Chen Disser (1121212), страница 5
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The metrics to measure the success in this research are the solution time and thefor resolving the violated global constraints. We study methods for automatically selectingsolution quality of solving large problems.the optimal number of partitions in order to minimize the total time complexity.The keys to the success of using constraint partitioning to solve MINLPs depend on the11b) Resolution of violated global constraints. Although constraint partitioning leads to12much simpler subproblems, the approach is not exploited in existing optimization algorithmsconstraints efficiently. In this theory, we develop a necessary and sufficient condition thatexcept in some special cases. The approach leads to global constraints across subproblemsgoverns all constrained local minima, when a MINLP problem is formulated in a penaltythat need to be resolved.
These global constraints may be either constraints in the origi-function. ESPC in mixed space extends the previous condition developed for discrete opti-nal problem that involve variables in different subproblems, or new constraints created tomization [98, 91, 92, 97, 99, 89, 87, 14, 85, 86, 84, 90, 88]. This research shows that eachenforce the consistency of internal states across subproblems.
The general difficulty lies inconstrained local minimum of a MINLP problem is associated with a saddle point of a newthe exponentially large space across the subproblems to be searched in resolving violatedpenalty function and when penalties are sufficiently large. Using this result, one way to lookglobal constraints. In this research, we study how to efficiently resolve the violated globalfor a constrained local minimum of a MINLP is to increase gradually the penalties of violatedconstraints by developing a mathematical foundation to characterize the local optimal solu-constraints in the corresponding unconstrained penalty function and to find repeatedly localtion under constraint partitioning, and by reducing the subspace to be searched in resolvingminima by an existing algorithm until a feasible solution to the constrained model is found.b) We show that ESPC can be decomposed for constraint-partitioned MINLPs.
Eachviolated global constraints.c) Applications on planning and nonlinear programming. In this research, we applydecomposed ESPC is defined with respect to a subproblem consisting of its local constraintsthe constraint partitioning approach to solve planning problems and large-scale nonlinearand an objective function that is made up of the objective of the original problem and thatprogramming benchmarks.
Planning is a core problem for artificial intelligence, and has wideis biased by a weighted sum of the violated global constraints. As such, each subproblemapplications in logistics, mobile communication, transportation, operations management,is very similar to the original problem and can be solved by the same planner with littleand aerospace engineering. We explore the temporal and logical locality of constraints inor no modification. We show that each subproblem is similar to the original problem butplanning problems and study the implementation of fully automated planning systems basedof a smaller scale. We further show that penalties always exist under similar relaxed con-on constraint partitioning.
We also apply the constraint partitioning approach to solve large-ditions for constrained local minima in subproblems, and that each decomposed ESPC isscale CNLP and MINLP benchmarks from engineering applications. In these applications,necessary individually and sufficient collectively.
Since the decomposed ESPC is satisfiedwe study the automated recognition of constraint structures, the determination of optimalby constrained local minima in each subproblem (that also satisfy the local constraints), itpartitioning, and the efficient resolution of global constraints.is much more effective than the local constraints alone for limiting the search space whenresolving violated global constraints. Based on the theory of ESPC, we propose a partition-1.4Contributions and Significance of Researchand-resolve procedure. The procedure iterates between calling a basic solver to solve theconstraint-partitioned subproblems, and using a constraint-reweighting strategy to resolveThe main contributions of this thesis are as follows:the violated global constraints across the subproblems.a) We propose an extended saddle-point condition (ESPC) for resolving violated globalc) We have developed a leading planner based on the constraint-partitioning approach.1314We have observed clustered constraint structures in many real-world planning applicationsand show that most existing methods solve a planning problem as a whole without constraintand have proposed effective partitioning strategies that exploit the constraint structure.partitioning.We have also studied specific techniques for planning, including landmark analysis, subgoalIn Chapter 3, we present our theoretical foundation for constraint partitioning.
Afterordering, search space pruning, and producible resource detection, that lead to further de-introducing the basic concepts, including mixed-space neighborhood and mixed-space con-composition of a problem and faster solution of subproblems. Our planner has won thestrained local minimum, we present the main theorem, the extended saddle point conditionfirst prize in the suboptimal temporal metric track and the second prize in the suboptimal(ESPC), that states a one-to-one correspondence between a constrained local minimum andpropositional track of the 4th International Planning Competition (IPC4) in 2004, and isan extended saddle point defined on a penalty function.
We prove the theorem and explainthe only planner that has won two prizes in the competition. We have also improved thethe significance of the result. Next, we extend the ESPC condition to the MINLPs underefficiency of NASA’s space-rover planning system by up to 1000 times.constraint partitioning. After formulating the MINLP problem under constraint partition-d) We have successfully applied the constraint partitioning approach on large-scale math-ing in a mathematical form, we develop the concepts of neighborhood and constrained localematical programming benchmarks.
We have proposed automated partitioning strategies forminimum under constraint partitioning, and present the partitioned ESPC condition. Fi-selecting the partitioning dimension and for determining the optimal number of partitions innally, we present an iterative search framework for finding points that satisfy the partitionedorder to minimize the overall search time. The proposed method has achieved a significantESPC condition, and discuss the global convergence of this search scheme.reduction in solution time, and has solved some large-scale mixed-integer and continuousconstrained nonlinear optimization problems not solvable before.In Chapter 4, we study the application of the proposed approach on automated planning. In particular, we study two planning models, including PDDL2.2 planning and ASEPNplanning for NASA.
For each of the planning models, we demonstrate the constraint struc-1.5Thesis outlineture of the problem, the automated partitioning strategy, the strategy for resolving globalconstraints, and the implementation details of the planning systems.
We also show exper-This thesis is organized as follows.imental results of our planning systems on the Third and Fourth International PlanningIn Chapter 2, we review previous work. We first review existing penalty methods forCompetitions, and NASA’s benchmarks for planning.constrained optimization, discuss their assumptions and limitations, and explain why existingIn Chapter 5, we present the application on large-scale mathematical programming benchpenalty methods cannot efficiently support constraint partitioning. Second, we review othermarks, including both mixed-integer problems and continuous problems.
We first describeexisting mathematical programming methods, with a focus on existing partitioning methods.the test problem sets and demonstrate the constraint structure of the problems. We thenWe compare different classes of partitioning methods, discuss their limitations, and point outdiscuss an automated partitioning strategy to select the partitioning dimension and thewhat is new in our partitioning approach. Finally, we survey existing planning algorithms,optimal number of partitions. We also examine strategies for updating penalty values in1516resolving violated global constraints.
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