Time Optimal Algorithm Research Articles

An Automated Comparative Observation System for Sun-Induced Chlorophyll Fluorescence of Vegetation Canopies.

Detecting sun-induced chlorophyll fluorescence (SIF) offers a new approach for remote sensing photosynthesis. However, to analyse the response characteristics of SIF under different stress states, a long-term time-series comparative observation of vegetation under different stress states must be carried out at the canopy scale, such that the similarities and differences in SIF change law can be summarized under different time scales. A continuous comparative observation system for vegetation canopy SIF is designed in this study. The system, which is based on a high-resolution spectrometer and an optical multiplexer, can achieve comparative observation of multiple targets. To simultaneously measure the commonly used vegetation index and SIF in the O2-A and O2-B atmospheric absorption bands, the following parameters are used: a spectral range of 475.9 to 862.2 nm, a spectral resolution of approximately 0.9 nm, a spectral sampling interval of approximately 0.4 nm, and the signal-to-noise ratio (SNR) can be as high as 1000:1. To obtain data for both the upward radiance of the vegetation canopy and downward irradiance data with a high SNR in relatively short time intervals, the single-step integration time optimization algorithm is proposed. To optimize the extraction accuracy of SIF, the FluorMOD model is used to simulate sets of data according to the spectral resolution, spectral sampling interval and SNR of the spectrometer in this continuous observation system. These data sets are used to determine the best parameters of Fraunhofer Line Depth (FLD), Three FLD (3FLD) and the spectral fitting method (SFM), and 3FLD and SFM are confirmed to be suitable for extracting SIF from the spectral measurements. This system has been used to observe the SIF values in O2-A and O2-B absorption bands and some commonly used vegetation index from sweet potato and bare land, the result of which shows: (1) the daily variation trend of SIF value of sweet potato leaves is basically same as that of photosynthetically active radiation (PAR); and (2) the bare land is a non-fluorescent emitter, the SIF of which is significantly smaller than that of sweet potato; and (3) analysis result based on the measured data is basically same as that based on simulated data. The above results verified the reliability of the SIF extracted from the measured data and the feasibility of comparatively observing the SIF value and the commonly used vegetation index of multiple vegetation canopy with this continuous observation system. This approach is beneficial for comprehensively analysing the stress response characteristics of vegetation canopies.

Reference trajectory tuning of model predictive control

An approach to minimize tuning effort of nominal Model Predictive Control algorithms is proposed. The algorithm dynamically calculates output set points to accommodate user-defined output importance, which is more intuitive than selecting values for the MPC weighing matrices. Instead of tuning the weights on the outputs deviations from their set points, weights on the input values and input increments, which are the usual tuning parameters of MPC, the desired output control performance of the MPC can be specified by performance factors. The proposed method extends the existing methods that consider a reference trajectory for the output tracking to the case of zone control and input targets. The proposed method also assumes that, as in most commercial MPC packages, the controller has two layers: a static layer and an extended dynamic layer. The method is illustrated by three case studies, contemplating both SISO and MIMO systems. It is observed that: the output set point tracking performance can be changed without modifying the MPC tuning weights, the approach is capable of achieving similar performance to conventional MPC tuned by multiobjective optimization techniques from the literature, with a fraction of computer effort, and it can be integrated with Real Time Optimization algorithms to control complex systems, always respecting output constraints.

An almost optimal algorithm for Voronoi diagrams of non-disjoint line segments

This paper presents an almost optimal algorithm that computes the Voronoi diagram of a set S of n line segments that may intersect or cross each other. If there are k intersections among the input segments in S, our algorithm takes O(nα(n)log⁡n+k) time, where α(⋅) denotes the inverse of the Ackermann function. The best known running time prior to this work was O((n+k)log⁡n). Since the lower bound of the problem is shown to be Ω(nlog⁡n+k) in the worst case, our algorithm is worst-case optimal for k=Ω(nα(n)log⁡n), and is only a factor of α(n) away from any optimal-time algorithm, which is still unknown. For the purpose, we also present an improved algorithm that computes the medial axis or the Voronoi diagram of a polygon with holes.

Synchronous counting and computational algorithm design

Consider a complete communication network on n nodes. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are “odd” and which are “even”. Furthermore, the solution needs to be self-stabilising (reaching correct operation from any initial state) and tolerate f Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms either require a source of random bits or a large number of states per node. In this work, we give fast state-optimal deterministic algorithms for the first non-trivial case f=1. To obtain these algorithms, we develop and evaluate two different techniques for algorithm synthesis. Both are based on casting the synthesis problem as a propositional satisfiability (SAT) problem; a direct encoding is efficient for synthesising time-optimal algorithms, while an approach based on counter-example guided abstraction refinement discovers non-optimal algorithms quickly.

Tight bound on mobile Byzantine Agreement

This paper investigates the problem of Byzantine Agreement in a synchronous system where malicious agents can move from process to process, corrupting their host. Earlier works on the problem are based on biased models which, as we argue in the paper, give an unfair advantage either to the correct processes or to the adversary controlling the malicious agents. Indeed, earlier studies of the problem assume that, after a malicious agent has left a process, that process, said to be cured, is able to instantly and accurately detect the fact that it was corrupted in earlier rounds, and thus can take local actions to recover a valid state (Garay's model). We found no justification for that assumption which clearly favors correct processes. Under that model, an algorithm is known for n>4t, where n is the number of processes and t the maximum number of malicious agents. The tightness of the bound is however unknown. In contrast, more recent works on the problem remove the assumption on detection and assume instead that a malicious agent may have left corrupted messages in the send queue of a cured process in addition to a corrupted state. As a result, the adversary controlling the malicious agents can corrupt the messages sent by cured processes, in addition to those sent by the newly corrupted ones, thus doubling the number of effective faults. Under that model, which favors the malicious agents, the problem can be solved if and only if n>6t. In this paper, we refine the latter model to avoid the above biases. While a cured process may send messages (based on a state corrupted by the malicious agent), it will behave correctly in the way it sends those messages: i.e., send messages according to the algorithm. Surprisingly, in this model we could derive a new non-trivial tight bound for Byzantine Agreement. We prove that at least 5t+1 processors are needed in order to tolerate t mobile Byzantine agents and provide a time optimal algorithm that matches this lower bound, altogether with a formal specification of the problem.

A speed and departure time optimization algorithm for the pollution-routing problem

We propose a new speed and departure time optimization algorithm for the pollution-routing problem (PRP), which runs in quadratic time and returns an optimal schedule. This algorithm is embedded into an iterated local search-based metaheuristic to achieve a combined speed, scheduling and routing optimization. The start of the working day is set as a decision variable for individual routes, thus enabling a better assignment of human resources to required demands. Some routes that were evaluated as unprofitable can now appear as viable candidates later in the day, leading to a larger search space and further opportunities of distance optimization via better service consolidation. Extensive computational experiments on available PRP benchmark instances demonstrate the good performance of the algorithm. The flexible departure times from the depot contribute to reduce the operational costs by 8.36% on the considered instances.

Optimal three-level presort loading of commercial bulk mail in the postal service industry

This study focuses on the presort loading of commercial bulk mail. Here, presort is the process by which a mailer prepares mail such that it is sorted to at least the finest extent required by the postal service provider for a claimed (discounted) price. We formulated this presort loading problem (PLP) as a special case of transportation problem with minimum quantity commitment (MQC) constraints. In addition, we developed a polynomial time optimal solution algorithm for the PLP and performed computational experiments on randomly generated problem instances under various discount structures. Results of the computational experiments show that mailers can potentially reduce their costs by sending mail less frequently, using small-sized mail trays; however, the discount structure does not affect the main results. There is some evidence that smaller cost reductions on mailing fees occur as the variation in the discount rate increases; however, the effects of discount structure are nominal compared with the gains from changing the mailing frequency. Mailing fee savings are more heavily influenced by the discount structure when MQC constraints become tighter.

On the equivalence of single machine earliness/tardiness problems with job rejection

We present optimal algorithms for single-machine scheduling problems with earliness criteria and job rejection and compare them with the algorithms for the corresponding problems with tardiness objectives. We present an optimal O(nlogn) algorithm for minimizing the maximum earliness on a single machine with job rejection. Our algorithm also solves the bi-criteria scheduling problem is which the objective is to simultaneously minimize the maximum earliness of the scheduled jobs and the total rejection cost of the rejected jobs. We also show that the optimal pseudo-polynomial time algorithm for the total tardiness problem with job rejection can be used to solve the corresponding total earliness problem with job rejection.

Optimal Channel Allocation for Multi-PU and Multi-SU Pairs in Underlay Cognitive Radio Networks

In the underlay cognitive radio networks, this paper defines the joint channel and power allocation problem, which aims to optimise the max-total and max-min throughputs of secondary users (SUs), with the constraints of interference on primary receivers. For the max-total problem, we formulate the problem as a bipartite matching and derive a maximum weighted matching-based sum throughput maximisation algorithm (STMA) to solve this problem. For the max-min problem, on the basis of the optimal relay assignment (ORA) algorithm, we derive a polynomial time optimal channel assignment algorithm (OCAA) to iteratively assign channels to each SU pair under the power constraint. Simulation results demonstrate the effectiveness of our algorithms when compared with random method.

Single machine batch scheduling problem to minimize makespan with controllable setup and jobs processing times

This paper concerns with a single-machine scheduling problem underbatch availability in which both the setup of each batch and the processing times of jobs are controllable by allocating a resource. The completion time ofa job in a batch is that of the last job in the batch. Two batchscheduling problems are investigated. The objective is todetermine the job sequence, the partition of the job sequence intobatches and the resource allocation scheme to minimize makespan,subject to the total amount of resource is bounded by a givenvalue $U$ in the first problem; while in the second problem is tominimize a total cost of makespan and resource without resourcelimitation, respectively. We show that the problems underlying canbe solved in polynomial time and present optimal algorithms.

Single machine total completion time scheduling problem with workload-dependent maintenance duration

A single-machine scheduling problem with workload-dependent maintenance duration is considered. The objective is to minimize total completion time. For the case where the derivation of the maintenance duration function is greater than or equal to 1, a polynomial time optimal algorithm is proposed. For the case where the derivation of the maintenance duration function is less than 1, a polynomial time approximation scheme is proposed.

Network protection with multiple availability guarantees

This paper develops a novel network protection scheme that provides guarantees on both the fraction of time a flow has full connectivity, as well as a quantifiable minimum grade of service during downtimes. In particular, a flow can be below the full demand for at most a maximum fraction of time; if after a network failure the flow is below its full demand, it must still support at least a fraction q of that demand. This is in contrast to current protection schemes that offer either availability-guarantees with no bandwidth guarantees during the downtime, or full protection schemes that offer 100% availability after a single link failure.We show that the multiple availability guaranteed problem is NP-Hard, and develop an optimal solution in the form of an MILP. If a connection is allowed to drop to 50% of its bandwidth for just 1 out of every 20 failures, then a 24% reduction in spare capacity can be achieved over traditional full protection schemes. Allowing for more frequent drops to partial flow, additional savings can be achieved. Algorithms are developed to provision resources for connections that provide multiple availability guarantees for both the sharing and non-sharing case. For the case of q=0, corresponding to the standard availability constraint, an optimal pseudo-polynomial time algorithm is presented.

Fuzzy joint points based clustering algorithms for large data sets

The fuzzy joint points (FJP) method is one of the successful fuzzy approaches to density-based clustering. Besides the basic FJP method, there are other methods based on the FJP approach such as, Noise-Robust FJP (NRFJP), and Fuzzy Neighborhood DBSCAN (FN-DBSCAN). These FJP-based methods suffer from the low speed of the FJP algorithm, thus applications that deal with large databases cannot benefit from them. The Modified FJP (MFJP) method addresses this issue and achieves an improvement in speed, but it is not satisfactory from the point of applicability. In this work, we integrate various methods with FJP to establish an optimal-time algorithm. An even faster algorithm which uses the FJP approach in a somewhat supervised fashion is also proposed. Along with theoretic comparison, experimental results are presented to show the significant speed improvement, which will allow the FJP-based methods to be used on large data sets.

An optimal algorithm for computing all subtree repeats in trees.

Given a labelled tree T, our goal is to group repeating subtrees of T into equivalence classes with respect to their topologies and the node labels. We present an explicit, simple and time-optimal algorithm for solving this problem for unrooted unordered labelled trees and show that the running time of our method is linear with respect to the size of T. By unordered, we mean that the order of the adjacent nodes (children/neighbours) of any node of T is irrelevant. An unrooted tree T does not have a node that is designated as root and can also be referred to as an undirected tree. We show how the presented algorithm can easily be modified to operate on trees that do not satisfy some or any of the aforementioned assumptions on the tree structure; for instance, how it can be applied to rooted, ordered or unlabelled trees.

Design and Implementation of High-Performance Real-Time Free-Form NURBS Interpolator in Micro CNC Machine Tool

This paper provides a suitable methodology to implement a high-performance and precise NURBS interpolator considering machine dynamics. The NURBS tool path curve is realized in real time by mapping the feedrate with a cubic curve with respect to time satisfying the machine dynamics and chord error. This is done by analyzing the feedrate profile offline and scheduling it with respect to time using a time optimal jerk limited algorithm. The proposed and the conventional NURBS interpolators are implemented in a three axis micro machine tool and the machining performance with respect to surface finish at different feedrates is compared. It is found that the feedrate profile obtained using the proposed interpolator scheme results in improved surface finish. Experimental evidences regarding the improvement in surface finish using a NURBS interpolator are shown for the first time according the authors knowledge. The proposed interpolator is designed with flexibility so that it can be implemented in all types of conventional CNC 3 axis machines also.

The Integration of Supply Chain under the Environment of E-Commerce Based on the Deteriorating Inventory Model

As the industrial environment becomes more competitive, supply chain management has become essential. The objective of this research is to develop a multi-echelon inventory model for a deteriorating item and to derive an optimal joint total cost. Inventory models for the manufacturer and the retailer were developed when deteriorating rates were constant, and demand rate of customer decreased linearly with time and depended on retailers’ current inventory level. The objective was to develop an optimal ordering strategy for retailers to minimize the average total cost of this inventory system. This paper establishes an inventory model of manufacturers and retailers, and gives the optimal production time algorithm. Then, we will carry out simulation test for example. We calculate the system of minimum average total cost that respectively from producers, retailers and integration. Thus, it confirms that the average total cost which from the supply chain integration is lower than from the manufacturer or retailer alone.

Rescheduling for machine disruption to minimize makespan and maximum lateness

We consider a scheduling problem where a set of jobs has already been scheduled to minimize some cost objective on a single machine when the machine becomes unavailable for a period of time. The decision-maker needs to reschedule the jobs without excessively disrupting the original schedule. The disruption is measured as the maximum time deviation, for any given job, between the original and new schedules. We examine a general model where the maximum time disruption appears both as a constraint and as part of the cost objective. For a scheduling cost modeled as the makespan or maximum lateness, we provide a pseudopolynomial time optimal algorithm, a constant factor approximation algorithm, and a fully polynomial time approximation scheme. The approximation algorithm has an asymptotically achievable worst-case performance ratio of 2 and has average performance close to optimal. Managerial insights are given on how scheduling costs are affected by machine disruption and the approximation algorithm.

A Multicriteria Dial‐a‐Ride Problem with an Ecological Measure and Heterogeneous Vehicles

ABSTRACTThe Dial‐a‐Ride Problem is a complex combinatorial optimization problem with many real‐world applications in transportation of persons. It consists in routing a fleet of vehicles based at a common depot in order to satisfy users' transportation requests. Each request may consist, in a number of persons, a specified pickup location, a destination location, desired departure and arrival time windows. In this paper, we investigate a new and general model for the transportation of persons. It involves three objective functions that have to be optimized in order to measure the potential efficiency of the Dial‐a‐Ride Problem solution on different aspects: the cost for the transportation operator, the quality of service for users and the impact on the environment. For an efficient search through the solution space, we use a multiobjective genetic algorithm, which allows us to identify a good approximation of the set of Pareto optimal solutions. Among this set of solutions, the decision‐maker can select the solution with best compromise according to its preferences, without introducing a priori information about these ones. The proposed genetic algorithm is based on an optimal timing algorithm that computes pickup and delivery dates when the requests are sequenced on the vehicles. Copyright © 2014 John Wiley & Sons, Ltd.

Blockers and antiblockers of stable matchings

An implicit linear description of the stable matching polytope is provided in terms of the blocker and antiblocker sets of constraints of the matroid-kernel polytope. The explicit identification of both these sets is based on a partition of the stable pairs in which each agent participates. Here, we expose the relation of such a partition to rotations. We provide a time-optimal algorithm for obtaining such a partition and establish some new related results; most importantly, that this partition is unique.

Time optimal control of one and double one winding VCM motor

Abstract This article presents the time optimal control system adopted to control double winding VCM motor. This kind of control is widely used in hard disk drive servo for head positioning. Mathematical model of double winding VCM motor is presented, and its implementation in MATLAB/Simulink is shown. The extended time optimal control algorithm is implemented on dSpace DS1104 board. The results obtained from simulation and real measurements are compared and discussed