Non-interference Constraints Research Articles

Integrated scheduling of multiple heterogeneous equipment and maintenance operations during discharging process in a container terminal under uncertainty

The integrated scheduling problem of container-handling equipment has been gaining prestige in recent years instead of decomposing the problem into a succession of subordinate sub-problems. This is due to decreasing operational costs, waiting time, completion time, and increasing efficiency. This study introduces an unprecedented integrated scheduling problem in a container terminal, wherein a broad range of heterogeneous container-handling equipment are considered, including gantry cranes, straddle carriers, transtainers, trailers, and outbound trucks. In this regard, an optimization model is developed for planning the discharging of heterogeneous containers, including storage and clearance, in three distinctive operational yards, including quay, storage, and clearance. Additionally, a wide range of realistic concerns are reflected, including maintenance operations, transport efficiency, and non-interference constraints. Furthermore, since maintenance operations’ times undeniably impact scheduling programming and involve various uncertainties, a new two-stage data-driven approach is offered to estimate reliable maintenance times. In the first stage, a hybrid machine learning approach is devised to estimate maintenance times, including the improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), the Takagi–Sugeno–Kang (TSK) fuzzy system, and the minibatch gradient descent with regularization, DropRule, and AdaBound (MBGD-RDA). In the second stage, since estimated maintenance operation times have uncertainty, the distributionally robust optimization (DRO) method with φ-divergence is utilized to tackle this challenge. Finally, a case study and various simulation experiments are investigated to illustrate the validation and applicability of the suggested framework.

Scalable enforcement of geometric non-interference constraints for gradient-based optimization

Many design optimization problems include constraints to prevent intersection of the geometric shape being optimized with other objects or with domain boundaries. When applying gradient-based optimization to such problems, the constraint function must provide an accurate representation of the domain boundary and be smooth, amenable to numerical differentiation, and fast-to-evaluate for a large number of points. We propose the use of tensor-product B-splines to construct an efficient-to-evaluate level set function that locally approximates the signed distance function for representing geometric non-interference constraints. Adapting ideas from the surface reconstruction methods, we formulate an energy minimization problem to compute the B-spline control points that define the level set function given an oriented point cloud sampled over a geometric shape. Unlike previous explicit non-interference constraint formulations, our method requires an initial setup operation, but results in a more efficient-to-evaluate and scalable representation of geometric non-interference constraints. This paper presents the results of accuracy and scaling studies performed on our formulation. We demonstrate our method by solving a medical robot design optimization problem with non-interference constraints. We achieve constraint evaluation times on the order of 10-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-6}$$\\end{document} seconds per point on a modern desktop workstation, and a maximum on-surface error of less than 1.0% of the minimum bounding box diagonal for all examples studied. Overall, our method provides an effective formulation for non-interference constraint enforcement with high computational efficiency for gradient-based design optimization problems whose solutions require at least hundreds of evaluations of constraints and their derivatives.

Efficient and optimal mechanisms with radio spectrum sharing

Optimal mechanism design with spectrum sharing differs from the traditional setting mainly in that some technological constraints (e.g., non-interference constraints) need to be taken into account explicitly. In this paper we characterize surplus-maximizing (efficient) and revenue-maximizing (optimal) mechanisms in a spectrum sharing context where a principal allocates transmitted power among a group of potentially interested users (transmitter-receiver pairs). Under regularity conditions about value distributions and non-interference constraints, we show that efficiency (optimality) typically involves spectrum sharing by multiple users, and the exact allocation of transmitted power is determined such that the ratio of marginal value (virtual value) over marginal cost (in terms of the cost to the interference generated) is equal among all shared users. We show that efficient and optimal mechanisms in our setting are actually dominant-strategy incentive compatible, and that they can also be implemented by well-designed all-pay or discriminatory-price auctions.

The Quay Crane Scheduling Problem With Stability Constraints

The quay crane scheduling problem (QCSP) is one of the most important problems for the operations at container ports. The QCSP aims to decide a QC schedule for loading and unloading containers so as to minimize the vessel turnaround time. The QCSP is subject to various kinds of constraints, e.g., task precedence constraints and QC noninterference constraints. This paper extends the QCSP by taking into consideration the stability constraints, which are crucial for the safety reason but often omitted in the existing literature. We provide a mathematical model for the QCSP with stability constraints (QCSPSCs). A bicriteria evolutionary algorithm is proposed to solve the QCSPSC. The algorithm consists of a sliding-window heuristic to fix the schedule, which violates the stability constraints. Extensive experiments are conducted to demonstrate the effectiveness of the algorithm. The computational results of the traditional QCSP and the QCSPSC are also compared and analyzed. Note to Practitioners —Stability is a vital factor for the safety of the ship and the goods inside. At a terminal, when a berthed container ship receives loading and unloading operations performed by quay cranes (QCs), it is required that the ship stability criterion does not exceed a certain threshold. In practice, ship operation managers are keen in minimizing the ship’s turnaround time via an efficient QC schedule for loading and unloading containers without leaning the ship to one side. The schedule is then implemented by automatic scheduling systems or simulation tools in the terminal routines. This paper presents some practical stability constraints and integrates them into the traditional QC scheduling model. The results show that by considering the stability constraints, the ship will become more stable, but the turnaround time will not be affected significantly. We believe that the introduction of ship stability constraints can not only fill in the gap between the research on QC scheduling and the real-world ship handling practices but also enrich the studies on logistics planning and port operations.

Combined quay crane assignment and quay crane scheduling with crane inter-vessel movement and non-interference constraints

Integrated models of the quay crane assignment problem (QCAP) and the quay crane scheduling problem (QCSP) exist. However, they have shortcomings in that some do not allow movement of quay cranes between vessels, others do not take into account precedence relationships between tasks, and yet others do not avoid interference between quay cranes. Here, an integrated and comprehensive optimization model that combines the two distinct QCAP and QCSP problems which deals with the issues raised is put forward. The model is of the mixed-integer programming type with the objective being to minimize the difference between tardiness cost and earliness income based on finishing time and requested departure time for a vessel. Because of the extent of the model and the potential for even small problems to lead to large instances, exact methods can be prohibitive in computational time. For this reason an adapted genetic algorithm (GA) is implemented to cope with this computational burden. Experimental results obtained with branch-and-cut as implemented in CPLEX and GA for small to large-scale problem instances are presented. The paper also includes a review of the relevant literature.

Crane scheduling problem with non-interference constraints in a steel coil distribution centre

This article deals with a parallel machine scheduling problem subject to non-interference constraints. This situation often appears at logistic centres, such as depots, warehouses and stockyards. The analyzed scenario is based on a real case at a distribution centre of steel coils, where two cranes using the same rail must load dispatching trucks. We analyze this case by modelling the situation through a parallel machine perspective and considering two mechanisms to deal with the machine interference, . In the first approach, the machine interference is dealt by scheduling whole trucks. In the second one, we schedule the trucks and the coils within. The proposed mathematical models are able to solve small and medium instances, thus, we develop two genetic algorithms to solve real size instances, allowing the analysis of different storage policies. Results show that the genetic approach is able to find near-optimal solutions independently of the policy, with solutions gap ranging from 10 to 2.1%.

Scheduling cranes to retrieve steel coils in a warehouse

This article proposes a mixed integer model and a genetic algorithm to address a two cranes scheduling problem with non-interference constraints. The problem is about trucks’ loading scheduling with two cranes. Cranes must load trucks with a predefined amount of coils without preemption and the coils retrieval must be scheduled as well. The equipments are subject to non-interference constraints because they share the same rail inside the shed. The mathematical model and the heuristic are computationally tested among different instances.

Two Formulations for non-Interference Parallel Machine Scheduling Problems

This article deals with a job scheduling on two cranes subject to non-interference constraints. It is based on a real case at a distribution center of steel coils, where two cranes sharing the same rail must load a sequence of trucks, which has a defined demand of coils. The problem is mathematically modeled as a parallel machines with ordering variables and with time index variables. The proposed formulations are computationally tested among different instances. Based on the results, we discuss which formulation might work best for these problems.

Scheduling small number of quay cranes with non-interference constraint

Quay crane (QC) scheduling significantly affects the turn-around time of a container vessel, and it plays an important role in container terminal operation. Lee et al. (An approximation algorithm for quay crane scheduling with non-interference constraints in port container terminals, Presented at Tristan VI, Phuket, June 10–15, 2007) present a 2-approximation algorithm for QC scheduling problem with non-interference constraint. In this paper we revisit Lee’s heuristic for the scenario with small number of QCs, and prove that it is 4/3 and 5/3-approximation for the case with two QCs and the case with three QCs respectively.

A genetic algorithm approach for quay crane scheduling with non-interference constraints at Narvik container terminal

A fast, robust and efficient algorithm for solving the problem of scheduling two quay cranes with non-interference constraints at Narvik container terminal has been developed. To solve the problem, a genetic algorithm approach is used and adapted to the case of two cranes. This approach manages to provide practical solutions and significant time savings for a real-life crane-scheduling problem. Operators at Narvik container terminal find the solution to be user-friendly, and it allows the user to change parameter settings and obtain solutions in real time.

Quay crane scheduling with non-interference constraints in port container terminals

The quay crane scheduling problem studied in this paper is to determine a handling sequence of holds for quay cranes assigned to a container vessel considering interference between quay cranes. This paper provides a mixed integer programming model for the considered quay crane scheduling problem that is NP-complete in nature. A genetic algorithm is proposed to obtain near optimal solutions. Computational experiments are conducted to examine the proposed model and solution algorithm. The computational results show that the proposed genetic algorithm is effective and efficient in solving the considered quay crane scheduling problem.

Optimization of process plant layout with pipe routing

An optimization approach for the design of chemical plant geometric layout is presented. The task is decomposed into a sequence of subproblems that are solved using mixed integer linear programming models. The 3D layout problem with noninterference constraints is computationally difficult, and simultaneous treatment for placement of equipment and routing of pipes for the number of components comprising a typical plant is as yet impractical. In the approach presented, the optimization of the layout is computed first, and then is followed by the piping layout and routing. The models allow incorporation of practical design constraints. An example is presented that show the resulting design appear both reasonable and near-optimal. Different techniques are studied in order to do an automatic routing of a process plant layout. The procedure is based on a (partially arbitrary) selection of node positions where pipes can be routed, respecting restrictions of safety and minimum distances from components. These nodes are connected by arcs that avoid the physical space of components. The graph defined by the nodes and arcs are used to find the minimum cost for the pipes. Two methods may be used: a mixed integer linear program for the global minimization of the cost of all pipes, or a shortest path algorithm for the minimization of the cost of each pipe individually. The MILP approach can include capacity constraints, but it can be applied only for small problems. The shortest path approach is better for larger problems and can include pipes with branches and stress analysis.

Formulating and solving parametric design problems involving non-interference constraints

Improvements in computer-aided design (CAD) tools can significantly increase designer productivity, since the ability to explore a variety of possible designs quickly and effectively is essential for a designer. Using an optimization tool, systematic exploration of design spaces can be achieved readily. The general goal of the work presented here is to aid design by combining the strengths of optimization techniques with those of CAD systems. The specific objective of this paper is to introduce goal directed geometry (GDG) as a computational framework for parametric design, aiding the formulation of engineering problems with geometric considerations and their solution with a multi-objective optimization package. Using GDG, ‘What if’ questions can be posed and answered in a systematic fashion. Specific issues to be addressed include the development of a general parametric design problem formulation, development of static and dynamic geometric non-interference constraints for use in this formulation, and investigation of the efficacy of the adaptive linear programming (ALP) multiobjective optimization algorithm in solving such problems. Two examples are presented, one each to illustrate the use of the static and dynamic non-interference constraints. Results demonstrate that the GDG formulation can be applied readily to a wide variety of parametric design problems. Additionally, the ALP algorithm successfully navigates around geometric constraints, although care must be taken when linearizing highly non-linear design spaces.

Relative positioning of variational part models for design analysis

A collection of functionally oriented assembly relations serves as an implicit representation for part positions in an assembly. The actual determination of part positions from the assembly relations has been extensively researched for assemblies in which parts are at their nominal shapes and sizes. However, design-analysis algorithms such as those used in tolerance analysis require the determination of the final assembly configuration, where the individual part geometries incorporate simulated manufacturing variations. The paper describes a constrained-optimization technique for the determination of part positions in assemblies of nonideal parts. Because the manufacturing variations are relatively small, the authors' technique linearizes the rotational elements in the constraint formulation. The constraint-optimization formulation seeks to satisfy the assembly relations to the maximum extent possible that is consistent with their relative functional significance. Noninterference constraints between the mating parts are enforced.

On the Job-Shop Scheduling Problem

This is a proposal for the application of discrete linear programming to the typical job-shop scheduling problem—one that involves both sequencing restrictions and also noninterference constraints for individual pieces of equipment. Thus far, no attempt has been made to establish the computational feasibility of the approach in the case of large-scale realistic problems. This formulation seems, however, to involve considerably fewer variables than two other recent proposals [Bowman, E. H. 1959. The schedule-sequencing problem. Opns Res. 7 621–624; Wagner, H. 1959. An integer linear-programming model for machine scheduling. Naval Res. Log. Quart. (June).], and on these grounds may be worth some computer experimentation.