Generalized Assignment Problem Research Articles

Solution of fuzzy multi objective generalised assignment problem

In this paper, multi objective generalised assignment problem (MOGAP) with fuzzy parameters has been solved using three different approaches. Here, we consider three objective functions which are to be minimised. In the first approach, weighted sum method has been used and the problem is converted into a single objective one and then solved by extremum difference method (EDM) to get the optimal assignment. In the second one, modified fuzzy programming technique (MFPT) has been used for the same problem. Application of linear and exponential membership functions give comparative results with the goal that the better alternative can be obtained. The third one describes multi objective genetic algorithm (MOGA) to find the solution surface and the Pareto optimal front including the optimal assignment. The methods are demonstrated by a suitable numerical example.

Fairness and Load Balancing in SDWN Using Handoff-Delay-Based Association Control and Load Monitoring

Traffic loads in any 802.11 WLAN are distributed unevenly. This imbalance implies that some access points (APs) suffer from traffic congestions, while others are underutilized. The unbalanced load distributions cause annoying packet delay and throughput degradation which is unacceptable in current and future networks. A load-balancing algorithm should solve two challenges. The first is to accurately identify the APs’ loads to timely find traffic imbalances. And the second is to associate clients with APs to achieve optimal proportional fairness intelligently. Network metrics such as throughput, delay, jitter, and client amount cannot be used individually to accurately identify APs’ loads, because of the complexities of wireless communications. Which metrics to use and how to combine those network metrics to represent AP load are controversial. For intelligent association control, handoff delay (time to move a station from an AP to another) may last for 6 seconds. If the algorithm designers do not consider this delay in their optimization processes, unnecessary re-associations generated in their algorithm will offset the optimization profits. In this paper, we propose novel learning-based methods to monitor the network load to discover real-time load unbalances. We also model the load balancing problem as a utility maximization problem in which costs caused by handoff delay are considered. Then we utilize discretized linear programming theory and general assignment problem theory to solve it. We also compute the approximation ratio of our algorithm. We implement the whole load balancing system and evaluate the performances which show that our method outperforms a state-of-art algorithm in terms of throughput by up to12.7%, and it outperforms the received signal strength indicator (RSSI) based method by up to 28.13%.

Solution of fuzzy multi objective generalised assignment problem

Solution of fuzzy multi objective generalised assignment problem

Methodology to Solve the Combination of the Generalized Assignment Problem and the Vehicle Routing Problem: A Case Study in Drug and Medical Instrument Sales and Service

This article presents algorithms for solving a special case of the vehicle routing problem (VRP). We define our proposed problem of a special VRP case as a combination of two hard problems: the generalized assignment and the vehicle routing problem. The different evolution (DE) algorithm is used to solve the problem. The recombination process of the original DE is modified by adding two more sets of vectors—best vector and random vector—and using two other sets—target vector and trial vector. The linear probability formula is proposed to potentially use one out of the four sets of vectors. This is called the modified DE (MDE) algorithm. Two local searches are integrated into the MDE algorithm: exchange and insert. These procedures create a DE and MDE that use (1) no local search techniques, (2) two local search techniques, (3) only the exchange procedure, and (4) only the insert procedure. This generates four DE algorithms and four MDE algorithms. The proposed methods are tested with 15 tested instances and one case study. The current procedure is compared with all proposed heuristics. The computational result shows that, in the case study, the best DE algorithm (DE-4) has a 1.6% better solution than that of the current practice, whereas the MDE algorithm is 8.2% better. The MDE algorithm that uses the same local search as the DE algorithms generates a maximum 5.814% better solution than that of the DE algorithms.

Hybrid algorithms for the earliness–tardiness single-machine multiple orders per job scheduling problem with a common due date

In this paper, we study an earliness–tardiness scheduling problem for a single machine that is motivated by process conditions found in semiconductor wafer fabrication facilities (wafer fabs). In modern 300-mm wafer fabs, front opening unified pods (FOUPs) transfer wafers. The number of FOUPs is limited to avoid a congestion of the Automated Material Handling System. Several orders can be grouped in one FOUP. A nonrestrictive common due date for all the orders is assumed. Only orders that belong to the same family can be processed together in a single FOUP at the same time. We present a Mixed Integer Linear Programming (MILP) formulation for this problem. Moreover, we show that this scheduling problem is NP-hard. We propose several simple heuristics based on dispatching rules and assignment strategies from bin packing. Moreover, genetic algorithms are designed that assign the orders to the set of early and tardy orders, respectively. In addition, a random key genetic algorithm (RKGA) is described that proposes order sequences. The different algorithms are hybridized with job formation and sequencing heuristics. A more specialized algorithm that is based on the generalized assignment problem is presented for the special case of a single order family. Results of computational experiments based on randomly generated problem instances are presented. They demonstrate that the genetic algorithms perform well with respect to solution quality and computing time under a broad range of experimental conditions.

Variable-fixing then subgradient optimization guided very large scale neighborhood search for the generalized assignment problem

We propose a two-phase heuristic for the generalized assignment problem (GAP). The first phase—a generic variable-fixing method—heuristically eliminates up to 98% of the variables without sacrificing the solution quality. The second phase takes as input the small reduced GAP obtained during the first phase and applies a very large scale neighborhood search. The definition of the successive exponential size neighborhoods is guided by the subgradient method applied to the Lagrangian relaxation of the knapsack constraints via the reduced costs. Searching the proposed neighborhood is NP-hard and amounts to solving a monotone binary program (BP) with m constraints and p variables, where m and p are respectively the number of agents and tasks of the reduced GAP (monotone BPs are BPs with two nonzero coefficients of opposite sign per column). To the best of our knowledge, this is the first time the above ideas are exposed. Extensive testing on large scale GAP instances is presented and previously unknown better values for eight instances are obtained. Comparison to well-established methods shows that this new approach is competitive and constitutes a substantial addition to the arsenal of tools for solving GAP.

Exact and heuristic algorithms for the interval min-max regret generalized assignment problem

Abstract We consider the generalized assignment problem (GAP) with min-max regret criterion under interval costs. This problem models many real-world applications in which jobs must be assigned to agents but the costs of assignment may vary after the decision has been taken. We computationally examine two heuristic methods: a fixed-scenario approach and a dual substitution algorithm. We also examine exact algorithmic approaches (Benders-like decomposition and branch-and-cut) and further introduce a more sophisticated algorithm that incorporates various methodologies, including Lagrangian relaxation and variable fixing. The resulting Lagrangian-based branch-and-cut algorithm performs satisfactorily on benchmark instances.

Applying Algorithm Selection – a Case Study for the Generalised Assignment Problem

Many combinatorial optimisation problems are NP-Hard. Yet in practice high quality solutions are often obtained by (meta)heuristics. These work well in some cases, but not in others, indicating a potential for algorithm selection. In this extended abstract is discussed how to apply algorithm selection to a combinatorial optimisation problem and which challenges arise when doing so. The generalised assignment problem is used as case study.

An Energy-Efficient Multiobjective Scheduling Model for Monitoring in Internet of Things

To ensure robustness in wireless networks, monitoring the network state, performance and functioning of the nodes and links is crucial, especially for critical applications. This paper targets Internet of Things (IoT) networks. In the IoT, devices (things) are vulnerable due to security risks from the Internet. Moreover, they are resource-constrained and connected via lossy links. This paper addresses the optimized scheduling of the monitoring role between the embedded devices in IoT networks. The objective is to minimize energy consumption and communication overhead of monitoring, for each node. Several subsets of the potential monitoring nodes are generated by solving a minimal vertex cover (VC) problem with constraint generation. Assuming periodical functioning, VCs are optimally assigned to time periods in order to distribute the monitoring role throughout the entire network. The assignment of VCs to periods is modeled as a multiobjective generalized assignment problem. To further optimize the energy consumption of the monitors, they are sequenced across time periods to minimize the state transitions of nodes. This part of the problem is modeled as a traveling salesman path problem. The proposed model is tested on randomly generated instances and the experimental results illustrate its effectiveness to optimize the scheduled monitoring for fault tolerance in IoT networks.

Flexible allocation on related machines with assignment restrictions

We introduce the problem of Flexible Allocation on Related Machines with Assignment Restrictions (FARM). In this problem the input consists of a set of machines and a set of jobs. Each machine has a finite capacity, and each job has a resource requirement interval, a profit per allocated unit of resource, and a set of machines that can potentially supply the requirement. A feasible solution is an allocation of machine resources to jobs such that: (i) a machine resource can be allocated to a job only if it is a potential supplier of this job, (ii) the amount of machine resources allocated by a machine is bounded by its capacity, and (iii) the amount of resources that are allocated to a job is either in its requirement interval or zero. Notice that a job can be serviced by multiple machines. The goal is to find a feasible allocation that maximizes the overall profit. We focus on r- FARM in which the required resource of a job is at most an r-fraction of (or r times) the capacity of each potential machine, for some r≥0. FARM is motivated by resource allocation problems arising in cellular networks and in cloud computing. Specifically, FARM models the problem of assigning clients to base stations in 4G cellular networks. We present a 2-approximation algorithm for 1- FARM and a 11−r-approximation algorithm for r-FARM, for any r∈(0,1). Both are based on the local ratio technique and on maximum flow computations. We observe that an LP-rounding 2-approximation algorithm for the Generalized Assignment Problem also applies to 1-FARM. Finally, we give an Ω(rlogr) lower bound on the approximation ratio for r-FARM (assuming P≠NP).

Optimized assignment patterns in Mobile Edge Cloud networks

Given an existing Mobile Edge Cloud (MEC) network including virtualization facilities of limited capacity, and a set of mobile Access Points (AP) whose data traffic demand changes over time, we aim at finding plans for assigning APs traffic to MEC facilities so that the demand of each AP is satisfied and MEC facility capacities are not exceeded, yielding high level of service to the users. Since demands are dynamic we allow each AP to be assigned to different MEC facilities at different points in time, accounting for suitable switching costs. We propose a general data-driven framework for our application including an optimization core, a data pre-processing module, and a validation module to test plans accuracy. Our optimization core entails a combinatorial problem that is a multi-period variant of the Generalized Assignment Problem: we design a Branch-and-Price algorithm that, although exact in nature, performs well also as a matheuristics when combined with early stopping. Extensive experiments on both synthetic and real-world datasets demonstrate that our approach is both computationally effective and accurate when employed for prescriptive analytics.

A new approximation technique for resource‐allocation problems

We develop a rounding method based on random walks in polytopes, which leads to improved approximation algorithms and integrality gaps for several assignment problems that arise in resource allocation and scheduling. In particular, it generalizes the work of Shmoys and Tardos on the generalized assignment problem to the setting where some jobs can be dropped. New concentration bounds for random bipartite matching are developed as well.

The parking allocation problem for connected vehicles

In this paper, we propose a parking allocation model that takes into account the basic constraints and objectives of a problem where parking lots are assigned to vehicles. We assume vehicles are connected and can exchange information with a central intelligence. Vehicle arrival times can be provided by a GPS device, and the estimated number of available parking slots, at each future time moment and for each parking lot is used as an input. Our initial model is static and may be viewed as a variant of the generalized assignment problem. However, the model can be rerun, and the algorithm can handle dynamic changes by frequently solving the static model, each time producing an updated solution. In practice this approach is feasible only if reliable quality solutions of the static model are obtained within a few seconds since the GPS can continuously provide new input regarding the vehicle’s positioning and its destinations. We propose a 0–1 programming model to compute exact solutions, together with a variable neighborhood search-based heuristic to obtain approximate solutions for larger instances. Computational results on randomly generated instances are provided to evaluate the performance of the proposed approaches.

A hybrid heuristic algorithm for the sequencing generalized assignment problem in an assembly line

The generalized assignment problem (GAP) is an enlarged version of the classical assignment problem in which the assignment of several tasks to an agent is possible. The only restriction that can limit the assignment of the tasks to the agents is the capacity of the agent. In this study, a manpower planning is modeled as a GAP in an assembly line. The considered assembly line consists of a number of workstations in series where each workstation contains several jobs in parallel. The present research seeks to assign the best operator to the jobs in order to minimize the processing time in each workstation and in the whole of the system. The generalized assignment formulation is adapted to this case. A mixed-integer mathematical model is proposed for this problem and proved that the considered problem is NP-complete. The model is solved in various sizes by employing Gurobi mixed-integer solver. This paper presents a greedy heuristic combined with a local search for the generalized assignment problem. The slight deviation from the optimal solutions and the computational times which is extremely reduced, validate the efficiency of the proposed heuristic approach for solving such problems.

A hybrid particle swarm optimization for the generalized assignment problem with time window

This study focuses on the inbound logistics of the sugarcane industry, which has three main procedures consisting of cultivation, harvest and transportation. Generally, small-scale growers cannot manage all of the procedures effectively, because of their lack of bargaining power and inadequate equipment. For this reason a resource-sharing policy, such as harvester and truck sharing, is used by factories to reduce the cost of the sugarcane harvest, and increase harvester and truck utilization. To solve the generalized assignment problem (GAP) with time window, thus minimizing the total cost from the assignment of the third-party logistics providers to service small-scale growers under capacity and time limitations, a mathematical model has been developed for small-sized problems. For large-scale problems, particle swarm optimization (PSO) is applied and improved by the hybridization of PSO with k-cyclic moves algorithm (PSOK). The results demonstrate that the proposed metaheuristics can solve the problem efficiently since the results are equal to, or close to, the optimal solutions in which the averaged performances of PSO and PSOK are 99.61% and 99.64%, respectively and the averaged relative improvement is 0.1519%.

A Structural Approach to State-to-Output Decoupling

In this paper, we address a general eigenstructure assignment problem where the objective is to distribute the closed-loop modes over the components of the system outputs in such a way that if a certain mode appears in a given output, it is unobservable from any of the other output components. By combining classical geometric control results with the theory of combinatorics, we provide necessary and sufficient conditions for the solvability of this problem, herein referred to as state-to-output decoupling, under very mild assumptions. We propose solvability conditions expressed in terms of the dimensions of suitably defined controlled invariant subspaces of the system. In this way, the solvability of the problem can be evaluated a priori, in the sense that it is given in terms of the problem/system data. The proposed approach is constructive, so that when a controller that solves the problem indeed exists, it can be computed by using the machinery developed in this paper.

Productivity improvement through a sequencing generalised assignment in an assembly line system

This paper considers the assignment of heterogeneous workers to workstations of an assembly line in order to minimise the total production time. As the structure of the system implies that each of the workstations needs at least one worker, thus the problem can be considered as a generalised assignment problem (GAP). The objective is to perform an efficient human resource planning for a specified horizon consisting of several periods. Hence, we present an extension of the generalised assignment problem, consisting of a set of GAPs (one for each planning period) in which each GAP depends on the previous ones. A mixed integer mathematical model is presented for this sequencing assignment problem. The model is solved by an exact algorithm using Gurobi solver. It is proved that the problem is NP-hard and solving the medium and large size instances is not possible by the exact algorithms. Hence, two matheuristic approaches based on the disaggregated formulation of GAP are proposed. The first approach solves the problem through two sub-problems as the transportation formulation and assignment formulation. The second approach solves the problem by decomposition of the problem into several classical GAPs. The approaches are examined by a total of 27 instances. The results illustrate the efficiency of the proposed algorithms in the computational time and accuracy of the solutions.

Online assignment of non-SDN virtual network nodes to a physical SDN

Network virtualization is a promising solution to increase utilization of communication resources in data center networks. On the other side, software defined networks (SDNs) gather great attention from industry and academia to be used as the networking solution for data centers. Virtualizing SDNs and providing suitable virtual network embedding (VNE) techniques, paves the path for designing highly configurable virtualized cloud data centers. Considering the challenges which are arisen by using the SDNs as the substrate network for hosting non-SDN virtual networks, it is desired to develop an online VNE technique with a bounded competitive ratio as well as polynomial execution time in terms of problem size. To achieve this goal, this work is a primary step which solves the embedding problem with releasing the capacity constraints of physical network links. So, to the best of our knowledge, the problem of online virtual node assignment to physical nodes of SDNs with limited capacity of in-node and on-controller processing powers is presented for the first time in this work. Furthermore an online mapping algorithm is provided for the mentioned problem with poly-logarithmic competitive ratio. This can be considered as an online algorithm for general node assignment problem with batch arrivals of the requests and also can be used as a solution for online virtual machine allocation problem with batch arrivals of the requests.

Solution of a class of generalized assignment problem

Solution of a class of generalized assignment problem

Towards optimal solutions for the low power hard real-time task allocation on multiple heterogeneous processors

The usage of heterogeneous multicore platforms is appealing for applications, e.g. hard real-time systems, due to the potential reduced energy consumption offered by such platforms. However, even in such platforms the power wall phenomena still imposes limits to performance. Hard real-time systems are part of life critical environments and reducing the energy consumption on such systems is an onerous and complex process. We tackle the problem from the perspective of different representative integer programming mathematical formulations and their interplay on the search for optimal solutions for Rate Monotonic (RM) and Earliest Deadline First (EDF) scheduling algorithms. The proposed models are based on a well-established formulation in the operational research literature, namely, the Multilevel Generalized Assignment Problem (MGAP). This paper, therefore, assesses the problem of finding optimal allocations and frequency assignments of hard real-time tasks among heterogeneous processors targeting low power consumption, but taking into account timing constraints. Computational experiments show that finding optimal solutions reduces the estimated energy consumption of the evaluated cases when compared to state-of-the-art algorithms. • Representative theoretical models of several hard real-time scheduling policies. • New application of well-known classical combinatorial optimization problem: MGAP. • Applicability on embedded systems with low power and hard real-time requirements. • Optimal workload partitioning on heterogeneous processors in project time. • Computational experiments on finding optimal solutions for the proposed models.