Feasibility Checking Research Articles

Feasibility checking in Horn constraint systems through a reduction based approach

In this paper, we detail a new algorithm for the problem of checking linear and integer feasibility in a system of Horn constraints. For certain special cases, the proposed algorithm is faster than the “Lifting Algorithm” for Horn constraint feasibility described in [2]. Moreover, the new approach is based on different ideas and in fact exploits several properties of Horn constraint systems (HCS) which were heretofore unknown, to the best of our knowledge. In the case of constraints of bounded width (corresponding to “loosely coupled” systems), our algorithm can be modified to run in O(n3+m⋅n+m⋅n2log⁡(max⁡(m,n))) time, where n and m represent the number of variables and the number of constraints respectively, in the input HCS. Our main result establishes that checking the feasibility of an HCS can be reduced to three subproblems: negative-cost cycle detection in networks (NCCD), matrix–vector multiplication (MV), and the conversion of an HCS to a non-redundant set of difference constraints (H2D). The MV problem and the NCCD problem have both been studied extensively, as per the literature and there exist specialized, fast algorithms for the cases that are relevant to feasibility checking in Horn constraint systems. We have identified a new problem, viz., H2D, which warrants future research, since improved algorithms for the H2D problem could be implemented in our algorithm to decrease its running time even further.

Providing Differentiated Services in Multiaccess Systems With and Without Queue State Information

In this paper, we consider one quality-of-service (QoS) criterion, average packet delay (queueing delay plus service time), in a multiaccess system and investigate the basic problem whether a multiaccess system can meet the different average packet delay requirements of all users by combining information theory with queueing theory. Two different cases of the central scheduler with and without queue state information (QSI) are discussed. If the QSI is not available to the central scheduler, we show that static rate allocation policies (SRAPs) can achieve better average packet delay performance than probabilistic rate allocation policies. Based on this conclusion, the delay feasibility checking process reduces to checking whether the required service rate vector lies in the multiaccess capacity region. We find that for users with equal transmit power, only N inequalities are necessary for the checking process, whereas for users with unequal transmit powers, we provide a polynomial-time algorithm for such a decision. Furthermore, if the system cannot satisfy the average packet delay requirements of all users, we prove that as long as the sum power is larger than a threshold, there is always an approach to adjust the transmit powers of different users to satisfy the average packet delay requirements. On the other hand, if the QSI is available to the central scheduler, we propose two dynamic scheduling algorithms to achieve proportional average packet delay and compare their performances with optimal SRAP by simulations.

The impact of core precedences in a cyclic RCPSP with precedence delays

In this paper, we introduce a new kind of constraint, called a core precedence constraint, in a cyclic resource-constrained project scheduling problem (RCPSP) with precedence delays. We show, by an example, which kind of industrial constraints might be modeled by such core precedences in a periodic production setting. We then establish that these constraints can be quite easily added to an integer linear programming formulation of the cyclic RCPSP. Although core precedences seem to be very similar to classical precedence, they can induce infeasibility even without resource constraints. Moreover, we show that the feasibility checking problem is NP-complete in the strong sense, even assuming unit processing times and no resource constraints.

Capacity augmentation with VSM methodology for lean manufacturing

Purpose – The purpose of this study is to enhance the output of a manufacturing set-up in phases, by identifying the wastages in the existing line and, thereby, reducing them. Design/methodology/approach – Feasibility checking and optimization of capacity enhancement of a processing line have been discussed. Value stream mapping (VSM) methodology has been used as a data-driven decision-making tool to identify the constraints in the current state and subsequent states. The future state has been achieved in stages using VSM tool of lean manufacturing, coupled with the management philosophy of Theory of Constraints. An example of an Indian company has been added to demonstrate the suitability of the approach. Findings – The proposed approach addresses an important issue of phased increase in customer demand and the process of accommodating it through multi-phased maneuvering of productive capacity at constraint points instead of enhancing the capacity at one go. The underlying problem of capacity enhancement has been addressed using lean principles and the optimum feasible option has been designed so that the increase in cost is minimized along with satisfying the stepwise increase in demand. Research limitations/implications – This research work is applicable to the manufacturing sector. Originality/value – This paper proposes a methodology for phased upgrading of a production flow-line in keeping with a steady increase in customer demand. Here, VSM has been applied in a phased manner, and the constraint in the current state as well as in each subsequent phase has been identified and removed.

Response time estimation for task chains in destributed realtime systems

A method for estimation of time, requiered for external events processing by distributed program applications is presented. It is shown that feasibility of such applications may depend on variation of task execution time and message delivery time. The influence of this variation shall be taken into account during feasibility checking for task chain, that participate in reaction to concrete separate external events.

An ExpTime Tableau Method for Dealing with Nominals and Qualified Number Restrictions in Deciding the Description Logic SHOQ

We present the first tableau method with an EXPTIME (optimal) complexity for checking satisfiability of a knowledge base in the description logic ${\cal{SHOQ}}$, which extends ${\cal{ALC}}$ with transitive roles, hierarchies of roles, nominals and qualified number restrictions. The complexity is measured using unary representation for numbers (in number restrictions). Our procedure is based on global caching and integer linear feasibility checking.

Hybridization of Bound-and-Decompose and Mixed Integer Feasibility Checking to Measure Redundancy in Structured Linear Systems

Computing the degree of redundancy for structured linear systems is proven to be NP-hard. A linear system whose model matrix is of size n×p is considered structured if some p row vectors in the model matrix are linearly dependent. Bound-and-decompose and 0-1 mixed integer programming (MIP) are two approaches to compute the degree of redundancy, which were previously proposed and compared in the literature. In this paper, first we present an enhanced version of the bound-and-decompose algorithm, which is substantially (up to 30 times) faster than the original version. We then present a novel hybrid algorithm to measure redundancy in structured linear systems. This algorithm uses a 0-1 mixed integer feasibility checking algorithm embedded within a bound-and-decompose framework. Our computational study indicates that this new hybrid approach significantly outperforms the existing algorithms as well as our enhanced version of bound-and-decompose in several instances. We also perform a computational study that shows matrix density has a significant effect on the runtime of the algorithms.

Practical cross‐layer routing and channel assignment in cognitive radio ad hoc networks

AbstractIn the heterogeneous and unreliable channel environment of cognitive radio ad hoc networks (CRAHNs), a multipath route with channel assigned is preferable in both throughput and reliability. The cross‐layer multipath routing and channel assignment in CRAHNs is becoming a challenging issue. In this paper, this problem is characterized, formulated, and shown to be in the form of mixed integer programming. For this Non‐deterministic Polynomial‐time (NP)‐hard problem, the deficiency of the widely used linearization and sequential fixing algorithm is first analyzed. The main contribution of this paper is the development of a new backtracking algorithm with feasibility checking to search optimal solutions and a heuristic algorithm with high feasible solution‐obtained probability (HHFOP) for distributed application in CRAHNs. Through feasibility checking and solution bounds validating, backtracking algorithm with feasibility checking cuts off unnecessary searching space in early stage without loss of optimal solutions, making it much more efficient than brute searching. For practical application in CRAHNs with polynomial complexity, HHFOP first computes the maximal‐supported throughput through link‐channel assignment and link‐capacity coordination for each candidate path. Then the paths are combined, and the route throughput is optimized. Extensive simulation results demonstrate that HHFOP can achieve a high feasible solution‐obtained probability with little throughput degradation compared with linearization and sequential fixing algorithm, indicating its practicability for distributed applications in CRAHNs. Copyright © 2013 John Wiley & Sons, Ltd.

Solving MRCPSP by a Hybrid Genetic Algorithm

In this paper we present a genetic algorithm for the multi-mode resource-constrained project scheduling problem (MRCPSP), in which multiple execution modes are available for each of the activities of the project. To solve the problem, we apply a hybrid genetic algorithm, which makes use of nonrenewable resource feasibility checking procedure, local search based mutation and topological sort procedure. We present detailed computational results for the MRCPSP, which reveal that our procedure is effective in solving the problem.

A dynamic programming-based particle swarm optimization algorithm for an inventory management problem under uncertainty

This article presents a dynamic programming-based particle swarm optimization (DP-based PSO) algorithm for solving an inventory management problem for large-scale construction projects under a fuzzy random environment. By taking into account the purchasing behaviour and strategy under rules of international bidding, a multi-objective fuzzy random dynamic programming model is constructed. To deal with the uncertainties, a hybrid crisp approach is used to transform fuzzy random parameters into fuzzy variables that are subsequently defuzzified by using an expected value operator with optimistic–pessimistic index. The iterative nature of the authors’ model motivates them to develop a DP-based PSO algorithm. More specifically, their approach treats the state variables as hidden parameters. This in turn eliminates many redundant feasibility checks during initialization and particle updates at each iteration. Results and sensitivity analysis are presented to highlight the performance of the authors’ optimization method, which is very effective as compared to the standard PSO algorithm.

Island Configuration for Service Restoration of the Smart Distribution System

sland operation is a special operation mode for service restoration for the smart distribution system with distributed generation. In this paper, a model of island reconfiguration of the smart distribution system is proposed. The objection of this model is maximizing the total power supply profit. Meanwhile, load priority, controllable and uncontrollable load, and the restrictions of power balance, voltage and equipment capability are all taken into account. The island configuration problem is first simplified as a special knapsack problem, and based on the solution of this knapsack problem an initial island scheme is gained. By feasibility checking and adjusting, a island configuration is finally proposed. The results of the samples demonstrate that the model and method presented in this paper is feasible and valid.

2-InterConnected Facility Location: Specification, Complexity, and Exact Solutions

Abstract Connected facility location combines cost-efficient facility placement and the requirement to connect the facilities among each other. Such problems arise, e.g., in telecommunication applications where networks consist of a central core and local clients connected to it. Reliability of the core is a central issue, and we may hence require the core to be at least 2-connected. We establish the problem class of 2-interConnected Facility Location (2-iCFL), categorize its central variants, and prove that they are hard to approximate. However, our computational results show that our orientation-based ILPs allow us to effectively solve such problems to optimality for hundreds of nodes. We also establish constructive characterizations for feasible problem instances, to be used for algorithmic feasibility checks, preprocessing, and heuristics.

Design of hybrid regrouping PSO–GA based sub-optimal networked control system with random packet losses

In this paper, a new approach has been presented to design sub-optimal state feedback regulators over Networked Control Systems (NCS) with random packet losses. The optimal regulator gains, producing guaranteed stability are designed with the nominal discrete time model of a plant using Lyapunov technique which produces a few set of Bilinear Matrix Inequalities (BMIs). In order to reduce the computational complexity of the BMIs, a Genetic Algorithm (GA) based approach coupled with the standard interior point methods for LMIs has been adopted. A Regrouping Particle Swarm Optimization (RegPSO) based method is then employed to optimally choose the weighting matrices for the state feedback regulator design that gets passed through the GA based stability checking criteria i.e. the BMIs. This hybrid optimization methodology put forward in this paper not only reduces the computational difficulty of the feasibility checking condition for optimum stabilizing gain selection but also minimizes other time domain performance criteria like expected value of the set-point tracking error with optimum weight selection based LQR design for the nominal system.

An efficient General Variable Neighborhood Search for large Travelling Salesman Problem with Time Windows

General Variable Neighborhood Search (GVNS) is shown to be a powerful and robust methodology for solving travelling salesman and vehicle routing problems. However, its efficient implementation may play a significant role in solving large size instances. In this paper we suggest new GVNS heuristic for solving Travelling salesman problem with time windows. It uses different set of neighborhoods, new feasibility checking procedure and a more efficient data structure than the recent GVNS method that can be considered as a state-of-the-art heuristic. As a result, our GVNS is much faster and more effective than the previous GVNS. It is able to improve 14 out of 25 best known solutions for large test instances from the literature.

An efficient GVNS for solving Traveling Salesman Problem with Time Windows

Abstract Although GVNS is shown to be powerful and robust method for solving traveling salesman and vehicle routing problems, its efficient implementation may play significant role in solving large size instances. In this paper we suggest new GVNS heuristic for solving TSPTW. It uses more efficient data structure, different neighborhoods, new efficient feasibility checking procedure, for example, than a recent GVNS method [Da Silva, R. F., and S. Urrutia, A General VNS heuristic for the traveling salesman problem with time windows , Discrete Optimization 7 (2010), 203–211.], that may be considered as a state-of-the-art heuristic. As a result, our GVNS is significantly faster than previous GVNS and therefore is able to improve 14 out of 25 best known solutions for large test instances from the literature.

Cautious Operation Planning Under Uncertainties

This paper deals with day-ahead power systems security planning under uncertainties by posing an optimization problem over a set of power injection scenarios that could show up the next day and modeling the next day's real-time control strategies aiming at ensuring security with respect to contingencies by a combination of preventive and corrective controls. We seek to determine whether and which day-ahead decisions must be taken so that, for scenarios over the next day, there still exists an acceptable combination of preventive and corrective controls ensuring system security for any postulated contingency. We formulate this task as a three-stage feasibility checking problem, where the first stage corresponds to day-ahead decisions, the second stage to preventive control actions, and the third stage to corrective post-contingency controls. We propose a solution approach based on the problem decomposition into successive optimal power flow (OPF) and security-constrained optimal power flow (SCOPF) problems of a special type. Our approach is illustrated on the Nordic32 system and on a 1203-bus model of a real-life system.

Feasibility Check of an Assist System Through the Simulation of Bipedal Walking Using a CPG

A wearable mobile-base Walking Assist System (WAS) is simulated in this paper with the bipedal simulator we developed. The simulator employs a Central Pattern Generator (CPG) for bipedal walking pattern generation. The CPG-based walking pattern is one of the candidates for simulating human walking. Average Japanese body dimension data is applied to the bipedal model so that walking efficiency can be evaluated using the simulator. The effectiveness of the proposed simulator is confirmed by comparing real human walking and simulated walking in terms of the shape of the swing leg trajectory, data from the pressure sensor, and the feasibility of the prototype WAS. A prototype is developed and experimental results show the effectiveness of the bipedal simulator.

Non-fragile nonlinear fractional order observer design for a class of nonlinear fractional order systems

This paper deals with the problem of non-fragile observer design for a class of Lipschitz nonlinear fractional order systems. Using continuous frequency distribution, the stability conditions based on indirect approach to Lyapunov stability are derived. A systematic algorithm is presented, which checks for feasibility of a solution to the quadratic inequality and yields an observer whenever the solution is feasible. Finally a chaos synchronization example is provided to show the effectiveness of the proposed method.

Cloud Requirement and Cloud Analysis

Cloud computing is model which uses combine concept of software-as-a-service and œutility computing ,provide convenient and on-demand services to requested end users. Cloud Engineering is a discipline that uses combination of the business and technology thinking for purposes of engineering a cloud. The structure and principles of cloud engineering plays an important role for the engineering of usable and economic cloud. The cloud development life cycle (CDLC) is the one of the component in structure of cloud engineering with Base, Tools & Techniques and Management components. CDLC is the iterated life cycle model for development, deployment and delivery of cloud. CDLC consists of six phases that are flexible, isolated executable and having feedback. The work on this paper focuses on the Understanding Requirement and Analysis phase of the CDLC. This paper lists and discusses the basic, content and operational requirements for the engineering of economic cloud. It also discuses feasibility checks for the requirements. Analysis part of this phase does the analysis of their cloud computing solution with another available computing solution such as grid computing, volunteer computing, utility computing, autonomic computing, client-server model and peer to peer model; and also does cloud planning for cloud implementation phase

Corrective Line Switching With Security Constraints for the Base and Contingency Cases

Following a line outage, the fast corrective operations of transmission line switching might be used to regain N-1 security of the system without generation re-dispatch or load shedding. The problem to find feasible switching operations can be formulated as a constraint satisfaction problem (CSP). Feasibility checking, however, is difficult since changes in load flows caused by line switching operations are discontinuous, and many contingency cases need to be examined. In this paper, DC flow is considered for simplicity, and variables include binary line statuses and continuous phase angles. Security constraints for the base case, N-1, and selected N-2 cases are formulated in a unified way by using a separate set of phase angles for each case. The problem is solved by using constraint programming (CP), and a tree search procedure is developed. Since it is time consuming to handle continuous variables in the tree search, only binary variables are branched on. Once reaching a leaf node where the topology is fixed, the constraints become linear DC flow feasibility conditions and are examined by solving a linear programming problem. Effectiveness of the method is demonstrated on IEEE 30-bus and 118-bus systems.