This paper considers finite-horizon optimal control for dynamic systems subject to additive Gaussian-distributed stochastic disturbance and a chance constraint on the system state defined on a non-convex feasible spac...
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ISBN:
(纸本)9781424474264
This paper considers finite-horizon optimal control for dynamic systems subject to additive Gaussian-distributed stochastic disturbance and a chance constraint on the system state defined on a non-convex feasible space. The chance constraint requires that the probability of constraint violation is below a user-specified risk bound. A great deal of recent work has studied joint chance constraints, which are defined on the a conjunction of linear state constraints. These constraints can handle convex feasible regions, but do not extend readily to problems with non-convex state spaces, such as path planning with obstacles. In this paper we extend our prior work on chance constrained control in non-convex feasible regions to develop a new algorithm that solves the chance constrained control problem with very little conservatism compared to prior approaches. In order to address the non-convex chance constrained optimization problem, we present two innovative ideas in this paper. First, we develop a new bounding method to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. However, the slow computation of the branch and bound algorithm prevents practical applications. This issue is addressed by our second innovation called Fixed Risk Relaxation (FRR), which efficiently gives a tight lower bound to the convex chance-constrained optimization problem. Our empirical results show that the FRR typically makes branch and bound algorithm 10-20 times faster. In addition we show that the new algorithm is significantly less conservative than the existing approach.
Based on the distributed energy technology, MicroGrid has caused wide attention. It is of great significance to solve the problem of electricity generation in rural areas by establishing an independent MicroGrid syste...
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ISBN:
(纸本)9781629936017
Based on the distributed energy technology, MicroGrid has caused wide attention. It is of great significance to solve the problem of electricity generation in rural areas by establishing an independent MicroGrid system, which mainly consists of solar energy and wind energy. It becomes crucial to find a way to optimize the structure of MicroGrid according to various energy situations. Based on the analysis of the general structure and operation modes of MicroGrid, a hybrid power model, which containing photovoltaic power system (PV), wind power system (WT) and energy storage battery (BATT), has been established in this article. The optimization model and corresponding calculation method not only provide an innovative research method, but also contribute to the further research and application on design methods and operation modes of the distributed MicroGrid system. According to the model established in the article, a MicroGrid system of a village scale has been analysed as an example. With the help of MATLAB Software, the branch and bound algorithm is used in order to minimize the cost of MicroGrid. The optimal installed capacity of PV, WT and BATT is presented. The generating cost per kWh and power supply reliability are demonstrated in this article as well.
The paper contains experimental analysis of efficiency of a new class of algorithms i.e. composite algorithms aimed at solving of knapsack problem providing global optimal solution. These algorithms combine features o...
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ISBN:
(数字)9781538694688
ISBN:
(纸本)9781538694695
The paper contains experimental analysis of efficiency of a new class of algorithms i.e. composite algorithms aimed at solving of knapsack problem providing global optimal solution. These algorithms combine features of branch and bound algorithms together with branch and cut procedure - as latter is used dynamic programming: verified are modifications of branch and bound procedures, which cut off "bad" vectors of variables technique includes technologies used in dynamic programming, and vice versa - modifications of the algorithm, which implements dynamic programming, are involving bounds determination procedures used by branch and bound methods. It is shown experimentally that, in the case of the knapsack problem, the efficiency of these algorithms exceeds the effectiveness of the parent procedures, and this difference increases with the number of variables.
This paper considers a multicell downlink channel in which multiple base stations (BSs) cooperatively serve users by jointly precoding shared data transported from a central processor over limited-capacity backhaul li...
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ISBN:
(纸本)9781509041183
This paper considers a multicell downlink channel in which multiple base stations (BSs) cooperatively serve users by jointly precoding shared data transported from a central processor over limited-capacity backhaul links. We jointly design the beamformers and BS-user link selection so as to maximize the sum rate subject to user-specific signal-to-interference-noise (SINR) requirements, per-BS backhaul capacity and per-BS power constraints. As existing solutions for the considered problem are suboptimal and their optimality remains unknown due to the lack of globally optimal solutions, we characterized this gap by proposing an globally optimal algorithm for the problem of interest. Specifically, the proposed method is customized from a generic framework of a branch and bound algorithm applied to discrete monotonic optimization. We show that the proposed algorithm converges after a finite number of iterations, and can serve as a benchmark for existing suboptimal solutions and those that will be developed for similar contexts in the future. In this regard, we numerically compare the proposed optimal solution to a current state-of-the-art, which show that this suboptimal method only attains 70% to 90% of the optimal performance.
Minimum Satisfiability (MinSAT) denotes one of the optimization versions of the Boolean Satisfiability (SAT) problem. In some settings MinSAT is preferred to using Maximum Satis-fiability (MaxSAT). Several encodings a...
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ISBN:
(纸本)9781479902279
Minimum Satisfiability (MinSAT) denotes one of the optimization versions of the Boolean Satisfiability (SAT) problem. In some settings MinSAT is preferred to using Maximum Satis-fiability (MaxSAT). Several encodings and dedicated branch and bound algorithms for MinSAT have been recently proposed, and evaluated on small challenging randomly generated instances. Motivated by the observation that current best performing MaxSAT algorithms for structured and industrial instances are based on computing unsatisfiable cores with a SAT solver, this paper proposes novel approaches for MinSAT, that also target these instances. First, the paper proposes an algorithm based on iteratively calling a SAT solver which uses the computed models to relax clauses. Second, the paper proposes group-based MinSAT solving, which is essentially a novel reduction of the MinSAT problem into the Group MaxSAT problem. For a given MinSAT instance, the resulting Group MaxSAT formula is then translated into a standard MaxSAT formula which specifically targets unsatisfiability-based MaxSAT algorithms. Experimental results indicate that, similarly to MaxSAT, the proposed approaches outperform branch and bound algorithms on problem instances obtained from practical applications.
This paper proposes new machine based lower bounds for scheduling the flowshop with blocking constraints problem while minimizing the total tardiness and total weighted tardiness. Some characteristics of the developed...
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ISBN:
(纸本)9781479903146
This paper proposes new machine based lower bounds for scheduling the flowshop with blocking constraints problem while minimizing the total tardiness and total weighted tardiness. Some characteristics of the developed branch and bound algorithm are discussed and computational experiments on several random instances are presented. The obtained results compare favorably with previous works in the litterature.
In this paper, we study a project scheduling problem that is called resource constrained project scheduling problem under minimization of total weighted resource tardiness penalty cost (RCPSP-TWRTPC). In this problem,...
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In this paper, we study a project scheduling problem that is called resource constrained project scheduling problem under minimization of total weighted resource tardiness penalty cost (RCPSP-TWRTPC). In this problem, the project is subject to renewable resources, each renewable resource is available for limited time periods during the project life cycle, and keeping the resource for each extra period results in some tardiness penalty cost. We introduce a branch and bound algorithm to solve the problem exactly and use several bounding, fathoming, and dominance rules in our algorithm to shorten the enumeration process. We point out parameters affecting the RCPSP-TWRTPC degree of difficulty, generate extensive sets of sample instances for the problem, and perform comprehensive experimental analysis using the customized algorithm and also CPLEX solver. We analyze the algorithm behavior with respect to the changes in instances degree of difficulty and compare its performance for different cases with the CPLEX solver. The results reveal algorithm efficiency.
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