they quantify the dependency of a population's activity on the observed fitness values and genetic material, utilising an empirical model that uses a coarse-grained representation of population dynamics and records information about it. The model uses the k-means clustering algorithm to identify the population's "basins of activity". The exploitation behaviour is then captured by an entropy-based measure based on the model that quantifies the strength of the association between a population's activity distribution and the observed fitness landscape information. In experiments, we analysed the effects of the search operators and their parameter settings on the collective dynamic behaviour of populations. We also analysed the effect of using different problems on algorithm behaviours. We define a behavioural landscape for each problem to identify the appropriate behaviour to achieve good results and point out possible applications for the proposed model

Illuminating meaningful diversity in complex feature spaces through adaptive grid-based genetic algorithms

In many fields there exist problems for which multiple solutions of suitably high performance may be found across distinct regions of the search space. Optimisation of the search towards including these distinct solutions is important not only to understanding these spaces but also to avoiding local optima. This is the goal of a type of genetic algorithms called illumination algorithms. In Chapter 2, we demonstrate the use of an illumination algorithm in the exploration of networks sharing only a given set of structural features (valid networks). This method produces a population of valid networks that are more diverse than those produced using state of the art methods, however, it was found to be too inefficient to be usable in real-world problems. Additionally, setting an appropriate resolution of the search requires some amount of prior knowledge of the space of solutions. Addressing this problem is the focus of Chapter 3, in which we develop three extensions to the method: a) an exact method of mutation whereby only valid networks are explored, b) an adaptive mechanism for setting the resolution of the search, c) a principle for tuning mutations parameters to the search’ s resolution. We show that with these additions our method is able to increase the diversity of solutions found in significantly fewer iterations. Finally, in Chapter 4 we expand our method for use in more general problem spaces. We benchmark it against the state of the art. In all tested landscapes, we show that our method is able to identify more meaningful niches in the spaces in the same number of iterations. We conclude by highlighting the limits of our framework and discuss further directions

Power systems generation scheduling and optimisation using evolutionary computation techniques

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Optimal generation scheduling attempts to minimise the cost of power production while satisfying the various operation constraints and physical limitations on the power system components. The thermal generation scheduling problem can be considered as a power system control problem acting over different time frames. The unit commitment phase determines the optimum pattern for starting up and shutting down the generating units over the designated scheduling period, while the economic dispatch phase is concerned with allocation of the load demand among the on-line generators. In a hydrothermal system the optimal scheduling of generation involves the allocation of generation among the hydro electric and thermal plants so as to minimise total operation costs of thermal plants while satisfying the various constraints on the hydraulic and power system network. This thesis reports on the development of genetic algorithm computation techniques for the solution of the short term generation scheduling problem for power systems having both thermal and hydro units. A comprehensive genetic algorithm modelling framework for thermal and hydrothermal scheduling problems using two genetic algorithm models, a canonical genetic algorithm and a deterministic crowding genetic algorithm, is presented. The thermal scheduling modelling framework incorporates unit minimum up and down times, demand and reserve constraints, cooling time dependent start up costs, unit ramp rates, and multiple unit operating states, while constraints such as multiple cascade hydraulic networks, river transport delays and variable head hydro plants, are accounted for in the hydraulic system modelling. These basic genetic algorithm models have been enhanced, using quasi problem decomposition, and hybridisation techniques, resulting in efficient generation scheduling algorithms. The results of the performance of the algorithms on small, medium and large scale power system problems is presented and compared with other conventional scheduling techniques.Overseas Development Agenc

Optimization of seasonal irrigation scheduling by genetic algorithms

In this work, we first introduce a novel approach to the long term irrigation scheduling using Genetic Algorithms (GAs). We explore the effectiveness of GAs in the context of optimizing nonlinear crop models and describe application requirements and implementation of the technique. GAs were found to converge quickly to near-optimal solutions. Second, we analyze the relationship between GA control parameters (population size, crossover rate, and mutation rate) and performance. We identify a combination of population, mutation, and crossover which searched the fitness landscape efficiently. The results suggest that smaller populations are able to provide better performance at relatively low mutation rates. More stable outcomes were generated using low mutation rates. Without crossover the quality of solutions were generally impaired, and the search process was lengthened. Aside from crossover rate zero, no other crossover rates significantly differed. The behaviors observed for best, online, offline, and average performances were sensitive to the combined influences control parameters. Interaction among control parameters was strongly indicated. Finally, several adaptive penalty techniques are presented for handling constraints in GAs, and their effectiveness is demonstrated. The constant penalty function suffered from sensitivity to settings of penalty coefficients, and was not successful in satisfying constraints. The adaptive penalty functions utilizes violation distance based metrics and search time based scaling using generation or trials number, and fitness values to penalize infeasible solutions, as the distance from the feasible region or number of generations increases so does the penalty. They were quite successful in providing solutions with minimal effort. They adapt the penalty as the search continues, encouraging feasible solutions to emerge over the time. Adaptive approaches presented here are flexible, efficient, and robust to parameter settings

An investigation of models for identifying critical components in a system.

Lai, Tsz Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.Includes bibliographical references (leaves 193-207).Abstracts in English and Chinese.Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Overview --- p.1Chapter 1.2 --- Contributions --- p.2Chapter 1.3 --- Organization --- p.2Chapter 2 --- Literature Review --- p.4Chapter 2.1 --- Taxonomy --- p.4Chapter 2.2 --- Design of Infrastructure --- p.6Chapter 2.2.1 --- Facility Location Models --- p.7Chapter 2.2.1.1 --- Random Breakdowns --- p.7Chapter 2.2.1.2 --- Deliberate Attacks --- p.8Chapter 2.2.2 --- Network Design Models --- p.9Chapter 2.3 --- Protection of Existing Components --- p.10Chapter 2.3.1 --- Interdiction Models --- p.11Chapter 2.3.2 --- Facility Location Models --- p.12Chapter 2.3.2.1 --- Random Breakdowns --- p.12Chapter 2.3.2.2 --- Deliberate Attacks --- p.12Chapter 2.3.3 --- Network Design Models --- p.14Chapter 3 --- Identifying Critical Facilities: Median Problem --- p.16Chapter 3.1 --- Introduction --- p.16Chapter 3.2 --- Problem Formulation --- p.18Chapter 3.2.1 --- The p-Median Problem --- p.18Chapter 3.2.1.1 --- A Toy Example --- p.19Chapter 3.2.1.2 --- Problem Definition --- p.21Chapter 3.2.1.3 --- Mathematical Model --- p.22Chapter 3.2.2 --- The r-Interdiction Median Problem --- p.24Chapter 3.2.2.1 --- The Toy Example --- p.24Chapter 3.2.2.2 --- Problem Definition --- p.27Chapter 3.2.2.3 --- Mathematical Model --- p.28Chapter 3.2.3 --- The r-Interdiction Median Problem with Fortification --- p.29Chapter 3.2.3.1 --- The Toy Example --- p.30Chapter 3.2.3.2 --- Problem Definition --- p.32Chapter 3.2.3.3 --- Mathematical Model --- p.33Chapter 3.2.4 --- The r-Interdiction Median Problem with Fortification (Bilevel Formulation) --- p.35Chapter 3.2.4.1 --- Mathematical Model --- p.36Chapter 3.3 --- Solution Methodologies --- p.38Chapter 3.3.1 --- Model Reduction --- p.38Chapter 3.3.2 --- Variable Consolidation --- p.40Chapter 3.3.3 --- Implicit Enumeration --- p.45Chapter 3.4 --- Results and Discussion --- p.48Chapter 3.4.1 --- Data Sets --- p.48Chapter 3.4.1.1 --- Swain --- p.48Chapter 3.4.1.2 --- London --- p.49Chapter 3.4.1.3 --- Alberta --- p.49Chapter 3.4.2 --- Computational Study --- p.50Chapter 3.4.2.1 --- The p-Median Problem --- p.50Chapter 3.4.2.2 --- The r-Interdiction Median Problem --- p.58Chapter 3.4.2.3 --- The r-Interdiction Median Problem with Fortification --- p.63Chapter 3.4.2.4 --- The r-Interdiction Median Problem with Fortification (Bilevel Formulation) --- p.68Chapter 3.5 --- Summary --- p.76Chapter 4 --- Hybrid Approaches --- p.79Chapter 4.1 --- Framework --- p.80Chapter 4.2 --- Tabu Assisted Heuristic Search --- p.81Chapter 4.2.1 --- A Tabu Assisted Heuristic Search Construct --- p.83Chapter 4.2.1.1 --- Search Space --- p.84Chapter 4.2.1.2 --- Initial Trial Solution --- p.85Chapter 4.2.1.3 --- Neighborhood Structure --- p.85Chapter 4.2.1.4 --- Local Search Procedure --- p.86Chapter 4.2.1.5 --- Form of Tabu Moves --- p.88Chapter 4.2.1.6 --- Addition of a Tabu Move --- p.88Chapter 4.2.1.7 --- Maximum Size of Tabu List --- p.89Chapter 4.2.1.8 --- Termination Criterion --- p.89Chapter 4.3 --- Hybrid Simulated Annealing Search --- p.90Chapter 4.3.1 --- A Hybrid Simulated Annealing Construct --- p.91Chapter 4.3.1.1 --- Random Selection of Immediate Neighbor --- p.92Chapter 4.3.1.2 --- Cooling Schedule --- p.93Chapter 4.3.1.3 --- Termination Criterion --- p.94Chapter 4.4 --- Hybrid Genetic Search Algorithm --- p.95Chapter 4.4.1 --- A Hybrid Genetic Search Construct --- p.99Chapter 4.4.1.1 --- Search Space --- p.99Chapter 4.4.1.2 --- Initial Population --- p.100Chapter 4.4.1.3 --- Selection --- p.104Chapter 4.4.1.4 --- Crossover --- p.105Chapter 4.4.1.5 --- Mutation --- p.106Chapter 4.4.1.6 --- New Population --- p.108Chapter 4.4.1.7 --- Termination Criterion --- p.109Chapter 4.5 --- Further Assessment --- p.109Chapter 4.6 --- Computational Study --- p.114Chapter 4.6.1 --- Parameter Selection --- p.115Chapter 4.6.1.1 --- Tabu Assisted Heuristic Search --- p.115Chapter 4.6.1.2 --- Hybrid Simulated Annealing Approach --- p.121Chapter 4.6.1.3 --- Hybrid Genetic Search Algorithm --- p.124Chapter 4.6.2 --- Expected Performance --- p.128Chapter 4.6.2.1 --- Tabu Assisted Heuristic Search --- p.128Chapter 4.6.2.2 --- Hybrid Simulated Annealing Approach --- p.138Chapter 4.6.2.3 --- Hybrid Genetic Search Algorithm --- p.146Chapter 4.6.2.4 --- Overall Comparison --- p.150Chapter 4.7 --- Summary --- p.153Chapter 5 --- A Special Case of the Median Problems --- p.156Chapter 5.1 --- Introduction --- p.157Chapter 5.2 --- Problem Formulation --- p.158Chapter 5.2.1 --- The r-Interdiction Covering Problem --- p.158Chapter 5.2.1.1 --- Problem Definition --- p.159Chapter 5.2.1.2 --- Mathematical Model --- p.160Chapter 5.2.2 --- The r-Interdiction Covering Problem with Fortification --- p.162Chapter 5.2.2.1 --- Problem Definition --- p.163Chapter 5.2.2.2 --- Mathematical Model --- p.164Chapter 5.2.3 --- The r-Interdiction Covering Problem with Fortification (Bilevel Formulation) --- p.167Chapter 5.2.3.1 --- Mathematical Model --- p.168Chapter 5.3 --- Theoretical Relationship --- p.170Chapter 5.4 --- Solution Methodologies --- p.172Chapter 5.5 --- Results and Discussion --- p.175Chapter 5.5.1 --- The r-Interdiction Covering Problem --- p.175Chapter 5.5.2 --- The r-Interdiction Covering Problem with Fortification --- p.178Chapter 5.5.3 --- The r-Interdiction Covering Problem with Fortification (Bilevel Formulation) --- p.182Chapter 5.6 --- Summary --- p.187Chapter 6 --- Conclusion --- p.189Chapter 6.1 --- Summary of Our Work --- p.189Chapter 6.2 --- Future Directions --- p.19

Hybrid Optimisation Algorithms for Two-Objective Design of Water Distribution Systems

Multi-objective design or extended design of Water Distribution Systems (WDSs) has received more attention in recent years. It is of particular interest for obtaining the trade-offs between cost and hydraulic benefit to support the decision-making process. The design problem is usually formulated as a multi-objective optimisation problem, featuring a huge search space associated with a great number of constraints. Multi-objective evolutionary algorithms (MOEAs) are popular tools for addressing this kind of problem because they are capable of approximating the Pareto-optimal front effectively in a single run. However, these methods are often held by the “No Free Lunch” theorem (Wolpert and Macready 1997) that there is no guarantee that they can perform well on a wide range of cases. To overcome this drawback, many hybrid optimisation methods have been proposed to take advantage of multiple search mechanisms which can synergistically facilitate optimisation. In this thesis, a novel hybrid algorithm, called Genetically Adaptive Leaping Algorithm for approXimation and diversitY (GALAXY), is proposed. It is a dedicated optimiser for solving the discrete two-objective design or extended design of WDSs, minimising the total cost and maximising the network resilience, which is a surrogate indicator of hydraulic benefit. GALAXY is developed using the general framework of MOEAs with substantial improvements and modifications tailored for WDS design. It features a generational framework, a hybrid use of the traditional Pareto-dominance and the epsilon-dominance concepts, an integer coding scheme, and six search operators organised in a high-level teamwork hybrid paradigm. In addition, several important strategies are implemented within GALAXY, including the genetically adaptive strategy, the global information sharing strategy, the duplicates handling strategy and the hybrid replacement strategy. One great advantage of GALAXY over other state-of-the-art MOEAs lies in the fact that it eliminates all the individual parameters of search operators, thus providing an effective and efficient tool to researchers and practitioners alike for dealing with real-world cases. To verify the capability of GALAXY, an archive of benchmark problems of WDS design collected from the literature is first established, ranging from small to large cases. GALAXY has been applied to solve these benchmark design problems and its achievements in terms of both ultimate and dynamic performances are compared with those obtained by two state-of-the-art hybrid algorithms and two baseline MOEAs. GALAXY generally outperforms these MOEAs according to various numerical indicators and a graphical comparison tool. For the largest problem considered in this thesis, GALAXY does not perform as well as its competitors due to the limited computational budget in terms of number of function evaluations. All the algorithms have also been applied to solve the challenging Anytown rehabilitation problem, which considers both the design and operation of a system from the extended period simulation perspective. The performance of each algorithm is sensitive to the quality of the initial population and the random seed used. GALAXY and the Pareto-dominance based MOEAs are superior to the epsilon-dominance based methods; however, there is a tie between GALAXY and the Pareto-dominance based approaches. At the end, a summary of this thesis is provided and relevant conclusions are drawn. Recommendations for future research work are also made