Mixed Binary Integer Programming Research Articles

Bi-objective unrelated parallel machine joint scheduling of jobs and preventive maintenance with a dynamic speed-scaling technique

Nowadays, industries contribute to a substantial consumption of energy. This consumption leads to significant greenhouse gas emissions, energy dependence and ever-increasing costs for manufacturers. Controlling consumption and improving energy efficiency in industry are therefore major challenges in terms of environmental issues. In this context, this article examines an energy-efficient bi-objective unrelated parallel machine joint scheduling of jobs and preventive maintenance activities problem to minimize both makespan and total energy consumption. The parallel machines are speed-scaling. To solve the problem, we propose a bi-objective mixed integer linear programming (MILP) model. Since the problem involves assigning jobs to machines and selecting an appropriate processing speed level for each job, we characterize each individual by two vectors: a job-machine assignment vector and a speed vector. To the best of our knowledge, no papers considering both production scheduling and Preventive Maintenance periods with minimizing the bi-objective makespan and the total of energy consumption. The gap between theory and practice prevents the satisfying performance of the schedules in industry. The purpose of this paper is to establish a joint model for integrating the production and PM scheduling to optimize the bi-objective of the total of energy consumption (TEC) and makespan (Cmax) simultaneously; and to make the theory applied in practice more efficaciously. The performance of the proposed mixed binary integer programming model is evaluated based on the exact method of Branch and Bound integrated on the CPLEX solver plus analyses using MATLAB software. A study of the results proved the performance of the model developed.

Optimizing the supply of essential goods under closed-off management: A case study of COVID-19

The COVID-19 pandemic is threatening people's health and economic development around the world. Many areas and cities are opting for actions such as lockdown or closed-off management to prevent rapid spread of the virus. Under these actions, it is necessary and important to guarantee the supply of essential goods. In this paper, we develop a multi-objective optimization model to optimize the supply of essential goods under closed-off management. A mixed binary integer programming model is built to help identify the optimal safety stock level as well as the supply network so that the demands for essential goods could be guaranteed. The effectiveness of our method is demonstrated by an example. We also perform sensitivity analysis for key parameters. Our work provides a reasonable solution for the supply of essential goods under closed-off management.

Green Scheduling of Jobs and Flexible Periods of Maintenance in a Two-Machine Flowshop to Minimize Makespan, a Measure of Service Level and Total Energy Consumption

The success of an industry today depends on its ability to innovate. In terms of energy performance, this innovation is reflected in the ability of manufacturers to implement new solutions or technologies that enable better energy management. In this regard, this paper aims to address this gap by incorporating energy consumption as an explicit criterion in flowshop scheduling of jobs and flexible preventive maintenance. Leveraging the variable speed of machining operations leading to different energy consumption levels, we explore the potential for energy saving in manufacturing. We develop a mixed integer linear multiobjective optimization model for minimizing the makespan and the total energy consumption. In the literature, no papers considering both production scheduling and flexible periods of maintenance with minimizing both objective the total of energy consumption in flowshop and makespan. The performance of the proposed mixed binary integer programming model is evaluated based on the exact method of branch and bound algorithm. A study of the results proved the performance of the model developed.

Speed scaling technique integrated in scheduling of production and maintenance under energy constraints using genetic algorithms

Recently, energy scarcity and environmental pollution have become increasingly serious problems, while the scheduling of energy savings is attracting increasing attention from industries to minimize energy consumption. This article deals with the problem of scheduling production and maintenance under energy constraints in the flow shop. Two mixed binary integer programming models are provided to derive optimal scheduling to minimize total energy consumption (TEC). To solve this problem, we use an approximate method as a genetic algorithm (GA).

Energy efficient resource allocation based on relay selection and subcarrier pairing with channel uncertainty in cognitive radio network

More and more mobile devices join in the wireless networks, it has become a challenging problem how to mitigating the interferences and improving the energy efficiency in dynamic wireless communication environment. In this paper, a robust resource allocation algorithm is proposed to maximize the energy efficiency (EE) in a multi-carrier decode-and-forward (DF) cognitive radio(CR) relay network, which subjects to multiple constraints in aspects of relay transmit power, signal to noise ratio threshold, subcarrier pairing, relay selection and the primary user’s minimum transmit rate requirement. The original optimization problem is non-convex with consideration of the channel uncertainty, and it is the mixed binary integer programming problem. Subsequently, we use the worst-case method to deal with channel uncertainty and convert the original non-convex problem into a quasi-concave problem by the Dinkelbach method. We solve the NP-hard problem in two steps: fixing the subcarriers to get the optimal relay selection and allocating the subcarriers according to the optimal relay selection. By using the method of dual decomposition, we get the approximate optimal solution of the problem. Simulation results show that the proposed joint resource allocation scheme guarantees the desired service quality requirements, and the energy-efficiency obtained is improved comparing with some existing works. In addition, the proposed resource allocation algorithm shows better convergence performance under different topologies, which validates the resource allocation scheme has good scalability.

Joint Downlink and Uplink Edge Computing Offloading in Ultra-Dense HetNets

The deployment of ultra-dense heterogeneous networks (HetNets) are envisioned as the essentials to embrace of intelligent applications for the next-generation wireless networks. For ultra-dense HetNets, the small scale heterogeneous edge servers in macrocell and smallcell, decreasing downlink and uplink communication delay should be attracted more attention for latency-critical intelligent applications. Therefore, we aim at edge computation offloading of joint downlink (DL) and uplink (UL) together with communication and computing resource allocation. Then, we formulate the computation offloading optimization problem into minimizing the overall delay of task while saving energy consumption of user device. However,the joint downlink and uplink computing offloading problem with resource allocation is a mixed binary integer programming which is difficult to deal with. We convert the programming problem into resource allocation sub-problem and computing offloading sub-problem, and propose an efficient joint downlink and uplink offloading algorithm for ultra-dense HetNets. Numerical results validate the efficiency of the proposed algorithm in terms of the delay and energy saving of system.

Scheduling Jobs on a Single Machine With Dirt Cleaning Consideration to Minimize Total Completion Time

This paper studies a single-machine scheduling problem observed in the wafer manufacturing process, where the machine must receive periodical maintenance so that the dirt generated in the process does not exceed the limit. The objective is to minimize the total completion times. A mixed binary integer programming model is formulated, and, due to its computational intractability for large problems, three effective heuristics are proposed based on our developed properties. The proposed heuristics are evaluated by comparison with exact solutions on small problems and with lower bounds on large problems. The experimental results show that the INDEX-LOE heuristic yields high-quality solutions in comparison with those obtained from the other two heuristics. Furthermore, the impacts of dirt accumulation and cleaning time are discussed in detail.

A Bi-Level Programming Model of Liquefied Petroleum Gas Transportation Operation for Urban Road Network by Period-Security

As a clean energy, Liquefied Petroleum Gas (LPG) is consistent with the coordinated and sustainable development of both the economy and environment. However, LPG is a hazardous material (hazmat) and is thus always transported in cylinders by vehicles on urban road networks to meet varying demand. This transport can threaten the surrounding citizens, vehicles, and even the whole urban area. Hence, LPG transportation should be focused on maintaining its security while simultaneously minimizing shipping costs. When LPG is moved through an urban area, its threat level fluctuates with the network congestion level, which continually varies by different time periods. So, variation in the magnitude of the threat posed by LPG transportation causes additional changes in the safe-related cost as well as the shipping cost. This study aims to solve the problem of an LPG transportation operation on an urban road network according to congested periods; the solution is based on cutting its two types of cost. In general, we should choose an LPG transport period that results in a lower safety cost, however optimization of an LPG transportation operation must minimize both the safety cost and shipping cost. This paper presents the problem of LPG flow distribution and vehicle dispatch scheme by “period-security” to rationalize the LPG transport risk level. Firstly, the impedance function of LPG flow distribution was constructed with a focus on the safety cost in different periods. Meanwhile, a bi-level programming model was built, in which the upper mixed binary integer programming model aims to minimize the shipping cost and the lower model is a user-equilibrium model that is aimed at calculating the distribution of the LPG demands on the given lines and in feasible periods. Then, we designed a heuristic algorithm based on the Genetic Algorithm to solve the upper model and embedded the Frank-Wolfe Algorithm to get the optimal LPG flow distribution solution. Numerical examples are presented which validate that the LPG optimal operation can realize a minimal safety cost and the minimum shipping cost for three LPG demand values by considering the congestion situation.

Minimizing the number of tardy jobs on unrelated parallel machines with dirt consideration

ABSTRACTThis paper considers an unrelated parallel machine scheduling problem with the objective of minimizing the number of tardy jobs. Each machine should stop periodically to perform maintenance activities. The problem, motivated from a wafer manufacturing company, considers the job scheduling and maintenance activities simultaneously under dirt constraint. That is, the dirt accumulation in the machine does not exceed the prespecified dirt limit. A mixed binary integer programming (MBIP) model is developed to find optimal solutions, and two three-phase heuristics are proposed. The heuristics assign each job to its most efficient machine first. Then, an intension of Moore’s algorithm is applied for each machine, and finally the solution is improved by the forward/backward insert mechanism. The experimental results showed that the proposed heuristics perform well. Furthermore, the efficiency of the MBIP model and the impact of the dirt accumulation as well as maintenance time are studied in detail.

Energy Efficiency Maximization for C-RANs: Discrete Monotonic Optimization, Penalty, and $\ell _{0}$-Approximation Methods

We study downlink of multiantenna cloud radio access networks (C-RANs) with finite-capacity fronthaul links. The aim is to propose joint designs of beamforming and remote radio head (RRH)-user association, subject to constraints on users' quality-of-service, limited capacity of fronthaul links and transmit power, to maximize the system energy efficiency. To cope with the limited-capacity fronthaul we consider the problem of RRH-user association to select a subset of users that can be served by each RRH. Moreover, different to the conventional power consumption models, we take into account the dependence of baseband signal processing power on the data rate, as well as the dynamics of the efficiency of power amplifiers. The considered problem leads to a mixed binary integer program (MBIP) which is difficult to solve. Our first contribution is to derive a globally optimal solution for the considered problem by customizing a discrete branch-reduce-and-bound (DBRB) approach. Since the global optimization method requires a high computational effort, we further propose two suboptimal solutions able to achieve the near optimal performance but with much reduced complexity. To this end, we transform the design problem into continuous (but inherently nonconvex) programs by two approaches: penalty and \ell_{0}-approximation methods. These resulting continuous nonconvex problems are then solved by the successive convex approximation framework. Numerical results are provided to evaluate the effectiveness of the proposed approaches.

Joint Load Balancing of Downlink and Uplink for eICIC in Heterogeneous Network

The 3GPP has proposed enhanced intercell interference coordination (eICIC) by making the macrocell silent in the almost blank subframes (ABSs) to mitigate interference for low-power base stations (BSs) in the downlink direction. However, two important challenges are introduced: 1) the underutilization for macrocell in ABS and 2) the optimal downlink association may not be optimal for uplink transmission, i.e., downlink/uplink decoupling (DUDe). In this paper, we first propose a novel method based on configuring uplink transmission in the macrocell in ABSs (UM-ABS) for eICIC to improve the efficiency of the ABS. Then, the UM-ABS and DUDe are formulated as an optimization problem of investigating the joint load balancing of downlink and uplink for eICIC in heterogeneous networks (HetNets) while considering different service classes. The problem is actually a mixed binary integer programming problem, which is difficult to solve. We provide a relaxed-rounding solution to the model. Numerical results illustrate that the proposed algorithm achieves superior performance in comparison to state-of-the-art methods in terms of system throughput and the rate gain for users.

Modeling and optimization of an electric power distribution network planning system using mixed binary integer programming

In this paper, the electric distribution network expansion planning problem (EDNEPP) was solved by a mixed binary integer programming (MBIP) formulation of the network, where the steady-state operation of the network was modelled with non-linear mathematical expressions. The non-linear terms are linearized, using piecewise linearization of the non-linear expressions, so as to ensure the model computational compatibility with existing commercial optimization solvers. The linearized formulation is verified to ensure its solution optimality and degree of error deviation. The proposed network model formulation considers the alternatives of installation of new transformers of various capacities to reinforce already existing ones at substations of the network, choosing and construction of new substations given feasible locations, re-conductoring of existing feeders in the network, construction of new feeders given various conductor types alternatives, cost lost as a result of power interruption, and changes in the overall network topology. The cost of interruption would contain a cost term called ‘cost of goodwill’, which was brought into the model formulation, to measure the loss in confidence of consumers to distributors of power as a result of interrupted power supply, which is prevalent in developing nations. Two test systems of 23 and 54 nodes was used in showing the efficiency of the proposed network model formulation. http://dx.doi.org/10.4314/njt.v36i2.31

Resource Allocation for Full-Duplex Relay-Assisted Device-to-Device Multicarrier Systems

This letter analyzes the resource allocation problem for full-duplex relay-assisted device-to-device (D2D) multicarrier systems, where multiple D2D user groups (UGs) coexist in an underlaying manner. We formulate the optimization problem, which takes the maximization of the system throughput as an objective. Two resources, i.e., subcarrier and transmit power are considered to be appropriately allocated to UGs in order to meet the objective. The formulated problem can be independently divided into a quasi-concave problem and a mixed binary integer programming (MBIP) problem. The MBIP problem is NP-hard. Therefore, to solve this problem efficiently by standard optimization techniques, we propose an alternative algorithm, which is the linear relaxation of the MBIP problem. Then, we mathematically prove and numerically verify the equivalence of the MBIP problem and its linear relaxation. By this way, the resource allocation for UGs can be carried out by a small amount of computational overhead.

Energy Efficient Resource Allocation for Multiuser Relay Networks

In this paper, a novel resource allocation algorithm is investigated to maximize the energy efficiency (EE) in multiuser decode-and-forward (DF) relay interference networks. The EE optimization problem is formulated as the ratio of the spectrum efficiency (SE) over the entire power consumption of the network subject to total transmit power, subcarrier pairing, and allocation constraints. The formulated problem is a nonconvex fractional mixed binary integer programming problem, i.e., NP-hard to solve. Furthermore, we resolve the convexity of the problem by a series of convex transformations and propose an iterative EE maximization algorithm to jointly determine the optimal subcarrier pairing at the relay, subcarrier allocation to each user pair and power allocation to all source and the relay nodes. Additionally, we derive an asymptotically optimal solution by using the dual decomposition method. To gain more insights into the obtained solutions, we further analyze the resource allocation algorithm in a two-user case with interference-dominated and noise-dominated regimes. In addition, a suboptimal algorithm is investigated with reduced complexity at the cost of acceptable performance degradation. Simulation results are used to evaluate the performance of the proposed algorithms and demonstrate the impacts of various network parameters on the attainable EE and SE.

Minimizing total absolute deviation of job completion times on a single machine with cleaning activities

This paper considers a new single machine scheduling problem with several unavailability periods, where the machine has to be stopped in order to remove the dirt. The problem appears in the process in wafer manufacturing company. During the processing of a wafer on a specific machine, the dirt, including particle, organic materials and metal-salts, etc., on the surface of the wafer while processing, has to be taken away by a cleaning agent. Once the accumulation of dirt is over a threshold value, it is necessary to interrupt the machine processing and replace the cleaning agent in order to avoid damaging the wafer. The objective is to minimize the total absolute deviation of job completion times (TADC). The problem integrates production scheduling and cleaning activities and is strongly NP-hard. Many properties for solving the problem efficiently are explored. A mixed binary integer programming model is developed to find the optimal solution. Based on the properties explored, symmetry of the V-shaped rule, and the dynamic programming on scheduling the cleaning activities, an effective heuristic is developed. Computational results indicate that the performance of the heuristic is robust and significantly outperforms the modified TADC solution in the literature. Furthermore, the efficiency of the mixed binary integer programming model and the impact of the dirt accumulation as well as cleaning time are explored in detail.

Joint versus separate spectrum sensing and resource allocation in OFDMA‐based cognitive radio networks

In this study, the authors investigate the resource allocation issue for sensing-based orthogonal frequency-division multiple access (OFDMA) cognitive radio networks. They consider a network consisting multiple secondary users (SUs) and a secondary base station (BS) implementing a two-phase protocol. In the first phase, cooperative spectrum sensing is carried out to detect the vacant subchannels. In the second phase, SUs transmit data in the uplink to the BS by using OFDMA. They optimise the sensing parameters, transmit power and subchannel assignments jointly to minimise the total energy consumption with the constraints on SUs’ quality of service and detection probability of the primary user. This is a mixed binary integer programming problem which is NP (non-deterministic polynomial-time)-hard and generally intractable. They represent the problem as a bilevel problem and propose two efficient algorithms to solve the slave and master subproblems. They also study the separate optimisation, in which the sensing parameters of SUs are set regardless of the allocated resources. They investigate the energy savings of joint versus separate optimisation using numerical experiments. The results show that the joint optimisation method can introduce up to 16% of energy saving in zero sensing signal-to-noise ratio with the same total transmission bandwidth of 2.5 MHz.

Concurrent transmission for energy efficiency of user equipment in 5G wireless communication networks

In this paper, we investigate concurrent transmission among multiple radio access technologies (RATs) for energy efficiency (EE) of multi-mode user equipment (MUE) in 5G wireless communication networks. Considering both the static circuit power consumption of the MUE and channel state information of different RATs, we propose an EE maximization concurrent transmission (EXACT) strategy by fully utilizing the multi-RAT combining gain of concurrent transmission. In particular, we formulate such EE maximization concurrent transmission problem as a mixed binary integer programming (MIP), and under some given static circuit power conditions, the optimal RATs selection and transmission rates for establishing concurrent transmission among multiple RATs are derived. Furthermore, in order to deal with the challenging MIP, an approximate expression is derived to simplify the integer constraints, thus the original MIP is transformed into a nonlinear continuous optimization problem. Consequently, a low complexity heuristic algorithm for general static circuit power conditions, which can achieve the near-optimal solution, is presented. Simulation results confirm the effectiveness of the EXACT strategy and show that the EE performance of the MUE can be significantly improved by reasonable and effective utilization of multiple RATs to execute concurrent transmission.

A hybrid genetic algorithm for non-permutation flow shop scheduling problems with unavailability constraints

This article deals with the non-permutation flow shop scheduling problems with non-availability intervals. Specifically, two kinds of unavailability constraints are investigated and the jobs are non-resumable in both cases. In the first case, the non-availability intervals are periodically fixed and known in advance. In the second case, the intervals are flexible and the machines’ continuous working time cannot exceed a maximum allowed time. Two mixed binary integer programming models are provided for deriving the optimal schedules, respectively. The problems of minimising makespan in such flow shops are proved Non-deterministic Polynomial-time hard in strong sense. Then a hybrid incremental genetic algorithm (HIGA) that combines an incremental evolution strategy framework, a local refinement and a population diversity supervision scheme is proposed to solve the large-sized problems efficiently. The numerical experiments under different problem parameters’ settings indicate that the HIGA can achieve quite satisfactory performance compared with genetic algorithm and a constructive heuristic based on Nawaz, Enscore, Ham.

QoE-Driven Cross-Layer Optimization for Wireless Dynamic Adaptive Streaming of Scalable Videos Over HTTP

Recently, Dynamic Adaptive Streaming over HTTP (DASH) has attracted significant attention. In this paper, we consider DASH-based transmission of scalable videos in wireless broadband access networks (e.g., long-term evolution and WiMAX), and propose three methods to enhance the quality of experience of wireless DASH users. First, we design an improved mapping scheme from scalable video coding layers to DASH layers that can provide the desired bitrates, enhance the video end-to-end throughput, and reduce the HTTP communication overhead. Second, we develop a DASH-friendly scheduling and resource allocation algorithm by integrating the DASH-based media delivery and the radio-level adaptation via a cross-layer approach. It utilizes the characteristics of video content and scalable video coding, and greatly reduces the possibility of video playback interruption by considering the client buffer status. The optimization problem is formulated as a mixed binary integer programming problem, and is solved by a subgradient method. Finally, a DASH proxy-based bitrate stabilization algorithm is proposed to improve the video playback smoothness that can achieve the desired tradeoff between playback quality and stability. Simulations with the Qualnet tool demonstrate that our schemes achieve better performances than other methods in the literature.

Design of production management model integrated with fuzzy inference system and mixed binary integer program

Design of production management model integrated with fuzzy inference system and mixed binary integer program