Non-crossing Constraints Research Articles

A generalized classification scheme for crane scheduling with interference

Nowadays, many industries rely on cranes for efficiently executing storage and retrieval operations of goods. Areas of application are, for instance, container logistics in seaports and warehousing operations in automated storage and retrieval systems. Therefore, it is not astounding that plenty scientific papers on crane scheduling in many different yet closely related logistics settings have accumulated. In many of these problems, crane interference occurs. A prominent example is non-crossing constraints where cranes share a common pathway and cannot overtake each other. In order to structure this vast field of research, this paper provides a classification scheme for crane scheduling problems with crane interference. We apply this scheme to classify the existing literature, to determine the status-quo of complexity results, and to identify future research needs.

Disentanglement of Two Single Polymer Chains: Contacts and Knots.

Understanding the consequences of the noncrossing constraint is one of the remaining challenges in the physics of walks and polymers. To address this problem, we performed molecular simulations for the separation of only two initially connected, overlapping polymer chains with interactions tuned such that they are nearly random walks. The separation time for a configuration strongly correlates with the number of monomer contacts between both chains. We obtain a broad distribution of separation times with a slowly decaying tail. Knots only play a role for those configurations that contribute to the tail of the distribution. In contrast, when starting from the same initial configuration but allowing for chain crossings, separation is qualitatively faster and the time distribution narrow. The simulation results are rationalized by analytical theory. A theory of contacts based on polymer fractality and criticality is presented, along with the expected effects of knots.

Approximation algorithm for uniform quay crane scheduling at container ports

At a container port, container vessels are served by quay cranes for loading and unloading containers. Each vessel is typically split into bays from head to tail where containers are stored. Parallel quay cranes can process different bays simultaneously, and their processing efficiency significantly affects the turn-around time of a container vessel. Sharing a single traveling rail, the quay cranes cannot crossover each other, and this phenomenon is referred as the non-crossing constraint. In addition, the quay cranes may have different processing speeds due to gradual equipment updates. Inspired by updating activities of cranes in modern container terminals, this paper studies a scheduling problem with two uniform quay cranes, aiming at minimizing the turn-around time of a vessel, i.e., the makespan. We mainly develop an integrated approximation algorithm which is [Formula: see text]-approximation, where the two quay cranes are of processing speeds 1 and [Formula: see text], respectively.

Cooperative twin-crane scheduling

This paper treats the crane scheduling in a container port where two cooperative gantry cranes (denoted as twin cranes) jointly store import containers arriving from the seaside in a storage yard. We aim to minimize the makespan while non-crossing constraints among cranes need to be considered and preemptive container moves are allowed, i.e., the seaside crane sets down a container in some intermediate position where the landside crane takes over and delivers the container to its final storage position in the yard. Elementary complexity proofs are provided and efficient heuristic solution procedures are introduced and tested.

Genetic Algorithm for Integrated Models of Continuous Berth Allocation Problem and Quay Crane Scheduling with Non Crossing Constraint

Background/Objectives: This paper focused on integrated Continuous Berth Allocation Problem (BAPC) and Quay Crane Scheduling Problem (QCSP) by considering non-crossing constraint to make it more realistic. Methods/Statistical analysis: Genetic Algorithm (GA) is a metaheuristic method that has been used extensively in Berth Allocation Problem (BAP). Crossover and mutation are selected as operators in this paper. Findings: The integrated model is formulated as a Mix Integer Problem (MIP) with the objective to minimize the sum of the processing times. A vessel's processing time is measured between arrival and departure includingwaiting time to be berthed and servicing time.The new algorithm of GA arecompatible with the integrated model and useful for finding near-optimal solutions. Three phase new algorithms of GA are proposed and provide a wider search to the solution space. Application/Improvements: Three phase of GA is another significant and promising variant of genetic algorithms in BAPC and QCSP. The probabilities of crossover and mutation determine the degree of solution accuracy and the convergence speed that GA canobtain. By using fixed values of crossover and mutation, the algorithm utilize the population information in each generation and adaptively adjust the crossover and mutation. So, the population diversity and sustain the convergence capacity is maintained.

Scheduling Multiple Yard Cranes with Crane Interference and Safety Distance Requirement

Container terminals require robust scheduling algorithms for yard cranes to optimally determine the sequence of storage and retrieval operations in yard blocks for higher container terminal performance. This paper investigates the multiple yard crane scheduling problem within a generic yard block and considers the operational restrictions such as the crane noncrossing constraint and models the crane travel time realistically. Further, the fact that any two adjacent cranes must keep an operational safety distance is also taken into consideration. These physical constraints limit the mobility of yard cranes and greatly render the scheduling difficulty for such pieces of equipment. This paper proposes a clustering-reassigning approach, which fully considers all of the operational constraints in practice. The complexity of the approach is o(n3), where n is the number of container moves to be scheduled, making it suitable for real-time scheduling. Numerical experiments and benchmark with a continuous time-based mixed-integer linear programming model indicate that the clustering-reassigning approach can provide satisfactory near optimal solutions for different sets of test cases in a real-time scheduling context.

Non-crossing weighted kernel quantile regression with right censored data.

Regarding survival data analysis in regression modeling, multiple conditional quantiles are useful summary statistics to assess covariate effects on survival times. In this study, we consider an estimation problem of multiple nonlinear quantile functions with right censored survival data. To account for censoring in estimating a nonlinear quantile function, weighted kernel quantile regression (WKQR) has been developed by using the kernel trick and inverse-censoring-probability weights. However, the individually estimated quantile functions based on the WKQR often cross each other and consequently violate the basic properties of quantiles. To avoid this problem of quantile crossing, we propose the non-crossing weighted kernel quantile regression (NWKQR), which estimates multiple nonlinear conditional quantile functions simultaneously by enforcing the non-crossing constraints on kernel coefficients. The numerical results are presented to demonstrate the competitive performance of the proposed NWKQR over the WKQR.

A decomposition heuristic for the twin robots scheduling problem

AbstractThis article provides an efficient heuristic based on decomposition for the twin robots scheduling problem (TRSP). TRSP concerns two moving robots executing storage and retrieval requests in parallel along a shared pathway. The depots are located at both ends of the line and a dedicated robot is assigned to each of them. While moving goods between their respective depots and some storage locations on the line, noncrossing constraints among robots need to be considered. Our heuristic uses a dynamic programming framework to determine the schedule of one robot while keeping the other one's fixed. It finds near‐optimal solutions even for large problem instances with hundreds of jobs in a short time span. © 2014 Wiley Periodicals, Inc. 62:16–22, 2015

A note on a model for quay crane scheduling with non-crossing constraints

This article studies the quay crane scheduling problem with non-crossing constraints, which is an operational problem that arises in container terminals. An enhancement to a mixed integer programming model for the problem is proposed and a new class of valid inequalities is introduced. Computational results show the effectiveness of these enhancements in solving the problem to optimality.

Interactive focus maps using least-squares optimization

We present a new algorithm that enlarges a focus region in a given network map without removing non-focus (i.e., context) network parts from the map or changing the map’s size. In cartography, this problem is usually tackled with fish-eye projections, which, however, introduce severe distortion. Our new algorithm minimizes distortion and, with respect to this objective, produces results of similar quality compared to an existing algorithm. In contrast to the existing algorithm, the new algorithm achieves real-time performance that allows its application in interactive systems. We target applications where a user sets a focus by brushing parts of the network or the focus region is defined as the neighborhood of a moving user.A crucial feature of the algorithm is its capability of avoiding unwanted edge crossings. Basically, we first solve a least-squares optimization problem without constraints for avoiding edge crossings. The solution we find is then used to identify a small set of constraints needed for a crossing-free solution and, beyond this, allows us to start an animation enlarging the focus region before the final, crossing-free solution is found. Moreover, memorizing the non-crossing constraints from an initial run of the algorithm allows us to achieve a better runtime on any further run – assuming that the focus region does not move too much between two consecutive runs. As we show with experiments on real-world data, this enables response times well below 1 second.

One-dimensional vehicle scheduling with a front-end depot and non-crossing constraints

This paper considers the scheduling problem of multiple vehicles executing a given set of jobs in parallel along a shared pathway. The job set consists of storage and retrieval tasks, transporting goods between a front-end depot and given storage locations on the line. Non-crossing constraints need to be applied to the vehicle movements. This problem setting is relevant when a train is loaded with containers by multiple straddle carriers on the landside of a container terminal. Other potential applications exist in multi-shuttle automated storage and retrieval systems and multi-stage production systems where items are transported by parallel hoists. We formalize the problem, analyze its computational complexity, and develop exact and heuristic solution procedures.

Determining crane areas for balancing workload among interfering and noninterfering cranes

AbstractThis article treats the problem of subdividing an area for storing containers such that the workload is evenly shared among the cranes operating the resulting subareas. We consider two crane sets: while noncrossing constraints between cranes of the same set need to be observed, cranes of different sets do not interfere. Such a problem setting is, for instance, relevant for scheduling the (un‐)loading of vessels by parallel quay cranes operating on opposing berths or in container yards with cross‐over cranes. We formalize the resulting optimization problem, prove computational complexity, and present exact and heuristic solution procedures. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012

Quay crane scheduling for an indented berth

This article explores the quay crane scheduling problem at an indented berth. The indented berth is known as an innovative implementation in the container terminals to tackle the challenge from the emergence of more and more mega-containerships. A mixed integer programming model by considering the non-crossing and safety distance constraints is formulated. A Tabu search heuristic is developed to solve the proposed problem. The computational results from this research indicate that the designed Tabu search is an effective method to handle the quay crane scheduling problem at an indented berth.

Simultaneous multiple non-crossing quantile regression estimation using kernel constraints

Quantile regression (QR) is a very useful statistical tool for learning the relationship between the response variable and covariates. For many applications, one often needs to estimate multiple conditional quantile functions of the response variable given covariates. Although one can estimate multiple quantiles separately, it is of great interest to estimate them simultaneously. One advantage of simultaneous estimation is that multiple quantiles can share strength among them to gain better estimation accuracy than individually estimated quantile functions. Another important advantage of joint estimation is the feasibility of incorporating simultaneous non-crossing constraints of QR functions. In this paper, we propose a new kernel-based multiple QR estimation technique, namely simultaneous non-crossing quantile regression (SNQR). We use kernel representations for QR functions and apply constraints on the kernel coefficients to avoid crossing. Both unregularised and regularised SNQR techniques are considered. Asymptotic properties such as asymptotic normality of linear SNQR and oracle properties of the sparse linear SNQR are developed. Our numerical results demonstrate the competitive performance of our SNQR over the original individual QR estimation.

Long Non-crossing Configurations in the Plane

We revisit some maximization problems for geometric networks design under the non-crossing constraint, first studied by Alon, Rajagopalan and Suri (ACM Symposium on Computational Geometry, 1995). Given a set of n points in the plane in general position (no three points collinear), compute a longest non-crossing configuration composed of straight line segments that is: (a) a matching, (b) a Hamiltonian path, and (c) a spanning tree. We obtain some new results for (b) and (c), as well as for the Hamiltonian cycle problem. (i) For the longest non-crossing Hamiltonian path problem, we give an approximation algorithm with ratio $\frac{2}{\pi+1}\approx0.4829$ . The previous best ratio, due to Alon et al., was $\frac{1}{\pi }\approx0.3183$ . The ratio of our algorithm is close to $\frac{2}{\pi}\approx0.6366$ on a relatively broad class of instances: for point sets whose perimeter (or diameter) is much shorter than the maximum length matching. For instance “random” point sets meet the condition with high probability. The algorithm runs in O(n 7/3log n) time. (ii) For the longest non-crossing spanning tree problem, we give an approximation algorithm with ratio 0.502 which runs in O(nlog n) time. The previous ratio, 1/2, due to Alon et al., was achieved by a quadratic time algorithm. Along the way, we first re-derive the result of Alon et al. with a faster algorithm and a very simple analysis. (iii) For the longest non-crossing Hamiltonian cycle problem, we give an approximation algorithm whose ratio is close to 2/π on a relatively broad class of instances: for point sets where the product 〈diameter×convex hull size〉 is much smaller than the maximum length matching. Again “random” point sets meet the condition with high probability. However, this algorithm does not come with a constant approximation guarantee for all instances. The algorithm runs in O(n 7/3log n) time. No previous approximation results were known for this problem.

The crane scheduling problem: models and solution approaches

In this paper, we study the crane scheduling problem for a vessel after the vessel is moored on a terminal and develop both exact and heuristic solution approaches for the problem. For small-sized instances, we develop a time-space network flow formulation with non-crossing constraints for the problem and apply an exact solution approach to obtain an optimal solution. For medium-sized instances, we develop a Lagrangian relaxation approach that allows us to obtain tight lower bounds and near-optimal solutions. For large-sized instances, we develop two heuristics and show that the error bounds of our heuristics are no more than 100%. Finally, we perform computational studies to show the effectiveness of our proposed solution approaches.

An improved approach for quay crane scheduling with non-crossing constraints

Common deficiencies found in previous studies that modelled quay crane scheduling with non-crossing constraints (QCSNC) in port container terminals are identified. Remedies for the problems are proposed to prevent the occurrence of unrealistic optimal solutions for QCSNC. Additionally, two approximation schemes for QCSNC are studied. The first one is called the best partition (BP) method, which can be solved by dynamic programming (DP) with time complexity of 𝒪(mn 2). A more efficient algorithm is designed to improve the original DP by adopting binary search. Next, based on BP and an exact algorithm for QCSNC (with pseudo-polynomial computational time), the second approximation scheme, called the enhanced best partition (EBP) method, is proposed to achieve a better estimation of the optimal makespan for QCSNC. The results of numerical experiments show that EBP is an effective approximation scheme for the problem of QCSNC.

Efficient simulation of noncrossing fibers and chains in a hydrodynamic solvent

An efficient simulation method is presented for Brownian fiber suspensions, which includes both uncrossability of the fibers and hydrodynamic interactions between the fibers mediated by a mesoscopic solvent. To conserve hydrodynamics, collisions between the fibers are treated such that momentum and energy are conserved locally. The choice of simulation parameters is rationalized on the basis of dimensionless numbers expressing the relative strength of different physical processes. The method is applied to suspensions of semiflexible fibers with a contour length equal to the persistence length, and a mesh size to contour length ratio ranging from 0.055 to 0.32. For such fibers the effects of hydrodynamic interactions are observable, but relatively small. The noncrossing constraint, on the other hand, is very important and leads to hindered displacements of the fibers, with an effective tube diameter in agreement with recent theoretical predictions. The simulation technique opens the way to study the effect of viscous effects and hydrodynamic interactions in microrheology experiments where the response of an actively driven probe bead in a fiber suspension is measured.

Minimal distance transformations between links and polymers: principles andexamples

The calculation of Euclidean distance between points is generalized to one-dimensionalobjects such as strings or polymers. Necessary and sufficient conditions for the minimaltransformation between two polymer configurations are derived. Transformations consist ofpiecewise rotations and translations subject to Weierstrass–Erdmann corner conditions.Numerous examples are given for the special cases of one and two links. Thetransition to a large number of links is investigated, where the distance convergesto the polymer length times the mean root square distance (MRSD) betweenpolymer configurations, assuming that curvature and non-crossing constraints can beneglected. Applications of this metric to protein folding are investigated. Potentialapplications are also discussed for structural alignment problems such as pharmacophoreidentification, and inverse kinematic problems in motor learning and control.

On-line scheduling with non-crossing constraints

We consider the problem of on-line scheduling with non-crossing constraints. The objective is to minimize the latest completion time. We provide optimal competitive ratio heuristics for the on-line list and on-line time problems with unit processing times, and a 3-competitive heuristic for the general on-line time problem.