In this paper we investigate two generalizations of the continuous mixing set studied by Miller and Wolsey [5] and Van Vyve [7]: the intersection set X-I = {(sigma,r,y) is an element of R-+(n) x R-+(n) x Z(+)(n) : sig...
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ISBN:
(纸本)9783540727910
In this paper we investigate two generalizations of the continuous mixing set studied by Miller and Wolsey [5] and Van Vyve [7]: the intersection set X-I = {(sigma,r,y) is an element of R-+(n) x R-+(n) x Z(+)(n) : sigma(k) + r(t) + y(t) >= b(kt), 1 <= k,t <= n} and the continuous mixing set with flows X-CMF = {(s,r,x,y) is an element of R+ x R-+(n) R-+(n) x Z(+)(n) : s + r(t) + x(t) >= b(t), x(t) <= y(t), 1 <= t <= n}, which appears as a strong relaxation of some single-item lot-sizing problems. We give two extended formulations for the convex hull of each of these sets. In particular, for X-CMF the sizes of the extended formulations are polynomial in the size of the original description of the set, thus proving that the corresponding linear optimization problem can be solved in polynomial time.
Management of container ports, withthe aim of increasing the efficiency, is considered as a complex problem in coastal transportation engineering. In view of the steadily growing trend of the container ship sizes, mo...
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A mixed integerprogramming problem, is an optimization problem that includes bothinteger decision variables and continuous *** engineering and management problems are mixed integerprogramming problems, most of whic...
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this book constitutes the refereed proceedings of the 19thinternationalconference on integerprogramming and combinatorialoptimization, IPCO 2017, held in Waterloo, IN, Canada, in June 2017.
ISBN:
(数字)9783319592503
ISBN:
(纸本)9783319592497
this book constitutes the refereed proceedings of the 19thinternationalconference on integerprogramming and combinatorialoptimization, IPCO 2017, held in Waterloo, IN, Canada, in June 2017.
We present the first criterion space search algorithm, the triangle splitting method, for finding the efficient frontier of a biobjective mixed integer program. the algorithm is relatively easy to implement and conver...
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We consider dynamically generating linear constraints (cutting planes) to tighten relaxations for polynomial optimization problems. Many optimization problems have feasible set of the form S boolean AND P, where S is ...
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ISBN:
(数字)9783030179533
ISBN:
(纸本)9783030179533;9783030179526
We consider dynamically generating linear constraints (cutting planes) to tighten relaxations for polynomial optimization problems. Many optimization problems have feasible set of the form S boolean AND P, where S is a closed set and P is a polyhedron. integer programs are in this class and one can construct intersection cuts using convex "forbidden" regions, or S-free sets. Here, we observe that polynomial optimization problems can also be represented as a problem with linear objective function over such a feasible set, where S is the set of real, symmetric matrices representable as outer-products of the form xx(T). Accordingly, we study outer-product-free sets and develop a thorough characterization of several (inclusion-wise) maximal intersection cut families. In addition, we present a cutting plane approach that guarantees polynomial-time separation of an extreme point in P \ S using our outer-product-free sets. Computational experiments demonstrate the promise of our approach from the point of view of strength and speed.
Vehicle-to-Grid and a microgrid are emerging concepts which are expected to replace the conventional energy and transportation systems with more efficient and flexible ones. there have been research on the integration...
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ISBN:
(纸本)9781467399753
Vehicle-to-Grid and a microgrid are emerging concepts which are expected to replace the conventional energy and transportation systems with more efficient and flexible ones. there have been research on the integration of these technologies, but a microgrid with fuel cell vehicles (FCVs) have hardly been studied at the moment in spite of the several technical advantages of FCVs as generating units. this paper therefore presents the mathematical model of a microgrid which includes FCVs, on-site hydrogen stations, solar photovoltaic systems and a wind turbine. the optimal scheduling of hydrogen production, hydrogen refueling to FCVs and electricity supply from FCVs which minimizes the power imported from the main grid is obtained by solving a mixed integer linear programming problem. the computation results of a test case indicate that the model can be used for identifying a bottleneck in the energy flow of a microgrid. the presented model can be extended by including important factors to consider for further research on the integration of microgrids and FCVs.
the development of Systems-of-Systems (SoS) architectures is challenged by the inherent characteristics of SoS such as operational independence, heterogeneity of constituent systems, emergent behavior and large-scale ...
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ISBN:
(纸本)9781479966493
the development of Systems-of-Systems (SoS) architectures is challenged by the inherent characteristics of SoS such as operational independence, heterogeneity of constituent systems, emergent behavior and large-scale distribution. At present, the resulting complexity restricts the design space exploration of SoS architectures to be focused on cost and functionality. In this paper we extend our previous work on timing analysis and optimization in early SoS design phases by supporting reliability requirements in the generated SoS architecture. Our approach defines a SoS architecture development methodology that applies an architecture optimization method based on concise modeling with architecture patterns, timing and reliability requirements, and extensions to the Unified Profile for DoDAF and MODAF (UPDM). optimization using Mixed integer Linear programming (MILP) is used to satisfy the real-time and reliability requirements and optimization results are back annotated to UPDM models.
We address a spatial conservation planning problem in which the planner purchases a budget-constrained set of land parcels in order to maximize the expected spread of a population of an endangered species. Existing te...
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ISBN:
(纸本)9781577357384
We address a spatial conservation planning problem in which the planner purchases a budget-constrained set of land parcels in order to maximize the expected spread of a population of an endangered species. Existing techniques based on the sample average approximation scheme and standard integerprogramming methods have high complexity and limited scalability. We propose a fast combinatorialoptimization algorithm using Lagrangian relaxation and primal-dual techniques to solve the problem approximately. the algorithm provides a new way to address a range of conservation planning and scheduling problems. On the Red-cockaded Woodpecker data, our algorithm produces near optimal solutions and runs significantly faster than a standard mixed integer program solver. Compared with a greedy baseline, the solution quality is comparable or better, but our algorithm is 10-30 times faster. On synthetic problems that do not exhibit submodularity, our algorithm significantly outperforms the greedy baseline.
this paper presents a mixed-integeroptimization approach to the yearly hydrothermal scheduling problem. the proposed method is applied to a hydrothermal system comprising 29 thermal units and 13 hydroplants, includin...
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ISBN:
(纸本)9781424417438
this paper presents a mixed-integeroptimization approach to the yearly hydrothermal scheduling problem. the proposed method is applied to a hydrothermal system comprising 29 thermal units and 13 hydroplants, including 2 pumped storage plants, similar to the Greek Power System. the generation scheduling model is based on an hourly load curve. Perfect competition assumption is adopted and an thermal generators are assumed to bid their marginal cost. A large mixed-integerprogramming problem is formulated and implemented in GAMS. Binary variables represent thermal unit hourly commitment status. Results on an hourly basis, including thermal unit commitment and dispatch, hydroplant generation and pumping and system marginal price are presented.
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