Splitting for optimization

Duan, Qibin; Kroese, Dirk P.

doi:10.1016/j.cor.2016.04.015

Cited by 10 publications

(9 citation statements)

References 11 publications

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“…In [24] a new optimization method was introduced based on the well-known splitting method for rare-event simulation; see, e.g., [ Because there is a substantial difference between multi-objective and single-objective optimization, the methodology of the single-objective SCO method must be modified significantly to make the splitting idea work for MOO problems. First, when selecting the "elite set" the traditional sorting method is not suitable, so we provide a new method for constructing the elite set.…”

Section: Discussionmentioning

confidence: 99%

“…First, when selecting the "elite set" the traditional sorting method is not suitable, so we provide a new method for constructing the elite set. Second, to obtain better candidates in the "splitting stage", we use a combination of the global sampling strategy used in [24] and a new local sampling strategy. Third, to keep track of all the good solutions ever found, we use an external "archive" of solutions.…”

Section: Discussionmentioning

confidence: 99%

“…As shown in numerical experiments, the SCO algorithm in [24] for single-objective optimization converges to a global optimum very efficiently and accurately, as a result of good balance between exploration and exploitation. Note that the sampling distribution for each elite point is randomly determined by the other elite points, such that it can guarantee that the mixture sampling distributions of all elite points cover the whole level set.…”

Section: Sampling Strategiesmentioning

confidence: 99%

“…However, for continuous optimization, the splitting method has not been applied. To fill the gap, in [24,25], new sampling and selecting techniques are proposed under a splitting framework, to solve continuous single-objective (SOO) and multi-objective (MOO) optimization problems.…”

Section: S(x) (12)mentioning

confidence: 99%

“…Following [24], the idea is to split the initial point by updating only one of its components each time, using a multivariate normal distribution with mean vector…”

Section: Sampling Strategiesmentioning

confidence: 99%

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Optimization by rare-event simulation

Duan¹

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In this dissertation we present several papers about two optimization methods that are derived from rare-event simulation techniques, i.e., the splitting method and the cross-entropy (CE) method.The splitting method is a well-known method for rare-event simulation, where sample paths of a Markov process are split into multiple copies during the simulation, so as to make the occurrence of a rare event more frequent. Motivated by the splitting algorithm we introduce a novel global optimization method for continuous optimization (SCO) that is both very fast and accurate. We also introduce a new multi-objective optimization (MOO) methodology based on the SCO algorithm. The method, called MOS, generalizes the elite set selection of the traditional splitting framework, and uses both local and global sampling to sample in the decision space. Both SCO and MOS were compared with state-of-the art algorithms using a prevailing set of benchmark problems. Numerical experiments demonstrate that the new splitting methods are competitive with famous methods in the fields.The thesis also contains two new applications of the CE method on Laguerre fitting problems.The Laguerre fitting problems are about recovering the weighted generator points from a given Laguerre tessellation. When the description of the Laguerre tessellation is exact, the solutions are not unique and different weighted generator points can create the same tessellation. To recover pertinent generator points we formulate the problem as an optimization problem and apply the modified CE method to solve it. However, the representation of a Laguerre tessellation is typically not exact when working with real data, such as tomographic image data. In this case, we formulate an optimization problem where we minimize the discrepancy between the image data and our approximated tessellations. We then solve the optimization problem using the CE method.Last, we introduce a new R package that implements the general CE methodology for optimization as well as some useful modifications. The usage and efficacy of CEoptim is demonstrated through a variety of optimization examples, including model fitting, combinatorial optimization, and maximum likelihood estimation.ii Declaration by AuthorThis thesis is composed of my original work, and contains no material previously published or written by another person except where due reference has been made in the text. I have clearly stated the contribution by others to jointly-authored works that I have included in my thesis.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Sampling Strategiesmentioning

confidence: 99%

Section: S(x) (12)mentioning

confidence: 99%

“…Following [24], the idea is to split the initial point by updating only one of its components each time, using a multivariate normal distribution with mean vector…”

Section: Sampling Strategiesmentioning

confidence: 99%

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