We consider the problem of single link failure in an elastic optical network, (also known as flex-grid WDM network). The task is to reroute optical connections that go through the broken link using free capacity of ot...
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ISBN:
(数字)9798350351859
ISBN:
(纸本)9798350351866
We consider the problem of single link failure in an elastic optical network, (also known as flex-grid WDM network). The task is to reroute optical connections that go through the broken link using free capacity of other links of the network. Nowadays, dynamic restoration gains popularity, in which the possiblity of rerouting is only inspected after a link failure is detected. Since the problem of recovery is NP-hard, heuristic algorithms are used to either find such routes, or suggest that the routes do not exist. In order to understand the quality of these heuristics, often mixed integer linear programming is used to obtain exact positive and negative answers. We present a detailed such model that checks whether restoration is possible without the use of additional regenerators. This means, that the new light paths need to satisfy a length constraint. As preprossing we apply a trimming procedure that takes advantage of this length constraint, and significantly speeds up the evaluation of these models. Our model is more general, and besides solving the problem of link restoration, also solves the full problem of wavelength and spectrum assignment.
A mixed integer linear programming (MILP) model is proposed in this paper that targets the optimal production scheduling in a single milk production *** model takes into account all the standard constraints encountere...
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A mixed integer linear programming (MILP) model is proposed in this paper that targets the optimal production scheduling in a single milk production *** model takes into account all the standard constraints encountered in production scheduling (material balances,inventory limitations,machinery capacity,labor shifts and manpower restrictions).Furthermore,it considers special features that characterize milk production,which are limitations in production sequencing mainly due to different fat contents and flavors of various products and sequence-dependent setup times and *** objective function that is minimized considers all major sources of variable cost that depend on the production schedule,*** cost,inventory cost and labor *** model is applied to a milk production line of a Sala industry in Iran and the results are presented and discussed.
In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. It is well known that this problem is NP-hard, and therefore we seek efficient, but not optimal, solutions ...
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In this paper, we address the multi pursuer version of the pursuit evasion problem in polygonal environments. It is well known that this problem is NP-hard, and therefore we seek efficient, but not optimal, solutions by relaxing the problem and applying the tools of mixed integer linear programming (MILP) and Receding Horizon Control (RHC). Approaches using MILP and RHC are known to produce efficient algorithms in other path planning domains, such as obstacle avoidance. Here we show how the MILP formalism can be used in a pursuit evasion setting to capture the motion of the pursuers as well as the partitioning of the pursuit search region into a cleared and a contaminated part. RHC is furthermore a well known way of balancing performance and computation requirements by iteratively solving path planning problems over a receding planning horizon, and adapt the length of that horizon to the computational resources available. The proposed approach is implemented in Matlab/Cplex and illustrated by a number of solved examples.
In this paper, we develop mixed-integerlinearprogramming models for assigning the most appropriate teaching assistants to the tutorials in a department. The objective is to maximize the number of tutorials that are ...
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In this paper, we develop mixed-integerlinearprogramming models for assigning the most appropriate teaching assistants to the tutorials in a department. The objective is to maximize the number of tutorials that are taught by the most suitable teaching assistants, accounting for the fact that different teaching assistants have different capabilities and each teaching assistant's teaching load cannot exceed a maximum value. Moreover, with optimization models, the teaching load allocation, a time-consuming process, does not need to be carried out in a manual manner. We have further presented a number of extensions that capture more practical considerations. Extensive numerical experiments show that the optimization models can be solved by an off-the-shelf solver and used by departments in universities.
We propose an optimal design method for digital IIR filters with powers-of-two coefficients. This method is based upon the formulation of a linear optimization problem that minimizes the filter's complexity for gi...
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We propose an optimal design method for digital IIR filters with powers-of-two coefficients. This method is based upon the formulation of a linear optimization problem that minimizes the filter's complexity for given specifications. It is shown that by taking the logarithm to the transfer function of cascade-form IIR filters, the design problem becomes linear and can be solved by mixed integer linear programming (MILP). Design examples are presented to demonstrate the efficiency of the proposed method.
A mixed integer linear programming (MILP)–based distributed optimization of three-phase unbalanced active distribution network is proposed. Modern distribution networks have becoming more and more active with increas...
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ISBN:
(数字)9798350372403
ISBN:
(纸本)9798350372410
A mixed integer linear programming (MILP)–based distributed optimization of three-phase unbalanced active distribution network is proposed. Modern distribution networks have becoming more and more active with increasing deployment of microgrids, distributed energy resources (DERs) and flexible loads. Considering various ownership and control models of microgrids, DERs and loads, a distributed optimization was formulated and solved using the alternating direction method of multipliers (ADMM) algorithm. By ADMM, the distribution management system (DMS) and these active components are coordinated through price signals, which are adjusted from the nodal power unbalance per node per phase. To enable resolution of the ADMM-based distributed optimization using MILP solver, various linearization methods were proposed to linearize the augmented Lagrangian and other nonlinear terms. Results of case studies using a three-phase active distribution system with three microgrids and several DERs and flexible loads validated the effectiveness of proposed MILP-based distributed optimization. In addition, the capability of proposed method in mitigating phase power unbalance has been demonstrated.
mixed integer linear programming (MILP) is an important problem in the combinatorial optimization domain, which has wide applications in practical optimization scenarios. Given that most MILP problems fall into the NP...
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mixed integer linear programming (MILP) is an important problem in the combinatorial optimization domain, which has wide applications in practical optimization scenarios. Given that most MILP problems fall into the NP-hard category, which the traditional methods may fail to solve, recent research has tried to derive MILP solutions using machine learning techniques. The whole MILP-solving procedure involves lots of modules, such as pre-solving, cut selection, node section, etc., and these modules are closely related and influence each other. However, the previous machine learning-based approaches neglect the connections between these modules, and focus on single-module learning techniques. To address this, we propose an initial step towards a more comprehensive multi-agent learning framework that allows different modules to interact and collaborate. Specifically, our current implementation involves two key modules: HEM for cut selection applied at the root node and GCNN for variable selection. By employing HEM to influence the training of GCNN, these two agents thus work in unison. Through extensive experiments on four MILP datasets in diverse scenarios, we observe significant improvements in solving time and PD integral metrics compared with the state-of-the-art learning-based MILP solving methods. This work lays the groundwork for future development of a fully integrated multi-agent framework.
This paper addresses the problem of finding optimal trajectories for multiple autonomous systems. mixed integer linear programming (MILP) is described for designing time and energy- or fuel-optimal maneuvers that acco...
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This paper addresses the problem of finding optimal trajectories for multiple autonomous systems. mixed integer linear programming (MILP) is described for designing time and energy- or fuel-optimal maneuvers that account for the presence of other vehicles. The paper shows how integer constraints can be added to linearprogramming to account for obstacle avoidance and collision avoidance among the group of autonomous systems
The authors propose a new model for dynamic traffic assignment, modeling the traffic system by a mixedintegerlinear program solvable in finite time. The model represents link travel times, which must be the same for...
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The authors propose a new model for dynamic traffic assignment, modeling the traffic system by a mixedintegerlinear program solvable in finite time. The model represents link travel times, which must be the same for all vehicles which enter a link together during a single time period by means of 0-1 integer variables. Given the values of these variables, the problem is to assign traffic, modeled as multiperiod multicommodity flow, subject to constraints on capacity implied by the link travel times. An optimal solution to the model gives the vehicle routings corresponding to minimum total travel time, achieving the most efficient use of road capacity. The solution gives unambiguous link travel times as a function of time of entry to the link, suitable for individual route optimization if all but a small priority class of traffic accepts the system-optimal routing.< >
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