Analysis of combinatorial search spaces for a class of NP-hard problems, An

2011 Spring.Includes bibliographical references.Given a finite but very large set of states X and a real-valued objective function ƒ defined on X, combinatorial optimization refers to the problem of finding elements of X that maximize (or minimize) ƒ. Many combinatorial search algorithms employ some perturbation operator to hill-climb in the search space. Such perturbative local search algorithms are state of the art for many classes of NP-hard combinatorial optimization problems such as maximum k-satisfiability, scheduling, and problems of graph theory. In this thesis we analyze combinatorial search spaces by expanding the objective function into a (sparse) series of basis functions. While most analyses of the distribution of function values in the search space must rely on empirical sampling, the basis function expansion allows us to directly study the distribution of function values across regions of states for combinatorial problems without the need for sampling. We concentrate on objective functions that can be expressed as bounded pseudo-Boolean functions which are NP-hard to solve in general. We use the basis expansion to construct a polynomial-time algorithm for exactly computing constant-degree moments of the objective function ƒ over arbitrarily large regions of the search space. On functions with restricted codomains, these moments are related to the true distribution by a system of linear equations. Given low moments supplied by our algorithm, we construct bounds of the true distribution of ƒ over regions of the space using a linear programming approach. A straightforward relaxation allows us to efficiently approximate the distribution and hence quickly estimate the count of states in a given region that have certain values under the objective function. The analysis is also useful for characterizing properties of specific combinatorial problems. For instance, by connecting search space analysis to the theory of inapproximability, we prove that the bound specified by Grover's maximum principle for the Max-Ek-Lin-2 problem is sharp. Moreover, we use the framework to prove certain configurations are forbidden in regions of the Max-3-Sat search space, supplying the first theoretical confirmation of empirical results by others. Finally, we show that theoretical results can be used to drive the design of algorithms in a principled manner by using the search space analysis developed in this thesis in algorithmic applications. First, information obtained from our moment retrieving algorithm can be used to direct a hill-climbing search across plateaus in the Max-k-Sat search space. Second, the analysis can be used to control the mutation rate on a (1+1) evolutionary algorithm on bounded pseudo-Boolean functions so that the offspring of each search point is maximized in expectation. For these applications, knowledge of the search space structure supplied by the analysis translates to significant gains in the performance of search

Computational complexity of evolutionary algorithms, hybridizations, and swarm intelligence

Bio-inspired randomized search heuristics such as evolutionary algorithms, hybridizations with local search, and swarm intelligence are very popular among practitioners as they can be applied in case the problem is not well understood or when there is not enough knowledge, time, or expertise to design problem-specific algorithms. Evolutionary algorithms simulate the natural evolution of species by iteratively applying evolutionary operators such as mutation, recombination, and selection to a set of solutions for a given problem. A recent trend is to hybridize evolutionary algorithms with local search to refine newly constructed solutions by hill climbing. Swarm intelligence comprises ant colony optimization as well as particle swarm optimization. These modern search paradigms rely on the collective intelligence of many single agents to find good solutions for the problem at hand. Many empirical studies demonstrate the usefulness of these heuristics for a large variety of problems, but a thorough understanding is still far away. We regard these algorithms from the perspective of theoretical computer science and analyze the random time these heuristics need to optimize pseudo-Boolean problems. This is done in a mathematically rigorous sense, using tools known from the analysis of randomized algorithms, and it leads to asymptotic bounds on their computational complexity. This approach has been followed successfully for evolutionary algorithms, but the theory of hybrid algorithms and swarm intelligence is still in its very infancy. Our results shed light on the asymptotic performance of these heuristics, increase our understanding of their dynamic behavior, and contribute to a rigorous theoretical foundation of randomized search heuristics

Global Landscape Structure and the Random MAX-SAT Phase Transition

We revisit the fitness landscape structure of random MAX-SAT instances, and address the question: what structural features change when we go from easy underconstrained instances to hard overconstrained ones? Some standard techniques such as autocorrelation analysis fail to explain what makes instances hard to solve for stochastic local search algorithms, indicating that deeper landscape features are required to explain the observed performance differences. We address this question by means of local optima network (LON) analysis and visualisation. Our results reveal that the number, size, and, most importantly, the connectivity pattern of local and global optima change significantly over the easy-hard transition. Our empirical results suggests that the landscape of hard MAX-SAT instances may feature sub-optimal funnels, that is, clusters of sub-optimal solutions where stochastic local search methods can get trapped

How to exploit fitness landscape properties of timetabling problem: A newoperator for quantum evolutionary algorithm

© 2020 Elsevier Ltd. All rights reserved. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1016/j.eswa.2020.114211The fitness landscape of the timetabling problems is analyzed in this paper to provide some insight into theproperties of the problem. The analyses suggest that the good solutions are clustered in the search space andthere is a correlation between the fitness of a local optimum and its distance to the best solution. Inspiredby these findings, a new operator for Quantum Evolutionary Algorithms is proposed which, during the searchprocess, collects information about the fitness landscape and tried to capture the backbone structure of thelandscape. The knowledge it has collected is used to guide the search process towards a better region in thesearch space. The proposed algorithm consists of two phases. The first phase uses a tabu mechanism to collectinformation about the fitness landscape. In the second phase, the collected data are processed to guide thealgorithm towards better regions in the search space. The algorithm clusters the good solutions it has foundin its previous search process. Then when the population is converged and trapped in a local optimum, itis divided into sub-populations and each sub-population is designated to a cluster. The information in thedatabase is then used to reinitialize the q-individuals, so they represent better regions in the search space.This way the population maintains diversity and by capturing the fitness landscape structure, the algorithmis guided towards better regions in the search space. The algorithm is compared with some state-of-the-artalgorithms from PATAT competition conferences and experimental results are presented.Peer reviewe

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing

Characterising fitness landscapes with fitness-probability cloud and its applications to algorithm configuration

Metaheuristics are approximation optimisation techniques widely applied to solve complex optimisation problems. Despite a large number of developed metaheuristic algorithms, a limited amount of work has been done to understand on which kinds of problems the proposed algorithm will perform well or poorly and why. A useful solution to this dilemma is to use fitness landscape analysis to gain an in-depth understanding of which algorithms, or algorithm variants are best suited for solving which kinds of problem instances, even to dynamically determine the best algorithm configuration during different stages of a search algorithm. This thesis for the first time bridges the gap between fitness landscape analysis and algorithm configuration, i.e., finding the best suited configuration of a given algorithm for solving a particular problem instance. Studies in this thesis contribute to the following: a. Developing a novel and effective approach to characterise fitness landscapes and measure problem difficulty with respect to algorithms. b. Incorporating fitness landscape analysis in building a generic (problem-independent) approach, which can perform automatic algorithm configuration on a per-instance base, and in designing novel and effective algorithm configurations. c. Incorporating fitness landscape analysis in establishing a generic framework for designing adaptive heuristic algorithms

Scheduling and Resource Efficiency Balancing. Discrete Species Conserving Cuckoo Search for Scheduling in an Uncertain Execution Environment

The main goal of a scheduling process is to decide when and how to execute each of the project’s activities. Despite large variety of researched scheduling problems, the majority of them can be described as generalisations of the resource-constrained project scheduling problem (RCPSP). Because of wide applicability and challenging difficulty, RCPSP has attracted vast amount of attention in the research community and great variety of heuristics have been adapted for solving it. Even though these heuristics are structurally different and operate according to diverse principles, they are designed to obtain only one solution at a time. In the recent researches on RCPSPs, it was proven that these kind of problems have complex multimodal fitness landscapes, which are characterised by a wide solution search spaces and presence of multiple local and global optima. The main goal of this thesis is twofold. Firstly, it presents a variation of the RCPSP that considers optimisation of projects in an uncertain environment where resources are modelled to adapt to their environment and, as the result of this, improve their efficiency. Secondly, modification of a novel evolutionary computation method Cuckoo Search (CS) is proposed, which has been adapted for solving combinatorial optimisation problems and modified to obtain multiple solutions. To test the proposed methodology, two sets of experiments are carried out. Firstly, the developed algorithm is applied to a real-life software development project. Secondly, the performance of the algorithm is tested on universal benchmark instances for scheduling problems which were modified to take into account specifics of the proposed optimisation model. The results of both experiments demonstrate that the proposed methodology achieves competitive level of performance and is capable of finding multiple global solutions, as well as prove its applicability in real-life projects

Runtime Analysis of Success-Based Parameter Control Mechanisms for Evolutionary Algorithms on Multimodal Problems

Evolutionary algorithms are simple general-purpose optimisers often used to solve complex engineering and design problems. They mimic the process of natural evolution: they use a population of possible solutions to a problem that evolves by mutating and recombining solutions, identifying increasingly better solutions over time. Evolutionary algorithms have been applied to a broad range of problems in various disciplines with remarkable success. However, the reasons behind their success are often elusive: their performance often depends crucially, and unpredictably, on their parameter settings. It is, furthermore, well known that there are no globally good parameters, that is, the correct parameters for one problem may differ substantially to the parameters needed for another, making it harder to translate previous successfully implemented parameters to new problems. Therefore, understanding how to properly select the parameters is an important but challenging task. This is commonly known as the parameter selection problem. A promising solution to this problem is the use of automated dynamic parameter selection schemes (parameter control) that allow evolutionary algorithms to identify and continuously track optimal parameters throughout the course of evolution without human intervention. In recent years the study of parameter control mechanisms in evolutionary algorithms has emerged as a very fruitful research area. However, most existing runtime analyses focus on simple problems with benign characteristics, for which fixed parameter settings already run efficiently and only moderate performance gains were shown. The aim of this thesis is to understand how parameter control mechanisms can be used on more complex and challenging problems with many local optima (multimodal problems) to speed up optimisation. We use advanced methods from the analysis of algorithms and probability theory to evaluate the performance of evolutionary algorithms, estimating the expected time until an algorithm finds satisfactory solutions for illustrative and relevant optimisation problems as a vital stepping stone towards designing more efficient evolutionary algorithms. We first analyse current parameter control mechanisms on multimodal problems to understand their strengths and weaknesses. Subsequently we use this knowledge to design parameter control mechanisms that mitigate the weaknesses of current mechanisms while maintaining their strengths. Finally, we show with theoretical and empirical analyses that these enhanced parameter control mechanisms are able to outperform the best fixed parameter settings on multimodal optimisation

The 2011 International Planning Competition

After a 3 years gap, the 2011 edition of the IPC involved a total of 55 planners, some of them versions of the same planner, distributed among four tracks: the sequential satisficing track (27 planners submitted out of 38 registered), the sequential multicore track (8 planners submitted out of 12 registered), the sequential optimal track (12 planners submitted out of 24 registered) and the temporal satisficing track (8 planners submitted out of 14 registered). Three more tracks were open to participation: temporal optimal, preferences satisficing and preferences optimal. Unfortunately the number of submitted planners did not allow these tracks to be finally included in the competition. A total of 55 people were participating, grouped in 31 teams. Participants came from Australia, Canada, China, France, Germany, India, Israel, Italy, Spain, UK and USA. For the sequential tracks 14 domains, with 20 problems each, were selected, while the temporal one had 12 domains, also with 20 problems each. Both new and past domains were included. As in previous competitions, domains and problems were unknown for participants and all the experimentation was carried out by the organizers. To run the competition a cluster of eleven 64-bits computers (Intel XEON 2.93 Ghz Quad core processor) using Linux was set up. Up to 1800 seconds, 6 GB of RAM memory and 750 GB of hard disk were available for each planner to solve a problem. This resulted in 7540 computing hours (about 315 days), plus a high number of hours devoted to preliminary experimentation with new domains, reruns and bugs fixing. The detailed results of the competition, the software used for automating most tasks, the source code of all the participating planners and the description of domains and problems can be found at the competition’s web page: http://www.plg.inf.uc3m.es/ipc2011-deterministicThis booklet summarizes the participants on the Deterministic Track of the International Planning Competition (IPC) 2011. Papers describing all the participating planners are included

Hybrid meta-heuristics for combinatorial optimization

Combinatorial optimization problems arise, in many forms, in vari- ous aspects of everyday life. Nowadays, a lot of services are driven by optimization algorithms, enabling us to make the best use of the available resources while guaranteeing a level of service. Ex- amples of such services are public transportation, goods delivery, university time-tabling, and patient scheduling. Thanks also to the open data movement, a lot of usage data about public and private services is accessible today, sometimes in aggregate form, to everyone. Examples of such data are traffic information (Google), bike sharing systems usage (CitiBike NYC), location services, etc. The availability of all this body of data allows us to better understand how people interacts with these services. However, in order for this information to be useful, it is necessary to develop tools to extract knowledge from it and to drive better decisions. In this context, optimization is a powerful tool, which can be used to improve the way the available resources are used, avoid squandering, and improve the sustainability of services. The fields of meta-heuristics, artificial intelligence, and oper- ations research, have been tackling many of these problems for years, without much interaction. However, in the last few years, such communities have started looking at each other’s advance- ments, in order to develop optimization techniques that are faster, more robust, and easier to maintain. This effort gave birth to the fertile field of hybrid meta-heuristics.openDottorato di ricerca in Ingegneria industriale e dell'informazioneopenUrli, Tommas