Long path problems

We demonstrate the interesting, counter-intuitive result that simple paths to the global optimum can be so long that climbing the path is intractable. This means that a unimodal search space, which consists of a single hill and in which each point in the space is on a simple path to the global optimum, can be difficult for a hillclimber to optimize. Various types of hillclimbing algorithms will make constant progress toward the global optimum on such long path problems. They will continuously improve their best found solutions, and be guaranteed to reach the global optimum. Yet we cannot wait for them to arrive. Early experimental results indicate that a genetic algorithm (GA) with crossover alone outperforms hillclimbers on one such long path problem. This suggests that GAs can climb hills faster than hillclimbers by exploiting building blocks when they are present. Although these problems are artificial, they introduce a new dimension of problem difficulty for evolutionary computation. Path length can be added to the ranks of multimodality, deception/misleadingness, noise, variance, etc., as a measure of fitness landscapes and their amenability to evolutionary optimization

On the Easiest and Hardest Fitness Functions

The hardness of fitness functions is an important research topic in the field of evolutionary computation. In theory, the study can help understanding the ability of evolutionary algorithms. In practice, the study may provide a guideline to the design of benchmarks. The aim of this paper is to answer the following research questions: Given a fitness function class, which functions are the easiest with respect to an evolutionary algorithm? Which are the hardest? How are these functions constructed? The paper provides theoretical answers to these questions. The easiest and hardest fitness functions are constructed for an elitist (1+1) evolutionary algorithm to maximise a class of fitness functions with the same optima. It is demonstrated that the unimodal functions are the easiest and deceptive functions are the hardest in terms of the time-fitness landscape. The paper also reveals that the easiest fitness function to one algorithm may become the hardest to another algorithm, and vice versa

What makes a problem hard for a genetic algorithm? Some anomalous results and their explanation

What makes a problem easy or hard for a genetic algorithm (GA)? This question has become increasingly important as people have tried to apply the GA to ever more diverse types of problems. Much previous work on this question has studied the relationship between GA performance and the structure of a given fitness function when it is expressed as a Walsh polynomial . The work of Bethke, Goldberg, and others has produced certain theoretical results about this relationship. In this article we review these theoretical results, and then discuss a number of seemingly anomalous experimental results reported by Tanese concerning the performance of the GA on a subclass of Walsh polynomials, some members of which were expected to be easy for the GA to optimize. Tanese found that the GA was poor at optimizing all functions in this subclass, that a partitioning of a single large population into a number of smaller independent populations seemed to improve performance, and that hillelimbing outperformed both the original and partitioned forms of the GA on these functions. These results seemed to contradict several commonly held expectations about GAs.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46892/1/10994_2004_Article_BF00993046.pd

Fitness landscape analysis of a class of np-hard problems

A number of fitness landscape properties of randomly generated instances of a class of NP-hard combinatorial optimisation problems are empirically studied in this research. We believe that the studied properties give insight into the structure of the problem landscape and can be representative of the problem difficulty, in particular with respect to local search algorithms. The properties include: types of search position, number of local and global optima and plateaux, quality of optima and plateaux, basin size and its correlation with fitness, time to local optima, cost of finding the global solution, and the quality of optima obtained with a fixed budget search. Our work focuses on studying how these properties vary with different values of problem parameters. We also compare these properties across different landscapes that were induced by different neighbourhood operators or different penalty functions of the following problems: the number partitioning problem, the binary knapsack problem, and the quadratic binary knapsack problem. Unlike existing studies of these problems, we study instances generated at random from various distributions. We found a general trend where in all the three problems, some of their landscape features were found to vary between the different distributions. We captured this variation by a single, easy to calculate, parameter and we showed that it has a potentially useful application in guiding the choice of the neighbourhood operator of local search heuristics

Evolving Effective Micro Behaviors for Real-Time Strategy Games

Real-Time Strategy games have become a new frontier of artificial intelligence research. Advances in real-time strategy game AI, like with chess and checkers before, will significantly advance the state of the art in AI research. This thesis aims to investigate using heuristic search algorithms to generate effective micro behaviors in combat scenarios for real-time strategy games. Macro and micro management are two key aspects of real-time strategy games. While good macro helps a player collect more resources and build more units, good micro helps a player win skirmishes against equal numbers of opponent units or win even when outnumbered. In this research, we use influence maps and potential fields as a basis representation to evolve micro behaviors. We first compare genetic algorithms against two types of hill climbers for generating competitive unit micro management. Second, we investigated the use of case-injected genetic algorithms to quickly and reliably generate high quality micro behaviors. Then we compactly encoded micro behaviors including influence maps, potential fields, and reactive control into fourteen parameters and used genetic algorithms to search for a complete micro bot, ECSLBot. We compare the performance of our ECSLBot with two state of the art bots, UAlbertaBot and Nova, on several skirmish scenarios in a popular real-time strategy game StarCraft. The results show that the ECSLBot tuned by genetic algorithms outperforms UAlbertaBot and Nova in kiting efficiency, target selection, and fleeing. In addition, the same approach works to create competitive micro behaviors in another game SeaCraft. Using parallelized genetic algorithms to evolve parameters in SeaCraft we are able to speed up the evolutionary process from twenty one hours to nine minutes. We believe this work provides evidence that genetic algorithms and our representation may be a viable approach to creating effective micro behaviors for winning skirmishes in real-time strategy games

Coevolutionary Approaches to Generating Robust Build-Orders for Real-Time Strategy Games

We aim to find winning build-orders for Real-Time Strategy games. Real-Time Strategy games provide a variety of challenges, from short-term control to longer term planning. We focus on a longer-term planning problem; which units to build and in what order to produce the units so a player successfully defeats the opponent. Plans which address unit construction scheduling problems in Real-Time Strategy games are called build-orders. A robust build-order defeats many opponents, while a strong build-order defeats opponents quickly. However, no single build-order defeats all other build-orders, and build-orders that defeat many opponents may still lose against a specific opponent. Other researchers have only investigated generating build-orders that defeat a specific opponent, rather than finding robust, strong build-orders. Additionally, previous research has not applied coevolutionary algorithms towards generating build-orders. In contrast, our research has three main contributions towards finding robust, strong build-orders. First, we apply a coevolutionary algorithm towards finding robust build-orders. Compared to exhaustive search, a genetic algorithm finds the strongest build-orders while a coevolutionary algorithm finds more robust build-orders. Second, we show that case-injection enables coevolution to learn from specific opponents while maintaining robustness. Build-orders produced with coevolution and case-injection learn to defeat or play like the injected build-orders. Third, we show that coevolved build-orders benefit from a representation which includes branches and loops. Coevolution will utilize multiple branches and loops to create build-orders that are stronger than build-orders without loops and branches. We believe this work provides evidence that coevolutionary algorithms may be a viable approach to creating robust, strong build-orders for Real-Time Strategy games

A grammar-based technique for genetic search and optimization

The genetic algorithm (GA) is a robust search technique which has been theoretically and empirically proven to provide efficient search for a variety of problems. Due largely to the semantic and expressive limitations of adopting a bitstring representation, however, the traditional GA has not found wide acceptance in the Artificial Intelligence community. In addition, binary chromosones can unevenly weight genetic search, reduce the effectiveness of recombination operators, make it difficult to solve problems whose solution schemata are of high order and defining length, and hinder new schema discovery in cases where chromosome-wide changes are required.;The research presented in this dissertation describes a grammar-based approach to genetic algorithms. Under this new paradigm, all members of the population are strings produced by a problem-specific grammar. Since any structure which can be expressed in Backus-Naur Form can thus be manipulated by genetic operators, a grammar-based GA strategy provides a consistent methodology for handling any population structure expressible in terms of a context-free grammar.;In order to lend theoretical support to the development of the syntactic GA, the concept of a trace schema--a similarity template for matching the derivation traces of grammar-defined rules--was introduced. An analysis of the manner in which a grammar-based GA operates yielded a Trace Schema Theorem for rule processing, which states that above-average trace schemata containing relatively few non-terminal productions are sampled with increasing frequency by syntactic genetic search. Schemata thus serve as the building blocks in the construction of the complex rule structures manipulated by syntactic GAs.;As part of the research presented in this dissertation, the GEnetic Rule Discovery System (GERDS) implementation of the grammar-based GA was developed. A comparison between the performance of GERDS and the traditional GA showed that the class of problems solvable by a syntactic GA is a superset of the class solvable by its binary counterpart, and that the added expressiveness greatly facilitates the representation of GA problems. to strengthen that conclusion, several experiments encompassing diverse domains were performed with favorable results