Ant algorithms and simulated annealing for multicriteria dynamic programming

The paper presents a comparison of ant algorithms and simulated annealing as well as their applications in multicriteria discrete dynamic programming. The considered dynamic process consists of finite states and decision variables. In order to describe the effectiveness of multicriteria algorithms, four measures of the quality of the nondominated set approximations are used.     

Improved approximation algorithms for MAXk-CUT and MAX BISECTION

Polynomial-time approximation algorithms with nontrivial performance guarantees are presented for the problems of (a) partitioning the vertices of a weighted graph intok blocks so as to maximize the weight of crossing edges, and (b) partitioning the vertices of a weighted graph into two blocks of equal cardinality, again so as to maximize the weight of crossing edges. The approach, pioneered by Goemans and Williamson, is via a semidefinite programming relaxation. The first author was supported in part by NSF Grant CCR-9225008. The work described here was undertaken while the second author was visiting Carnegie Mellon University; at that time he was a Nuffield Science Research Fellow, and was supported in part by Grant GR/F 90363 of the UK Science and Engineering Research Council, and Esprit Working Group 7097 “RAND”.     

Evolutionary programming using a mixed mutation strategy

Different mutation operators have been proposed in evolutionary programming, but for each operator there are some types of optimization problems that cannot be solved efficiently. A mixed strategy, integrating several mutation operators into a single algorithm, can overcome this problem. Inspired by evolutionary game theory, this paper presents a mixed strategy evolutionary programming algorithm that employs the Gaussian, Cauchy, Lévy, and single-point mutation operators. The novel algorithm is tested on a set of 22 benchmark problems. The results show that the mixed strategy performs equally well or better than the best of the four pure strategies does, for all of the benchmark problems.     

动态环境中的进化算法

目前关于进化算法（EA）的研究主要局限于静态优化问题,然而很多现实世界中的问题是动态的,对于这类时变的优化问题通常并不是要求EA发现极值点,而是需要EA能够尽可能紧密地跟踪极值点在搜索空间内的运行轨迹.为此,综述了使EA适用于动态优化问题的各种方法,如增加种群多样性、保持种群多样性、引入某种记忆策略和采用多种群策略等.     

A dynamic programming method with lists for the knapsack sharing problem

In this paper, we propose a method to solve exactly the knapsack sharing problem (KSP) by using dynamic programming. The original problem (KSP) is decomposed into a set of knapsack problems. Our method is tested on correlated and uncorrelated instances from the literature. Computational results show that our method is able to find an optimal solution of large instances within reasonable computing time and low memory occupancy.     

Approximation algorithms for combinatorial multicriteria optimization problems

The computational complexity of combinatorial multiple objective programming problems is investigated. NP-completeness and # P -completeness results are presented. Using two definitions of approximability, general results are presented, which outline limits for approximation algorithms. The performance of the well-known tree and Christofides' heuristics for the traveling salesman problem is investigated in the multicriteria case with respect to the two definitions of approximability.     

Towards hybrid evolutionary algorithms

Metaheuristics have received considerable interest these recent years in the field of combinatorial optimization. However, the choice of a particular algorithm to optimize a certain problem is still mainly driven by some sort of devotion of its author to a certain technique rather than by a rationalistic choice driven by reason. Hybrid algorithms have shown their ability to provide local optima of high quality. Hybridization of algorithms is still in its infancy: certain combinations of algorithms have experimentally shown their performance, though the reasons of their success is not always really clear. In order to add some rational to these issues, we study the structure of search spaces and attempt to relate it to the performance of algorithms. We wish to explain the behavior of search algorithms with this knowledge and provide guidelines in the design of hybrid algorithms. This paper briefly reviews the current knowledge we have on search spaces of combinatorial optimization problems. Then, we discuss hybridization and present a general classification of the way hybridization can be conducted in the light of our knowledge of the structure of search spaces.     

Comparing accuracy of second-order approximation and dynamic programming

The accuracy of the solution of dynamic general equilibrium models has become a major issue. Recent papers, in which second-order approximations have been substituted for first-order, indicate that this change may yield a significant improvement in accuracy. Second order approximations have been used with considerable success when solving for the decision variables in both small and large-scale models. Additionally, the issue of accuracy is relevant for the approximate solution of value functions. In numerous dynamic decision problems, welfare is usually computed via this same approximation procedure. However, Kim and Kim (Journal of International Economics, 60, 471–500, 2003) have found a reversal of welfare ordering when they moved from first- to second-order approximations. Other researchers, studying the impact of monetary and fiscal policy on welfare, have faced similar challenges with respect to the accuracy of approximations of the value function. Employing a base-line stochastic growth model, this paper compares the accuracy of second-order approximations and dynamic programming solutions for both the decision variable and the value function as well. We find that, in a neighborhood of the equilibrium, the second-order approximation method performs satisfactorily; however, on larger regions, dynamic programming performs significantly better with respect to both the decision variable and the value function. We want to thank Jinill Kim and Harald Uhlig for discussions and a referee of the Journal for extensive comments on a previous version of our paper.     

Combinatorial algorithms for feedback problems in directed graphs

Given a weighted directed graph G=(V,A), the minimum feedback arc set problem consists of finding a minimum weight set of arcs A′⊆A such that the directed graph (V,A?A′) is acyclic. Similarly, the minimum feedback vertex set problem consists of finding a minimum weight set of vertices containing at least one vertex for each directed cycle. Both problems are NP-complete. We present simple combinatorial algorithms for these problems that achieve an approximation ratio bounded by the length, in terms of number of arcs, of a longest simple cycle of the digraph.     

Improved parallel approximation of a class of integer programming problems

We present a method to derandomizeRNC algorithms, converting them toNC algorithms. Using it, we show how to approximate a class of NP-hard integer programming problems inNC, to within factors better than the current-bestNC algorithms (of Berger and Rompel and Motwaniet al.); in some cases, the approximation factors are as good as the best-known sequential algorithms, due to Raghavan. This class includes problems such as global wire-routing in VLSI gate arrays and a generalization of telephone network planning in SONET rings. Also for a subfamily of the “packing” integer programs, we provide the firstNC approximation algorithms; this includes problems such as maximum matchings in hypergraphs, and generalizations. The key to the utility of our method is that it involves sums ofsuperpolynomially many terms, which can however be computed inNC; this superpolynomiality is the bottleneck for some earlier approaches, due to Berger and Rompel and Motwaniet al. A preliminary version of this work appeared inProc. International Colloquim on Automata, Languages and Programming, 1996, pages 562–573. Work done in parts at DIMACS (supported in part by NSF-STC91-19999 and by support from the N.J. Commission on Science and Technology), at the Institute for Advanced Study, Princeton (supported in part by Grant 93-6-6 of the Alfred P. Sloan Foundation), and at the National University of Singapore.     

Evolutionary algorithms for optimization problems with uncertainties and hybrid indices

Many optimization problems in real-world applications contain both explicit (quantitative) and implicit (qualitative) indices that usually contain uncertain information. How to effectively incorporate uncertain information in evolutionary algorithms is one of the most important topics in information science. In this paper, we study optimization problems with both interval parameters in explicit indices and interval uncertainties in implicit indices. To incorporate uncertainty in evolutionary algorithms, we construct a mathematical uncertain model of the optimization problem considering the uncertainties of interval objectives; and then we transform the model into a precise one by employing the method of interval analysis; finally, we develop an effective and novel evolutionary optimization algorithm to solve the converted problem by combining traditional genetic algorithms and interactive genetic algorithms. The proposed algorithm consists of clustering of a large population according to the distribution of the individuals and estimation of the implicit indices of an individual based on the similarity among individuals. In our experiments, we apply the proposed algorithm to an interior layout problem, a typical optimization problem with both interval parameters in the explicit index and interval uncertainty in the implicit index. Our experimental results confirm the feasibility and efficiency of the proposed algorithm.     

Decremental state space relaxation strategies and initialization heuristics for solving the Orienteering Problem with Time Windows with dynamic programming

We present an exact optimization algorithm for the Orienteering Problem with Time Windows (OPTW). The algorithm is based on bi-directional and bounded dynamic programming with decremental state space relaxation. We compare different strategies proposed in the literature to guide decremental state space relaxation: our experiments on instances derived from the literature show that there is no dominance between these strategies. We also propose a new heuristic technique to initialize the critical vertex set and we provide experimental evidence of its effectiveness.     

Evolutionary algorithms and de novo peptide design

One of the goals of computational chemistry is the automated de novo design of bioactive molecules. Despite significant progress in computational approaches to ligand design and efficient evaluation of binding energy, novel procedures for ligand design are required. Evolutionary computation provides a new approach to this design issue. This paper presents an automated methodology for computer-aided peptide design based on evolutionary algorithms. It provides an automatic tool for peptide de novo design, based on protein surface patches defined by user. Regarding the restrictive constrains of this problem a special emphasis has been made on the design of the evolutionary algorithms implemented.     

基于双群体进化规划的动态优化算法

动态优化问题的优化环境随时间变化导致了最优解随时间移动.为了有效地跟踪最优解,提出了一个基于双群体进化规划的动态优化算法.局部搜索群体运用高斯变异算子,并接受已有信息;全局搜索群体运用柯西变异算子,与已有信息隔离并传送较优个体至局部搜索群体.在进化过程中,它们的群体规模动态地变化.算法有效地利用了已有信息,实现了全局搜索与局部搜索的分离,适合于求解环境变化方式未知的动态优化问题.对三个动态优化模型进行了测试,并与随机初始化群体法进行了比较,仿真结果表明r提出的算法是有效的.     

Evolving dynamic Bayesian networks with Multi-objective genetic algorithms

A dynamic Bayesian network (DBN) is a probabilistic network that models interdependent entities that change over time. Given example sequences of multivariate data, we use a genetic algorithm to synthesize a network structure that models the causal relationships that explain the sequence. We use a multi-objective evaluation strategy with a genetic algorithm. The multi-objective criteria are a network's probabilistic score and structural complexity score. Our use of Pareto ranking is ideal for this application, because it naturally balances the effect of the likelihood and structural simplicity terms used in the BIC network evaluation heuristic. We use a basic structural scoring formula, which tries to keep the number of links in the network approximately equivalent to the number of variables. We also use a simple representation that favors sparsely connected networks similar in structure to those modeling biological phenomenon. Our experiments show promising results when evolving networks ranging from 10 to 30 variables, using a maximal connectivity of between 3 and 4 parents per node. The results from the multi-objective GA were superior to those obtained with a single objective GA. Brian J. Ross is a professor of computer science at Brock University, where he has worked since 1992. He obtained his BCSc at the University of Manitoba, Canada, in 1984, his M.Sc. at the University of British Columbia, Canada, in 1988, and his Ph.D. at the University of Edinburgh, Scotland, in 1992. His research interests include evolutionary computation, language induction, concurrency, and logic programming. He is also interested in computer applications in the fine arts. Eduardo Zuviria received a BS degree in Computer Science from Brock University in 2004 and a MS degree in Computer Science from Queen's University in 2006 where he held jobs as teacher and research assistant. Currently, he is attending a Ph.D. program at the University of Montreal. He holds a diploma in electronics from a technical college and has worked for eight years in the computer industry as a software developer and systems administrator. He has received several scholarships including the Ontario Graduate Scholarship, Queen's Graduate Scholarship and a NSERC- USRA scholarship.     

A pareto-based evolutionary algorithm using decomposition and truncation for dynamic multi-objective optimization

Maintaining a balance between convergence and diversity of the population in the objective space has been widely recognized as the main challenge when solving problems with two or more conflicting objectives. This is added by another difficulty of tracking the Pareto optimal solutions set (POS) and/or the Pareto optimal front (POF) in dynamic scenarios. Confronting these two issues, this paper proposes a Pareto-based evolutionary algorithm using decomposition and truncation to address such dynamic multi-objective optimization problems (DMOPs). The proposed algorithm includes three contributions: a novel mating selection strategy, an efficient environmental selection technique and an effective dynamic response mechanism. The mating selection considers the decomposition-based method to select two promising mating parents with good diversity and convergence. The environmental selection presents a modified truncation method to preserve good diversity. The dynamic response mechanism is evoked to produce some solutions with good diversity and convergence whenever an environmental change is detected. In the experimental studies, a range of dynamic multi-objective benchmark problems with different characteristics were carried out to evaluate the performance of the proposed method. The experimental results demonstrate that the method is very competitive in terms of convergence and diversity, as well as in response speed to the changes, when compared with six other state-of-the-art methods.     

Performance improvement of self-adaptive evolutionary methods with a dynamic lower bound

Recent research on self-adaptive evolutionary programming (EP) methods evidenced the problem of premature convergence. Self-adaptive evolutionary programming methods converge prematurely because their object variables evolve more slowly than do their strategy parameters, which subsequently leads to a stagnation of object variables at a non-optimum value. To address this problem, a dynamic lower bound has been proposed, which is defined here as the differential step lower bound (DSLB) on the strategy parameters. The DSLB on an object variable depends on its absolute distance from the corresponding object variable of the best individual in the population pool. The performance of the self-adaptive EP algorithm with DSLB has been verified over eight different test functions of varied complexities.     

Analysis of Approximation Algorithms for <Emphasis Type="Italic">k</Emphasis>-Set Cover Using Factor-Revealing Linear Programs

We present new combinatorial approximation algorithms for the k-set cover problem. Previous approaches are based on extending the greedy algorithm by efficiently handling small sets. The new algorithms further extend these approaches by utilizing the natural idea of computing large packings of elements into sets of large size. Our results improve the previously best approximation bounds for the k-set cover problem for all values of k≥6. The analysis technique used could be of independent interest; the upper bound on the approximation factor is obtained by bounding the objective value of a factor-revealing linear program. A preliminary version of the results in this paper appeared in Proceedings of the 16th International Symposium on Fundamentals of Computation Theory (FCT ’07), LNCS 4639, Springer, pp. 52–63, 2007. This work was partially supported by the European Union under IST FET Integrated Project 015964 AEOLUS and by the General Secretariat for Research and Technology of the Greek Ministry of Development under programme PENED 2003.     

Chunks and Tasks: A programming model for parallelization of dynamic algorithms

We propose Chunks and Tasks, a parallel programming model built on abstractions for both data and work. The application programmer specifies how data and work can be split into smaller pieces, chunks and tasks, respectively. The Chunks and Tasks library maps the chunks and tasks to physical resources. In this way we seek to combine user friendliness with high performance. An application programmer can express a parallel algorithm using a few simple building blocks, defining data and work objects and their relationships. No explicit communication calls are needed; the distribution of both work and data is handled by the Chunks and Tasks library. This makes efficient implementation of complex applications that require dynamic distribution of work and data easier. At the same time, Chunks and Tasks imposes restrictions on data access and task dependencies that facilitate the development of high performance parallel back ends. We discuss the fundamental abstractions underlying the programming model, as well as performance, determinism, and fault resilience considerations. We also present a pilot C++ library implementation for clusters of multicore machines and demonstrate its performance for irregular block-sparse matrix–matrix multiplication.