Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Self-adaptation of Genetic Operators Through Genetic Programming Techniques

Here we propose an evolutionary algorithm that self modifies its operators at the same time that candidate solutions are evolved. This tackles convergence and lack of diversity issues, leading to better solutions. Operators are represented as trees and are evolved using genetic programming (GP) techniques. The proposed approach is tested with real benchmark functions and an analysis of operator evolution is provided.Comment: Presented in GECCO 201

Class Association Rules Mining based Rough Set Method

This paper investigates the mining of class association rules with rough set approach. In data mining, an association occurs between two set of elements when one element set happen together with another. A class association rule set (CARs) is a subset of association rules with classes specified as their consequences. We present an efficient algorithm for mining the finest class rule set inspired form Apriori algorithm, where the support and confidence are computed based on the elementary set of lower approximation included in the property of rough set theory. Our proposed approach has been shown very effective, where the rough set approach for class association discovery is much simpler than the classic association method.Comment: 10 pages, 2 figure

An ant system algorithm for automated trajectory planning

The paper presents an Ant System based algorithm to optimally plan multi-gravity assist trajectories. The algorithm is designed to solve planning problems in which there is a strong dependency of one decision one all the previously made decisions. In the case of multi-gravity assist trajectories planning, the number of possible paths grows exponentially with the number of planetary encounters. The proposed algorithm avoids scanning all the possible paths and provides good results at a low computational cost. The algorithm builds the solution incrementally, according to Ant System paradigms. Unlike standard ACO, at every planetary encounter, each ant makes a decision based on the information stored in a tabu and feasible list. The approach demonstrated to be competitive, on a number of instances of a real trajectory design problem, against known GA and PSO algorithms

Decoding heterogeneous big data in an integrative way

Biotechnologies in post-genomic era, especially those that generate data in high-throughput, bring opportunities and challenges that are never faced before. And one of them is how to decode big heterogeneous data for clues that are useful for biological questions. With the exponential growth of a variety of data, comes with more and more applications of systematic approaches that investigate biological questions in an integrative way. Systematic approaches inherently require integration of heterogeneous information, which is urgently calling for a lot more efforts. In this thesis, the effort is mainly devoted to the development of methods and tools that help to integrate big heterogeneous information. In Chapter 2, we employed a heuristic strategy to summarize/integrate genes that are essential for the determination of mouse retinal cells in the format of network. These networks with experimental evidence could be rediscovered in the analysis of high-throughput data set and thus would be useful in the leverage of high-throughput data. In Chapter 3, we described EnRICH, a tool that we developed to help qualitatively integrate heterogeneous intro-organism information. We also introduced how EnRICH could be applied to the construction of a composite network from different sources, and demonstrated how we used EnRICH to successfully prioritize retinal disease genes. Following the work of Chapter 3 (intro-organism information integration), in Chapter 4 we stepped to the development of method and tool that can help deal with inter-organism information integration. The method we proposed is able to match genes in a one-to-one fashion between any two genomes. In summary, this thesis contributes to integrative analysis of big heterogeneous data by its work on the integration of intro- and inter-organism information

Automated multigravity assist trajectory planning with a modified ant colony algorithm

The paper presents an approach to transcribe a multigravity assist trajectory design problem into an integrated planning and scheduling problem. A modified Ant Colony Optimization (ACO) algorithm is then used to generate optimal plans corresponding to optimal sequences of gravity assists and deep space manoeuvers to reach a given destination. The modified Ant Colony Algorithm is based on a hybridization between standard ACO paradigms and a tabu-based heuristic. The scheduling algorithm is integrated into the trajectory model to provide a fast time-allocation of the events along the trajectory. The approach demonstrated to be very effective on a number of real trajectory design problems

最小k部分木問題に対する生物規範型ハイブリッドメタ戦略に基づく近似解法の研究

広島大学(Hiroshima University)博士(工学)Engineeringdoctora