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Convergence of stochastic search algorithms to finite size pareto set approximations

JOURNAL OF GLOBAL OPTIMIZATION 2008年第4期41卷 559-577页

作者： Schuetze, Oliver Laumanns, Marco Coello, Carlos A. Coello Dellnitz, Michael Talbi, El-Ghazali CINVESTAV IPN Dept Comp Sci Mexico City 07300 DF Mexico ETH Inst Operat Res CH-8092 Zurich Switzerland Univ Paderborn Inst Math Fac Comp Sci Elect Engn & Math D-33098 Paderborn Germany INRIA Futurs CNRS LIFL F-59655 Villeneuve Dascq France

In this work we investigate the convergence of stochastic search algorithms toward the Pareto set of continuous multi-objective optimization problems. The focus is on obtaining a finite approximation that should capture the entire solution set in a suitable sense, which will be defined using the concept of epsilon-dominance. Under mild assumptions about the process to generate new candidate solutions, the limit approximation set will be determined entirely by the archiving strategy. We propose and analyse two different archiving strategies which lead to a different limit behavior of the algorithms, yielding bounds on the obtained approximation quality as well as on the cardinality of the resulting Pareto set approximation.

关键词： multi-objective optimization convergence epsilon-dominance stochastic search algorithms

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Convergence of stochastic search algorithms to Gap-Free Pareto Front Approximations 07

Convergence of Stochastic Search Algorithms to Gap-Free Pare...

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Annual Conference of Genetic and Evolutionary Computation Conference

作者： Schuetze, Oliver Laumanns, Marco Tantar, Emilia Coello Coello, Carlos A. Talbi, El-ghazali LIFL INRIA Futurs CNRS Cite Sci F-59655 Villeneuve Dascq France ETH Inst Operat Res CH-8092 Zurich Switzerland IPN CINVESTAV Dept Comp Sci Mexico City 07300 DF Mexico CNRS INRIA Futurs LIFL F-59655 Villeneuve Dascq France

ISBN: (纸本)9781595936974

Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of epsilon-dominance. Though bounds on the quality of the limit approximation - which are entirely determined by the archiving strategy and the value of epsilon - have been obtained, the strategies do not guarantee to obtain a gap-free Pareto front approximation. Since such approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included into the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and tinder mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies.

关键词： multi-objective optimization convergence epsilon-dominance stochastic search algorithms

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A stochastic downhill search algorithm for estimating the local false discovery rate

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2004年第3期1卷 98-108页

作者： Scheid, S Spang, R Max Planck Inst Mol Genet D-14195 Berlin Germany

Screening for differential gene expression in microarray studies leads to difficult large-scale multiple testing problems. The local false discovery rate is a statistical concept for quantifying uncertainty in multiple testing. In this paper, we introduce a novel estimator for the local false discovery rate that is based on an algorithm which splits all genes into two groups, representing induced and noninduced genes, respectively. Starting from the full set of genes, we successively exclude genes until the gene-wise p-values of the remaining genes look like a typical sample from a uniform distribution. In comparison to other methods, our algorithm performs compatibly in detecting the shape of the local false discovery rate and has a smaller bias with respect to estimating the overall percentage of noninduced genes. Our algorithm is implemented in the Bioconductor compatible R package TWILIGHT version 1.0.1, which is available from http://***/software or from the Bioconductor project at http://***.

关键词： local false discovery rates stochastic search algorithms microarray analysis biology and genetics

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A GENETIC ALGORITHM FOR MULTIPROCESSOR SCHEDULING

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 1994年第2期5卷 113-120页

作者： HOU, ESH ANSARI, N REN, H Department of Electrical and Computer Engineering New Jersey Institute of Technology Newark NJ USA

The problem of multiprocessor scheduling can be stated as finding a schedule for a general task graph to be executed on a multiprocessor system so that the schedule length can be minimized. This scheduling problem is known to be NP-hard, and methods based on heuristic search have been proposed to obtain optimal and suboptimal solutions. Genetic algorithms have recently received much attention as a class of robust stochastic search algorithms for various optimization problems. In this paper, an efficient method based on genetic algorithms is developed to solve the multiprocessor scheduling problem. The representation of the search node is based on the order of the tasks being executed in each individual processor. The genetic operator proposed is based on the precedence relations between the tasks in the task graph. Simulation results comparing the proposed genetic algorithm, the list scheduling algorithm, and the optimal schedule using random task graphs, and a robot inverse dynamics computational task graph for various are presented.

关键词： DIRECT ACYCLIC GRAPH GENETIC algorithms GENETIC OPERATORS MULTIPROCESSOR SCHEDULING NP-HARD OPTIMIZATION stochastic search algorithms

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Coordinated motion of autonomous vehicles with the use of a distributed gradient algorithm

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APPLIED MATHEMATICS AND COMPUTATION 2008年第2期199卷 494-503页

作者： Rigatos, Gerasimos G. Ind Syst Inst Unit Ind Automat Rion 26504 Greece

Distributed stochastic search is proposed for cooperative behavior in multi-robot systems. Distributed gradient is examined. This method consists of multiple stochastic search algorithms that start from different points in the solutions space and interact to each other while moving towards the goal position. Distributed gradient is shown to be efficient when the motion of the robots towards the goal position is described by a quadratic cost function. The algorithm's performance is evaluated through simulation tests. (c) 2007 Elsevier Inc. All rights reserved.

关键词： multi-robot system cooperative behavior stochastic search algorithms distributed gradient Lyapunov stability

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Heuristic-Based Pipe Dimensioning Model for Water Distribution Networks

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JOURNAL OF PIPELINE SYSTEMS ENGINEERING AND PRACTICE 2012年第4期3卷 115-124页

作者： Suribabu, C. R. SASTRA Univ Sch Civil Engn CARE Thanjavur 613401 Tamil Nadu India

An economic design of water distribution system components plays an important role in the water-supplying agency because of the requirement of a large financial investment on construction, operation, and maintenance. Population-based stochastic search algorithms have become a futuristic method for optimal design of water distribution networks. However, the effectiveness of population-based stochastic search algorithms purely depends on several factors, such as population size, degree of randomness involved, penalty function, algorithm operators, and search space size. An analysis of published research shows that a large number of evaluations is required to arrive at the least cost combination of pipe diameters. This paper proposes a new approach, in which flow velocity in a pipe is considered as implicit information for pipe sizing. Three well-known benchmark networks were used to illustrate the applicability of the proposed approach for least-cost pipe sizing of water distribution networks. The result of the model application reveals that the computational effort required to arrive at an economical design is very minimal. DOI: 10.1061/(ASCE)PS.1949-1204.0000104. (C) 2012 American Society of Civil Engineers.

关键词： stochastic search algorithms Water distribution networks Optimum pipe sizing.

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Distributed gradient and particle swarm optimization for multi-robot motion planning

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ROBOTICA 2008年第3期26卷 357-370页

作者： Rigatos, Gerasimos G. Ind Syst Inst Unit Ind Automat Rion 26504 Greece

Two distributed stochastic search algorithms are proposed for motion planning of multi-robot systems: (i) distributed gradient, (ii) swarm intelligence theory. Distributed gradient consists of multiple stochastic search algorithms that start from different points in the solutions space and interact with each other while moving toward the goal position. Swarm intelligence theory is a derivative-free approach to the problem of multi-robot cooperation which works by searching iteratively in regions defined by each robot's best previous move and the best previous move of its neighbors. The performance of both approaches is evaluated through simulation tests.

关键词： multi-robot system motion planning stochastic search algorithms distributed gradient Lyapunov stability swarm intelligence

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ICRS-Filter: A randomized direct search algorithm for constrained nonconvex optimization problems

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CHEMICAL ENGINEERING REsearch & DESIGN 2016年第Feb.期106卷 178-190页

作者： Li, Biyu Nguyen, Viet H. Ng, Chieh. L. del Rio-Chanona, E. A. Vassiliadis, Vassilios S. Arellano-Garcia, Harvey Univ Cambridge Dept Chem Engn & Biotechnol Pembroke St Cambridge CB2 3RA England Univ Surrey Dept Chem & Proc Engn Guildford GU2 7XH Surrey England

This work presents a novel algorithm and its implementation for the stochastic optimization of generally constrained Nonlinear Programming Problems (NLP). The basic algorithm adopted is the Iterated Control Random search (ICRS) method of Casares and Banga (1987) with modifications such that random points are generated strictly within a bounding box defined by bounds on all variables. The ICRS algorithm serves as an initial point determination method for launching gradient-based methods that converge to the nearest local minimum. The issue of constraint handling is addressed in our work via the use of a filter based methodology, thus obviating the need for use of the penalty functions as in the basic ICRS method presented in Banga and Seider (1996), which handles only bound constrained problems. The proposed algorithm, termed ICRS-Filter, is shown to be very robust and reliable in producing very good or global solutions for most of the several case studies examined in this contribution. (C) 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

关键词： Nonconvex programming problem Randomized search Nonlinear programming stochastic search algorithms

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Multi-Robot Motion Planning Using Swarm Intelligence

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INTERNATIONAL JOURNAL OF ADVANCED ROBOTIC SYSTEMS 2008年第2期5卷 139-144页

作者： Rigatos, Gerasimos G. Ind Syst Inst Unit Ind Automat Rion 26504 Greece

Swarm intelligence theory is proposed for motion planning of multi-robot systems. Multiple particles start front different points in the solutions space and interact to each other while moving towards the goal position. Swarm intelligence theory is a derivative-free approach to the problem of multi-robotcooperation which works by searching iteratively in regions defined by each robot's best previous move and the best previous move of its neighbors. The method's performance is evaluated through simulation tests.

关键词： swarm intelligence multi-robot system motion planning stochastic search algorithms Lyapunov stability

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An improvement on the Migrating Birds Optimization with a problem-specific neighboring function for the multi-objective task allocation problem

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EXPERT SYSTEMS WITH APPLICATIONS 2017年第0期67卷 304-311页

作者： Oz, Dindar Yasar Univ Software Engn Dept TR-35100 Izmir Turkey

Allocating tasks to processors is a well-known NP-Hard problem in distributed computing systems. Due to the lack of practicable exact solutions, it has been attracted by the researchers working on heuristic based suboptimal search algorithms. With the recent inclusion of multiple objectives such as minimizing the cost, maximizing, the throughput and maximizing the reliability, the problem gets even more complex and an efficient approximate method becomes more valuable. In this work, I propose a new solution for the multi-objective task allocation problem. My solution consists in designing a problem-specific neighboring function for an existing metaheuristic algorithm that is proven to be successful in quadratic assignment problems. The neighboring function, namely greedy reassignment with maximum release (GR-MR), provides a dynamic mechanism to switch the preference of the search between the exploration and exploitation. The experiments validate both that the quality of the solutions are close to the optimal and the proposed method performs significantly better comparing to three other metaheuristic algorithms. Neighboring functions being the common reusable components of metaheuristic algorithms, GR-MR can also be utilized by other metaheuristic-based solutions in the future. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Distributed systems Task allocation problem Metaheuristic optimization algorithms stochastic search algorithms

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