The problem of additive function minimization under the restriction, given by the function, admitting dichotomous representation is discussed. A method for calculation of lower estimations and the method of branches a...
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The problem of additive function minimization under the restriction, given by the function, admitting dichotomous representation is discussed. A method for calculation of lower estimations and the method of branches and bounds, based on these estimations, are also described. In problems of complex estimation, the function f(x), giving an integrated estimation of an object, admits dichotomous representation as a tree. The method of dichotomous programming is generalization of the method of dynamic programming, and expands a set of problems solved on the basis of the given approach. The method for calculating bottom estimates, allows the application of the branch and bound method.
An oracle for a convex set S⊂Rn accepts as input any point z in Rn, and if zqqS, then it returns `yes', while if zqqS, then it returns `no' along with a separating hyperplane. We give a new algorithm that find...
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An oracle for a convex set S⊂Rn accepts as input any point z in Rn, and if zqqS, then it returns `yes', while if zqqS, then it returns `no' along with a separating hyperplane. We give a new algorithm that finds a feasible point in S in cases where an oracle is available. Our algorithm uses the analytic center of a polytope as test point, and successively modifies the polytope with the separating hyperplanes returned by the oracle. The key to establishing convergence is that hyperplanes judged to be `unimportant' are pruned from the polytope. If a ball of radius 2-L is contained in S, and S is contained in a cube of side 2L+1, then we can show our algorithm converges after O(nL2) iterations and performs a total of O(n4L3+TnL2) arithmetic operations, where T is the number of arithmetic operations required for a call to the oracle. The bound is independent of the number of hyperplanes generated in the algorithm. An important application in which an oracle is available is minimizing a convex function over S.
Sufficient optimality and sensitivity of a parameterized min-max programming with fixed feasible set are analyzed. Based on Clarke's subdifferential and Chaney's second-order directional derivative, sufficient...
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Sufficient optimality and sensitivity of a parameterized min-max programming with fixed feasible set are analyzed. Based on Clarke's subdifferential and Chaney's second-order directional derivative, sufficient optimality of the parameterized min-max programming is discussed first. Moreover, under a convex assumption on the objective function, a subdifferential computation formula of the marginal function is obtained. The assumptions are satisfied naturally for some application problems. Moreover, the formulae based on these assumptions are concise and convenient for algorithmic purpose to solve the applications.
The problem of finding the kth smallest of n elements can be solved either with O(n) algorithms or with O(n2) algorithms. Although they require a higher number of operations in the worst case, O(n2) algorithms are gen...
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In this paper, we propose a road-map to bridge theoretical and practical approaches in the discipline of the elevator operation problem (EOP). The theoretical approach is to obtain optimal solutions for static EOPs, h...
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ISBN:
(纸本)9781467389853
In this paper, we propose a road-map to bridge theoretical and practical approaches in the discipline of the elevator operation problem (EOP). The theoretical approach is to obtain optimal solutions for static EOPs, here "static" means all information on users of the elevator system is known before scheduling. The practical approach is to construct rule-bases for realistic situations. The proposed road-map is comprised of 5 stages: (1) to obtain a formally-optimal solution for a problem instance of a static EOP, (2) to construct a statically-peculiar optimal rule-base from the optimal solution, (3) to construct a dynamically-peculiar optimal rule-base which is effective for the problem instance and functions on a continuous elevator system, (4) to construct a dynamically-narrow rule-base which is effective for a set of problem instances, and (5) to construct a dynamically-wide rule-base which is effective for various sets of problem instances. In computer illustrations, preliminary verification on earlier stages are displayed.
The classical Location Set Covering Problem involves finding the smallest number of facilities and their locations so that each demand is covered by at least one facility. it was first introduced by Toregas in 1970. T...
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The classical Location Set Covering Problem involves finding the smallest number of facilities and their locations so that each demand is covered by at least one facility. it was first introduced by Toregas in 1970. This problem can represent several different application settings including the location of emergency services and the selection of conservation sites. The Location Set Covering Problem can be formulated as a 0-1 integer-programming model. Roth (1969) and Toregas and ReVelle (1973) developed reduction approaches that can systematically eliminate redundant columns and rows as well as identify essential sites. Such approaches can often reduce a problem to a size that is considerably smaller and easily solved by linear programming using branch and bound. Extensions to the Location Set Covering Model have been proposed so that additional levels of coverage are either encouraged or required. This paper focuses on one of the extended model forms called the Multi-level Location Set Covering Model. The reduction rules of Roth and of Toregas and ReVelle violate properties found in the multi-level model. This paper proposes a new set of reduction rules that can be used for the multi-level model as well as the classic single-level model. A demonstration of these new reduction rules is presented which indicates that such problems may be subject to significant reductions in both the numbers of demands as well as sites.
We propose two algorithms for the solution of the Optimal Power Flow (OPF) problem to global optimality. The algorithms are based on the spatial branch and bound framework with lower bounds on the optimal objective fu...
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ISBN:
(纸本)9781467345392;9781467345378
We propose two algorithms for the solution of the Optimal Power Flow (OPF) problem to global optimality. The algorithms are based on the spatial branch and bound framework with lower bounds on the optimal objective function value calculated by solving either the Lagrangian dual or the semidefinite programming (SDP) relaxation. We show that this approach can solve to global optimality the general form of the OPF problem including: generation power bounds, apparent and real power line limits, voltage limits and thermal loss limits. The approach makes no assumption on the topology or resistive connectivity of the network. This work also removes some of the restrictive assumptions of the SDP approaches [1], [2], [3], [4], [5]. We present the performance of the algorithms on a number of standard IEEE systems, which are known to have a zero duality gap. We also make parameter perturbations to the test cases that result in solutions that fail to satisfy the SDP rank condition and have a non-zero duality gap. The proposed branch and bound algorithms are able to solve these cases to global optimality.
Australia is the world's third largest exporter of raw sugar after Brazil and Thailand, with around $2.0 billion in export earnings. Transport systems play a vital role in the raw sugar production process by trans...
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ISBN:
(纸本)9780987214355
Australia is the world's third largest exporter of raw sugar after Brazil and Thailand, with around $2.0 billion in export earnings. Transport systems play a vital role in the raw sugar production process by transporting the sugarcane crop between farms and mills. In 2013, 87 per cent of sugarcane was transported to mills by cane railway. The total cost of sugarcane transport operations is very high. Over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. A cane railway network mainly involves single track sections and multiple track sections used as passing loops or sidings. The cane railway system performs two main tasks: delivering empty bins from the mill to the sidings for filling by harvesters;and collecting the full bins of cane from the sidings and transporting them to the mill. A typical locomotive run involves an empty train (locomotive and empty bins) departing from the mill, traversing some track sections and delivering bins at specified sidings. The locomotive then, returns to the mill, traversing the same track sections in reverse order, collecting full bins along the way. In practice, a single track section can be occupied by only one train at a time, while more than one train can use a passing loop (parallel sections) at a time. The sugarcane transport system is a complex system that includes a large number of variables and elements. These elements work together to achieve the main system objectives of satisfying both mill and harvester requirements and improving the efficiency of the system in terms of low overall costs. These costs include delay, congestion, operating and maintenance costs. An effective cane rail scheduler will assist the traffic officers at the mill to keep a continuous supply of empty bins to harvesters and full bins to the mill with a minimum cost. This paper addresses the cane rail scheduling problem under rail siding capacity constraints where limited and unlimited siding capacities were
Rapid transit construction projects are major endeavours that require long-term planning by several players, including politicians, urban planners, engineers, management consultants, and citizen groups. Traditionally,...
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Economic analysis was conducted on hypothetical agronomic research on new crop cultivars for Arkansas dryland soybean and wheat producers. In relation to farmers' attitudes toward risk, the macroeconomic effects a...
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Economic analysis was conducted on hypothetical agronomic research on new crop cultivars for Arkansas dryland soybean and wheat producers. In relation to farmers' attitudes toward risk, the macroeconomic effects and level of adoption of yield variability reducing cultivars were analyzed utilizing a production management decision-making model formulated with mathematical programming techniques. The study indicated that negative covariance between crops continues to be an effective means of reducing production risk associated with yield variability. However, under varying circumstances, agronomic research on the breeding of new soybean and wheat cultivars with reduced yield variability is worthwhile if there is only slight concurrent reduction in expected yields. -Author
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