Search results for: Multi-mode resource constrained project scheduling problem

Authors: M. Heydari, S. A. Torabi

Abstract:

The problem of lot sizing, sequencing and scheduling multiple products in flow line production systems has been studied by several authors. Almost all of the researches in this area assumed that setup times and costs are sequence –independent even though sequence dependent setups are common in practice. In this paper we present a new mixed integer non linear program (MINLP) and a heuristic method to solve the problem in sequence dependent case. Furthermore, a genetic algorithm has been developed which applies this constructive heuristic to generate initial population. These two proposed solution methods are compared on randomly generated problems. Computational results show a clear superiority of our proposed GA for majority of the test problems.

Keywords: Economic lot scheduling problem, finite horizon, genetic algorithm, mixed zero-one nonlinear programming, sequence-dependent.

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Authors: Jain-Shing Liu

Abstract:

In this work, we study the problem of determining the minimum scheduling length that can satisfy end-to-end (ETE) traffic demand in scheduling-based multihop WSNs with cooperative multiple-input multiple-output (MIMO) transmission scheme. Specifically, we present a cross-layer formulation for the joint routing, scheduling and stream control problem by incorporating various power and rate adaptation schemes, and taking into account an antenna beam pattern model and the signal-to-interference-and-noise (SINR) constraint at the receiver. In the context, we also propose column generation (CG) solutions to get rid of the complexity requiring the enumeration of all possible sets of scheduling links.

Keywords: Wireless Sensor Networks, Cross-Layer Design, CooperativeMIMO System, Column Generation.

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Authors: K. -H. Yang

Abstract:

In the past, the quay crane operations have been well studied. There were a certain number of scheduling algorithms for quay crane operations, but without considering some nuisance factors that might disrupt the quay crane operations. For example, bad grapples make a crane unable to load or unload containers or a sudden strong breeze stops operations temporarily. Although these disruptive conditions randomly occur, they influence the efficiency of quay crane operations. The disruption is not considered in the operational procedures nor is evaluated in advance for its impacts. This study applies simulation and optimization approaches to develop structures of pre-analysis and post-analysis for the Quay Crane Scheduling Problem to deal with disruptive scenarios for quay crane operation. Numerical experiments are used for demonstrations for the validity of the developed approaches.

Keywords: Disruptive Quay Crane Scheduling, pre-analysis, post-analysis, disruption.

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Authors: Hesham Abdel-Khalek, Sherif M. Hafez, Abdel-Hamid M. el-Lakany, Yasser Abuel-Magd

Abstract:

Investment in a constructed facility represents a cost in the short term that returns benefits only over the long term use of the facility. Thus, the costs occur earlier than the benefits, and the owners of facilities must obtain the capital resources to finance the costs of construction. A project cannot proceed without an adequate financing, and the cost of providing an adequate financing can be quite large. For these reasons, the attention to the project finance is an important aspect of project management. Finance is also a concern to the other organizations involved in a project such as the general contractor and material suppliers. Unless an owner immediately and completely covers the costs incurred by each participant, these organizations face financing problems of their own. At a more general level, the project finance is the only one aspect of the general problem of corporate finance. If numerous projects are considered and financed together, then the net cash flow requirements constitute the corporate financing problem for capital investment. Whether project finance is performed at the project or at the corporate level does not alter the basic financing problem .In this paper, we will first consider facility financing from the owner's perspective, with due consideration for its interaction with other organizations involved in a project. Later, we discuss the problems of construction financing which are crucial to the profitability and solvency of construction contractors. The objective of this paper is to present the steps utilized to determine the best combination of minimum project financing. The proposed model considers financing; schedule and maximum net area .The proposed model is called Project Financing and Schedule Integration using Genetic Algorithms "PFSIGA". This model intended to determine more steps (maximum net area) for any project with a subproject. An illustrative example will demonstrate the feature of this technique. The model verification and testing are put into consideration.

Keywords: Project Management, Large-scale ConstructionProjects, Cash flow, Interest, Investment, Loan, Optimization, Scheduling, Financing and Genetic Algorithms.

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Authors: Bita Tadayon, Nasser Salmasi

Abstract:

This research deals with a flexible flowshop scheduling problem with arrival and delivery of jobs in groups and processing them individually. Due to the special characteristics of each job, only a subset of machines in each stage is eligible to process that job. The objective function deals with minimization of sum of the completion time of groups on one hand and minimization of sum of the differences between completion time of jobs and delivery time of the group containing that job (waiting period) on the other hand. The problem can be stated as FFc / rj , Mj / irreg which has many applications in production and service industries. A mathematical model is proposed, the problem is proved to be NPcomplete, and an effective heuristic method is presented to schedule the jobs efficiently. This algorithm can then be used within the body of any metaheuristic algorithm for solving the problem.

Keywords: flexible flowshop scheduling, group processing, machine eligibility constraint, mathematical modeling.

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Authors: Smajo Bisanovic, Mensur Hajro, Muris Dlakic

Abstract:

This paper presents one comprehensive modelling approach for maintenance scheduling problem of thermal power units in competitive market. This problem is formulated as a 0/1 mixedinteger linear programming model. Model incorporates long-term bilateral contracts with defined profiles of power and price, and weekly forecasted market prices for market auction. The effectiveness of the proposed model is demonstrated through case study with detailed discussion.

Keywords: Maintenance scheduling, bilateral contracts, market prices, profit.

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Authors: C. D. Papanikolaou, V. A. Giouvanis, E. A. Karatasiou, D. S. Dimakas, M. A. Sakellariou-Makrantonaki

Abstract:

Irrigation is one of the most important cultivation practices for each crop, especially in areas where rainfall is enough to cover the crop water needs. In such areas, the farmers must irrigate in order to achieve high economical results. The precise irrigation scheduling contributes to irrigation water saving and thus a valuable natural resource is protected. Under this point of view, in the experimental field of the Laboratory of Agricultural Hydraulics of the University of Thessaly, a research was conducted during the growing season of 2012 in order to evaluate the growth, seed and oil production of sunflower as well as the water saving, by applying different methods of irrigation scheduling. Three treatments in four replications were organized. These were: a) surface drip irrigation where the irrigation scheduling based on the Penman-Monteith (PM) method (control); b) surface drip irrigation where the irrigation scheduling based on a soil moisture sensor (SMS); and c) surface drip irrigation, where the irrigation scheduling based on a soil potential sensor (WM).

Keywords: Irrigation scheduling, soil moisture sensors, sustainable agriculture, water saving.

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Authors: Tomoaki Hashimoto

Abstract:

In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research fields. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method for unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with unknown probability distribution.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints.

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Authors: Christian Böning, Henrik Prinzhorn, Eric C. Hund, Malte Stonis

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In this article, the flexible job-shop scheduling problem is extended by consideration of energy costs which arise owing to the power peak, and further decision variables such as work in process and throughput time are incorporated into the objective function. This enables a production plan to be simultaneously optimized in respect of the real arising energy and logistics costs. The energy-costs-aware flexible job-shop scheduling problem (EFJSP) which arises is described mathematically, and a memetic algorithm (MA) is presented as a solution. In the MA, the evolutionary process is supplemented with a local search. Furthermore, repair procedures are used in order to rectify any infeasible solutions that have arisen in the evolutionary process. The potential for lowering the real arising costs of a production plan through consideration of energy consumption levels is highlighted.

Keywords: Energy costs, flexible job-shop scheduling, memetic algorithm, power peak.

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Authors: Khalid Abd, Kazem Abhary, Romeo Marian

Abstract:

Multiple criteria decision making (MCDM) is an approach to ranking the solutions and finding the best one when two or more solutions are provided. In this study, MCDM approach is proposed to select the most suitable scheduling rule of robotic flexible assembly cells (RFACs). Two MCDM approaches, Analytic Hierarchy Process (AHP) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are proposed for solving the scheduling rule selection problem. The AHP method is employed to determine the weights of the evaluation criteria, while the TOPSIS method is employed to obtain final ranking order of scheduling rules. Four criteria are used to evaluate the scheduling rules. Also, four scheduling policies of RFAC are examined to choose the most appropriate one for this purpose. A numerical example illustrates applications of the suggested methodology. The results show that the methodology is practical and works in RFAC settings.

Keywords: AHP, TOPSIS, Scheduling rules selection

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Authors: A. Rong, P. B. Luh, R. Lahdelma

Abstract:

High penetration of intermittent renewable energy sources (RES) such as solar power and wind power into the energy system has caused temporal and spatial imbalance between electric power supply and demand for some countries and regions. This brings about the critical need for coordinating power production and power exchange for different regions. As compared with the power-only systems, the combined heat and power (CHP) systems can provide additional flexibility of utilizing RES by exploiting the interdependence of power and heat production in the CHP plant. In the CHP system, power production can be influenced by adjusting heat production level and electric power can be used to satisfy heat demand by electric boiler or heat pump in conjunction with heat storage, which is much cheaper than electric storage. This paper addresses multi-site CHP systems without considering RES, which lay foundation for handling penetration of RES. The problem under study is the unit commitment (UC) of the transmission-constrained multi-site CHP systems. We solve the problem by combining linear relaxation of ON/OFF states and sequential dynamic programming (DP) techniques, where relaxed states are used to reduce the dimension of the UC problem and DP for improving the solution quality. Numerical results for daily scheduling with realistic models and data show that DP-based algorithm is from a few to a few hundred times faster than CPLEX (standard commercial optimization software) with good solution accuracy (less than 1% relative gap from the optimal solution on the average).

Keywords: Dynamic programming, multi-site combined heat and power system, relaxed states, transmission-constrained generation unit commitment.

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Authors: Charles D. Otine, Samuel B. Kucel, Lena Trojer

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Selecting the data modeling technique for an information system is determined by the objective of the resultant data model. Dimensional modeling is the preferred modeling technique for data destined for data warehouses and data mining, presenting data models that ease analysis and queries which are in contrast with entity relationship modeling. The establishment of data warehouses as components of information system landscapes in many organizations has subsequently led to the development of dimensional modeling. This has been significantly more developed and reported for the commercial database management systems as compared to the open sources thereby making it less affordable for those in resource constrained settings. This paper presents dimensional modeling of HIV patient information using open source modeling tools. It aims to take advantage of the fact that the most affected regions by the HIV virus are also heavily resource constrained (sub-Saharan Africa) whereas having large quantities of HIV data. Two HIV data source systems were studied to identify appropriate dimensions and facts these were then modeled using two open source dimensional modeling tools. Use of open source would reduce the software costs for dimensional modeling and in turn make data warehousing and data mining more feasible even for those in resource constrained settings but with data available.

Keywords: About Database, Data Mining, Data warehouse, Dimensional Modeling, Open Source.

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Authors: Vahid Salmani, Saman Taghavi Zargar, Mahmoud Naghibzadeh

Abstract:

This paper presents a modified version of the maximum urgency first scheduling algorithm. The maximum urgency algorithm combines the advantages of fixed and dynamic scheduling to provide the dynamically changing systems with flexible scheduling. This algorithm, however, has a major shortcoming due to its scheduling mechanism which may cause a critical task to fail. The modified maximum urgency first scheduling algorithm resolves the mentioned problem. In this paper, we propose two possible implementations for this algorithm by using either earliest deadline first or modified least laxity first algorithms for calculating the dynamic priorities. These two approaches are compared together by simulating the two algorithms. The earliest deadline first algorithm as the preferred implementation is then recommended. Afterwards, we make a comparison between our proposed algorithm and maximum urgency first algorithm using simulation and results are presented. It is shown that modified maximum urgency first is superior to maximum urgency first, since it usually has less task preemption and hence, less related overhead. It also leads to less failed non-critical tasks in overloaded situations.

Keywords: Modified maximum urgency first, maximum urgency first, real-time systems, scheduling.

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Authors: Mohsen Ziaee

Abstract:

In this paper, a mixed integer linear programming (MILP) model is presented to solve the flexible job shop scheduling problem (FJSP). This problem is one of the hardest combinatorial problems. The objective considered is the minimization of the makespan. The computational results of the proposed MILP model were compared with those of the best known mathematical model in the literature in terms of the computational time. The results show that our model has better performance with respect to all the considered performance measures including relative percentage deviation (RPD) value, number of constraints, and total number of variables. By this improved mathematical model, larger FJS problems can be optimally solved in reasonable time, and therefore, the model would be a better tool for the performance evaluation of the approximation algorithms developed for the problem.

Keywords: Scheduling, flexible job shop, makespan, mixed integer linear programming.

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Authors: Bin Cai, Shilong Wang, Haibo Hu

Abstract:

The job shop scheduling problem (JSSP) is a notoriously difficult problem in combinatorial optimization. This paper presents a hybrid artificial immune system for the JSSP with the objective of minimizing makespan. The proposed approach combines the artificial immune system, which has a powerful global exploration capability, with the local search method, which can exploit the optimal antibody. The antibody coding scheme is based on the operation based representation. The decoding procedure limits the search space to the set of full active schedules. In each generation, a local search heuristic based on the neighborhood structure proposed by Nowicki and Smutnicki is applied to improve the solutions. The approach is tested on 43 benchmark problems taken from the literature and compared with other approaches. The computation results validate the effectiveness of the proposed algorithm.

Keywords: Artificial immune system, Job shop scheduling problem, Local search, Metaheuristic algorithm

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Authors: Mohammad S. Laghari, Gulzar A. Khuwaja

Abstract:

Many problems in computer vision and image processing present potential for parallel implementations through one of the three major paradigms of geometric parallelism, algorithmic parallelism and processor farming. Static process scheduling techniques are used successfully to exploit geometric and algorithmic parallelism, while dynamic process scheduling is better suited to dealing with the independent processes inherent in the process farming paradigm. This paper considers the application of parallel or multi-computers to a class of problems exhibiting spatial data characteristic of the geometric paradigm. However, by using processor farming paradigm, a dynamic scheduling technique is developed to suit the MIMD structure of the multi-computers. A hybrid scheme of scheduling is also developed and compared with the other schemes. The specific problem chosen for the investigation is the Hough transform for line detection.

Keywords: Hough transforms, parallel computer, parallel paradigms, scheduling.

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Authors: Anis Gharbi

Abstract:

This paper considers the problem of scheduling maintenance actions for identical aircraft gas turbine engines. Each one of the turbines consists of parts which frequently require replacement. A finite inventory of spare parts is available and all parts are ready for replacement at any time. The inventory consists of both new and refurbished parts. Hence, these parts have different field lives. The goal is to find a replacement part sequencing that maximizes the time that the aircraft will keep functioning before the inventory is replenished. The problem is formulated as an identical parallel machine scheduling problem where the minimum completion time has to be maximized. Two models have been developed. The first one is an optimization model which is based on a 0-1 linear programming formulation, while the second one is an approximate procedure which consists in decomposing the problem into several two-machine subproblems. Each subproblem is optimally solved using the first model. Both models have been implemented using Lingo and have been tested on two sets of randomly generated data with up to 150 parts and 10 turbines. Experimental results show that the optimization model is able to solve only instances with no more than 4 turbines, while the decomposition procedure often provides near-optimal solutions within a maximum CPU time of 3 seconds.

Keywords: Aircraft turbines, Scheduling, Identical parallel machines, 0-1 linear programming, Heuristic.

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Authors: Javier Roca, Etienne Pugnaghi, Gaëtan Libert

Abstract:

We introduce an extended resource leveling model that abstracts real life projects that consider specific work ranges for each resource. Contrary to traditional resource leveling problems this model considers scarce resources and multiple objectives: the minimization of the project makespan and the leveling of each resource usage over time. We formulate this model as a multiobjective optimization problem and we propose a multiobjective genetic algorithm-based solver to optimize it. This solver consists in a two-stage process: a main stage where we obtain non-dominated solutions for all the objectives, and a postprocessing stage where we seek to specifically improve the resource leveling of these solutions. We propose an intelligent encoding for the solver that allows including domain specific knowledge in the solving mechanism. The chosen encoding proves to be effective to solve leveling problems with scarce resources and multiple objectives. The outcome of the proposed solvers represent optimized trade-offs (alternatives) that can be later evaluated by a decision maker, this multi-solution approach represents an advantage over the traditional single solution approach. We compare the proposed solver with state-of-art resource leveling methods and we report competitive and performing results.

Keywords: Intelligent problem encoding, multiobjective decision making, evolutionary computing, RCPSP, resource leveling.

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Authors: Minghui Wang, Shanrui Hu

Abstract:

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

Keywords: doubly center matrix, electric network theory, iterative methods, least-square problem.

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Authors: Dongliang Wang, Jun Han, Dianfu Ma, Xianqi Zhao

Abstract:

Avionics software is safe-critical embedded software and its architecture is evolving from traditional federated architectures to Integrated Modular Avionics (IMA) to improve resource usability. ARINC 653 (Avionics Application Standard Software Interface) is a software specification for space and time partitioning in Safety-critical avionics Real-time operating systems. Arinc653 uses two-level scheduling strategies, but current modeling tools only apply to simple problems of Arinc653 two-level scheduling, which only contain time property. In avionics industry, we are always manually allocating tasks and calculating the timing table of a real-time system to ensure it-s running as we design. In this paper we represent an automatically generating strategy which applies to the two scheduling problems with dependent constraints in Arinc653 partition run-time environment. It provides the functionality of automatic generation from the task and partition models to scheduling policy through allocating the tasks to the partitions while following the constraints, and then we design a simulating mechanism to check whether our policy is schedulable or not

Keywords: Arinc653, scheduling, task allocation, simulation.

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Authors: Ismail El Gayar, Ossama Ismail, Yousri El Gamal

Abstract:

This paper presented a technique to solve one of the transportation problems that faces us in real life which is the Bus Scheduling Problem. Most of the countries using buses in schools, companies and traveling offices as an example to transfer multiple passengers from many places to specific place and vice versa. This transferring process can cost time and money, so we build a decision support system that can solve this problem. In this paper, a genetic algorithm with the shortest path technique is used to generate a competitive solution to other well-known techniques. It also presents a comparison between our solution and other solutions for this problem.

Keywords: Bus scheduling problem, decision support system, genetic algorithm, operation planning, shortest path, transportation.

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Authors: Wahyudin P. Syam, Ibrahim M. Al-Harkan

Abstract:

This study compares three meta heuristics to minimize makespan (Cmax) for Hybrid Flow Shop (HFS) Scheduling Problem with Parallel Machines. This problem is known to be NP-Hard. This study proposes three algorithms among improvement heuristic searches which are: Genetic Algorithm (GA), Simulated Annealing (SA), and Tabu Search (TS). SA and TS are known as deterministic improvement heuristic search. GA is known as stochastic improvement heuristic search. A comprehensive comparison from these three improvement heuristic searches is presented. The results for the experiments conducted show that TS is effective and efficient to solve HFS scheduling problems.

Keywords: Flow shop, genetic algorithm, simulated annealing, tabu search.

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Authors: B. Farhadinia

Abstract:

In this article, it is considered a class of optimal control problems constrained by differential and integral constraints are called canonical form. A modified measure theoretical approach is introduced to solve this class of optimal control problems.

Keywords: control problem, Canonical form, Measure theory.

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Authors: E. Koyuncu

Abstract:

The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: Fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling.

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Authors: Nasr Al-Hinai, Tarek Y. ElMekkawy

Abstract:

The performance of schedules released to a shop floor may greatly be affected by unexpected disruptions. Thus, this paper considers the flexible job shop scheduling problem when processing times of some operations are represented by a uniform distribution with given lower and upper bounds. The objective is to find a predictive schedule that can deal with this uncertainty. The paper compares two genetic approaches to obtain predictive schedule. To determine the performance of the predictive schedules obtained by both approaches, an experimental study is conducted on a number of benchmark problems.

Keywords: Genetic algorithm, met-heuristic, robust scheduling, uncertainty of processing times

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Authors: Aldy Gunawan, Kien Ming Ng, Kim Leng Poh

Abstract:

This paper presents a hybrid algorithm for solving a timetabling problem, which is commonly encountered in many universities. The problem combines both teacher assignment and course scheduling problems simultaneously, and is presented as a mathematical programming model. However, this problem becomes intractable and it is unlikely that a proven optimal solution can be obtained by an integer programming approach, especially for large problem instances. A hybrid algorithm that combines an integer programming approach, a greedy heuristic and a modified simulated annealing algorithm collaboratively is proposed to solve the problem. Several randomly generated data sets of sizes comparable to that of an institution in Indonesia are solved using the proposed algorithm. Computational results indicate that the algorithm can overcome difficulties of large problem sizes encountered in previous related works.

Keywords: Timetabling problem, mathematical programming model, hybrid algorithm, simulated annealing.

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Authors: Jian Zheng, Yoshiyasu Takahashi, Yuichi Kobayashi, Tatsuhiro Sato

Abstract:

In the study, we present a conceptual framework for developing a scheduling system that can generate self-explanatory and easy-understanding schedules. To this end, a user interface is conceived to help planners record factors that are considered crucial in scheduling, as well as internal and external sources relating to such factors. A hybrid approach combining machine learning and constraint programming is developed to generate schedules and the corresponding factors, and accordingly display them on the user interface. Effects of the proposed system on scheduling are discussed, and it is expected that scheduling efficiency and system understandability will be improved, compared with previous scheduling systems.

Keywords: Constraint programming, Factors considered in scheduling, machine learning, scheduling system.

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Authors: Reham A. El-mayet, Hesham M. El-Badawy, Salwa H. Elramly

Abstract:

New generation mobile communication networks have the ability of supporting triple play. In order that, Orthogonal Frequency Division Multiplexing (OFDM) access techniques have been chosen to enlarge the system ability for high data rates networks. Many of cross-layer modeling and optimization schemes for Quality of Service (QoS) and capacity of downlink multiuser OFDM system were proposed. In this paper, the Maximum Weighted Capacity (MWC) based resource allocation at the Physical (PHY) layer is used. This resource allocation scheme provides a much better QoS than the previous resource allocation schemes, while maintaining the highest or nearly highest capacity and costing similar complexity. In addition, the Delay Satisfaction (DS) scheduling at the Medium Access Control (MAC) layer, which allows more than one connection to be served in each slot is used. This scheduling technique is more efficient than conventional scheduling to investigate both of the number of users as well as the number of subcarriers against system capacity. The system will be optimized for different operational environments: the outdoor deployment scenarios as well as the indoor deployment scenarios are investigated and also for different channel models. In addition, effective capacity approach [1] is used not only for providing QoS for different mobile users, but also to increase the total wireless network's throughput.

Keywords: Cross-layer, effective capacity, LTE, OFDM, QoS, resource allocation, wireless networks.

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Authors: C. E. Nugraheni, L. Abednego

Abstract:

This paper introduces a framework based on the collaboration of multi agent and hyper-heuristics to find a solution of the real single machine production problem. There are many techniques used to solve this problem. Each of it has its own advantages and disadvantages. By the collaboration of multi agent system and hyper-heuristics, we can get more optimal solution. The hyper-heuristics approach operates on a search space of heuristics rather than directly on a search space of solutions. The proposed framework consists of some agents, i.e. problem agent, trainer agent, algorithm agent (GPHH, GAHH, and SAHH), optimizer agent, and solver agent. Some low level heuristics used in this paper are MRT, SPT, LPT, EDD, LDD, and MON

Keywords: Hyper-heuristics, multi-agent systems, scheduling problem.

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Authors: G. M. Komaki, S. Mobin, E. Teymourian, S. Sheikh

Abstract:

This paper addresses minimizing the makespan of the distributed permutation flow shop scheduling problem. In this problem, there are several parallel identical factories or flowshops each with series of similar machines. Each job should be allocated to one of the factories and all of the operations of the jobs should be performed in the allocated factory. This problem has recently gained attention and due to NP-Hard nature of the problem, metaheuristic algorithms have been proposed to tackle it. Majority of the proposed algorithms require large computational time which is the main drawback. In this study, a general variable neighborhood search algorithm (GVNS) is proposed where several time-saving schemes have been incorporated into it. Also, the GVNS uses the sophisticated method to change the shaking procedure or perturbation depending on the progress of the incumbent solution to prevent stagnation of the search. The performance of the proposed algorithm is compared to the state-of-the-art algorithms based on standard benchmark instances.

Keywords: Distributed permutation flow shop, scheduling, makespan, general variable neighborhood search algorithm.

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