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عنوان فارسی مقاله:
یک رویکرد مدل سازی بهینه برای بهینه سازی آنلاین با جستجوگر
عنوان انگلیسی مقاله:
A general modeling approach to online optimization with lookahead
سال انتشار : 2016
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بخشی از مقاله انگلیسی:
2. Online optimization with lookahead
In order to establish a clear, but yet flexible definition for an online optimization problem with lookahead, we first introduce some basic concepts with respect to the process of information release in an optimization problem and related processing possibilities of an algorithm. 2.1. Definition of lookahead According to Ausiello et al. [7], a (single-objective) optimization problem Π is a quadruple ðI; S; f ; optÞ where I is a set of instances, S is a function returning the set of solutions S(i) for any iAI, f is a function returning the objective value for any pair ði; sÞAI SðiÞ, and optAfmin; maxg is the optimization goal. However, this defi- nition does not account for the sequentiality in the instance revelation process that any online solution method has to obey, and it disregards previous answers of the solution method. We introduce the instance revelation rule as a mechanism to account for dynamic aspects in the revelation process of an instance. Essentially, this comprises a description of when input elements are released over time. Definition 1 (Instance revelation rule). An instance revelation rule is a rule that governs the temporal course of events in the release of information on the problem instance. The close link between dynamic input disclosure and a corresponding instance revelation rule is respected in the following definition which is an extension of the rather general definition for an instance of an optimization problem given by Garey and Johnson [25]. By including the instance revelation rule into the definition of a problem instance we explicitly account for the dynamic character of the online optimization paradigm. Definition 2 (Instance of an optimization problem). An instance of an optimization problem consists of a set of parameter values including an input sequence σ ¼ ðσ1; σ2; …Þ and an instance revelation rule r. From additional data, new possibilities for possible actions of an algorithm may arise. Hence, we need a way to settle all unclarities concerning the processing of the input elements which may be implied by additional data. Hence, we associate a set of rules with a problem. Definition 3 (Rule set). A rule set of a problem is a set of restrictions on the solution to an instance of the problem. Now, we can associate each instance iAI with a specific instance revelation rule that determines how the information of i is made available and with a rule set that affects the form of the set of feasible solutions S(i) for each iAI. We note that the rule set P gives us a description of the conditions under which an algorithm has to make its decisions during input element processing, whereas the feasible set S will only be known after all input elements have been released. Of course, each element in S has to obey the rules given in P. In order to prepare for the definition of lookahead, we make the following notational conventions: when we substitute instance revelation rule r by instance revelation rule r0 , then we write r-r0 and speak of an instance revelation rule substitution. When we substitute rule set P by rule set P0 , then we write P-P0 and speak of a rule set substitution. Definition 4 suggests that lookahead consists of an informational component (r-r0 ) and a processual component (P-P0 ). The subdivision of lookahead into these two components will be helpful to understand and explain the behavior of an algorithm in an online optimization problem.
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کلمات کلیدی:
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