Multi-model approach based on parametric sensitivities – A heuristic approximation for dynamic optimization of semi-batch processes with parametric uncertainties
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ABSTRACT This paper presents an easily understood and computationally efficient heuristic algorithm for the capacitated lot sizing problem (CLSP), the single machine lot‐sizing problem, with nonstationary costs, demands, and setup times. The algorithm solves problems with setup time or setup cost. A variation of the algorithm can solve problems when limited amounts of costly overtime are allowed. Results of experimentation indicate that the most significant effects on solution quality are due to the level of setup costs relative to holding costs and the size of the problems as determined by the number of items. Also affecting solution quality are tightness of the capacity constraint and variability of demand in a problem. When the capacity constraint is extremely tightly binding, it sometimes has difficulty finding solutions that do not require overtime.
Overtime
Holding cost
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The path flow estimator, an origin–destination demand estimation algorithm that relies on the computation of path flows, can be slow when applied to medium to large networks. A primal–dual heuristic that can significantly improve the computational efficiency of the algorithm when it is applied to large networks is developed. Numerical examples are provided to show the performance improvement of this primal–dual heuristic over the original path flow estimator algorithm.
Minimum-cost flow problem
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Polynomial-time approximation scheme
Change-making problem
Value (mathematics)
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The problem of planning a set of paths for the coalition of robots (agents) with different capabilities is considered in the paper. Some agents can modify the environment by destructing the obstacles thus allowing the other ones to shorten their paths to the goal. As a result the mutual solution of lower cost, e.g. time to completion, may be acquired. We suggest an original procedure to identify the obstacles for further removal that can be embedded into almost any heuristic search planner (we use Theta*) and evaluate it empirically. Results of the evaluation show that time-to-complete the mission can be decreased up to 9-12 % by utilizing the proposed technique.
Planner
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This paper deals with the dynamic multi-item capacitated lot-sizing problem under random period demands (SCLSP). Unfilled demands are backordered and a fillrate constraint is in effect. It is assumed that, according to the static-uncertainty strategy of Bookbinder and Tan (1988), all decisions concerning the time and the production quantities are made in advance for the entire planning horizon regardless of the realization of the demands. The problem is approximated with the set partitioning model and a heuristic solution procedure that combines column generation and the recently developed ABC β heuristic is proposed.
Column generation
Realization (probability)
Time horizon
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In this paper a new deterministic mathematical model for time-cost trade-off is introduced. The proposed method is based on path constraints in a network while other similar methods are modelled based on activities. Through this paper, the proposed model is constructed and thenvalidated by testing in a case study. The achieved results from model are compared with manual solution. The results of both proposed model and manual solution are exactly same which proves the accuracy of the model. Moreover, using network paths for constructing the constraints has the benefit of a lower number of constraints and leading to a faster and more straightforward solution. Lower number of constraints might lead to less computing effort. This can provide us an opportunity to solve some networks which are NP-hard by other similar approaches. Finally can summarize that the main advantages of the proposed model are simplicity in modelling and the usage of a fewer equations.
Simplicity
Network model
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This paper study flow intercepting facility location problems(FIFLP)with multi-demand and path choice of customers.There are different paths in the OD pairs on network,we introduce gravity model to decide the path choice probability and consider flow part intercepting through demand coefficient function.Under the facility number constraint,this paper gives the maximization flow model,and offers heuristic algorithm to solve the model.Firstly,we get the initial solution with Add algorithm and then we improve it with inter-change algorithm.Finally,a numerical example is presented,and through comparing the results with exact solution,it shows the feasibility and effectiveness of the heuristic algorithm.
Maximization
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This paper studies a heuristic method for the Maximum Origin-Destination Flow Path (MODFP) in an acyclic transportation network. We construct a mathematical formulation for finding the MODFP. Then by applying Benders' partitioning method, we generate two subproblems which should be solved in turn so that they may give an optimal solution. We solve one subproblem by an optimal seeking algorithm and the other by a hueristic method. so that, we finally obtain a good solution. The computational complexity of calculating the optimal solution of the first subproblem is 0(mn) and that of calculating the heuristic solution of the other subproblem is From the computational experiments, we estimated the performance of the heuristic method as being 99.3% and the computing time relative to optimal algorithm as being 28.76%.
Null-move heuristic
Consistent heuristic
Maximum flow problem
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Linear programming problems consist of two parts are objective function and inequality constraints. A redundant constraint is a constraint that does not change the feasible region. There are many methods for detecting redundant constraint. The methods for identifying redundant constraints which in the process only uses the objective function and inequality constraints, among others, Heuristic method, Llewellyn method, and Stojkovic-Stanimirovic methods. Heuristic method cannot identify weakly redundant constraints as redundant constraints. Llewellyn method comparing two constraints. Stojkovic-Stanimirovic depend on objective function. In this paper, we give some examples to recognize characteristics of these methods.
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This study focuses on the optimal network design problem of bike paths, which are on or adjacent to roadways but are physically separated from motorized traffic within the existing urban network. The problem seeks to maximize the total route utilities of cyclists and capture their actual route choice behavior using a path-size logit model. A mixed-integer nonlinear nonconvex model is developed for the problem and is reformulated and linearized into a mixed-integer linear program. The program is solved with a global optimization method and a matheuristic. Results are provided to illustrate the performance of these methods and the model properties.
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