Current Feasible Solution Research Articles

A Sequential Algorithm for Jerk Limited Speed Planning

In this article, we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration, and jerk constraints. Such a problem arises in industrial contexts, such as automated warehouses, where LGVs need to perform assigned tasks as fast as possible in order to increase productivity. It can be reformulated as an optimization problem with a convex objective function, linear velocity and acceleration constraints, and nonconvex jerk constraints, which, thus, represent the main source of the difficulty. While existing nonlinear programming (NLP) solvers can be employed for the solution of this problem, it turns out that the performance and robustness of such solvers can be enhanced by the sequential line-search algorithm proposed in this article. At each iteration, a feasible direction, with respect to the current feasible solution, is computed, and a step along such direction is taken in order to compute the next iterate. The computation of the feasible direction is based on the solution of a linearized version of the problem, and the solution of the linearized problem, through an approach that strongly exploits its special structure, represents the main contribution of this work. The efficiency of the proposed approach with respect to existing NLP solvers is proven through different computational experiments. Note to Practitioners—This article was motivated by the needs of LGV manufacturers. In particular, it presents an algorithm for computing the minimum-time speed law for an LGV along a preassigned path, respecting assigned velocity, acceleration, and jerk constraints. The solution algorithm should be: 1) fast, since speed planning is made continuously throughout the workday, not only when an LGV receives a new task but also during the execution of the task itself, since conditions may change, e.g., if the LGV has to be halted for security reasons and 2) reliable, i.e., it should return solutions of high quality, because a better speed profile allows to save time and even small percentage improvements, say a 5% improvement, has a considerable impact on the productivity of the warehouse, and, thus, determines a significant economic gain. The algorithm that we propose meets these two requirements, and we believe that it can be a useful tool for LGV manufacturers and users. It is obvious that the proposed method also applies to the speed planning problem for vehicles other than LGVs, e.g., road vehicles.

Application of Artificial Neural Network for Internal Combustion Engines: A State of the Art Review

The automotive industry is facing a crucial time. The transformation from internal combustion engines to new electrical technologies requires enormous investment, and hence the IC engines are likely to serve as a means of transportation for the coming decades. The search for sustainable green alternative fuel and operating parameter optimization is a current feasible solution and is a critical issue among the scientific community. Engine experiments are complicated, costly, and time-consuming, especially when the global economy is drastically down due to the COVID-19 pandemic and putting the limitation of social distancing. Industries are looking for proven computational solutions to address these issues. Recently, artificial neural network has been proven beneficial in several areas of engineering to reduce the time and experimentation cost. The IC engine is one of them. ANN has been used to predict and analyze different characteristics such as performance, combustion, and emissions of the IC engine to save time and energy. The complex nature of ANN may lead to computation time, energy, and space. Recent studies are centered on changing the network topology, deep learning, and design of ANN to get the highest performance. The present study summarizes the application of ANN to predict and optimize the complicated characteristics of various types of engines with different fuels. The study aims to investigate the network topologies adopted to design the model and thereafter statistical evaluation of the developed ANN models. A comparison of the ANN model with other prediction models is also presented.

On the Parallelization of Spectrum Defragmentation Reconfigurations in Elastic Optical Networks

Flexible-grid elastic optical networks (EONs) have attracted intensive research interests for the agile spectrum management in the optical layer. Meanwhile, due to the relatively small spectrum allocation granularity, spectrum fragmentation has been commonly recognized as one of the key factors that can deteriorate the performance of EONs. To alleviate spectrum fragmentation, various defragmentation (DF) schemes have been considered to consolidate spectrum utilization in EONs through connection reconfigurations. However, most of the previous approaches operate in the sequential manner (Seq-DF), i.e., involving a sequence of reconfigurations to progressively migrate highly fragmented spectrum utilization to consolidated state. In this paper, we propose to perform the DF operations in a parallel manner (Par-DF), i.e., conducting all the DF-related connection reconfigurations simultaneously. We first provide a detailed analysis on the latency and disruption of Seq-DF and Par-DF in EONs, and highlight the benefits of Par-DF. Then, we study two types of Par-DF approaches in EONs, i.e., reactive Par-DF (re-Par-DF) and proactive Par-DF (pro-Par-DF). We perform hardness analysis on them, and prove that the problem of re-Par-DF is ${\cal NP}$ -hard in the strong sense while pro-Par-DF is an ${\cal APX}$ -hard problem. Next, we focus on pro-Par-DF and propose a Lagrangian-relaxation (LR) based heuristic to solve it time-efficiently. The proposed algorithm decomposes the original problem into several independent subproblems and ensures that each of them can be solved efficiently. The LR based approach informs us the proximity of current feasible solution to the optimal one constantly, and offers a near-optimal performance (relative dual gap $ 5%) within 500 iterations in most simulations. Extensive simulations also verify that the proposed pro-Par-DF approach outperforms Seq-DF in terms of the DF Latency, Disruption and Cost.

Student overload at university: Large class teaching challenges

Burgeoning class sizes coupled with the traditional didactic means has become a way of navigating around the challenges lecturers face at university. Many issues continue to plague lecturers and students alike which inadvertently impacts on the teaching and learning experience. This study examines the challenges faced by lecturers with large classes at higher education institutions. A study conducted at two universities through the use of questionnaires found that lecturers at both institutions were faced with similar challenges in teaching/lecturing large classes. The current feasible solution to support the traditional form of lecturing is the use of ICT’s in reaching all students within large classes.

Inverse Polynomial Optimization

We consider the inverse optimization problem associated with the polynomial program [Formula: see text] and a given current feasible solution [Formula: see text]. We provide a systematic numerical scheme to compute an inverse optimal solution. That is, we compute a polynomial [Formula: see text] (which may be of the same degree as f, if desired) with the following properties: (a) y is a global minimizer of [Formula: see text] on K with a Putinar's certificate with an a priori degree bound d fixed, and (b) [Formula: see text] minimizes [Formula: see text] (which can be the l1, l2 or l∞-norm of the coefficients) over all polynomials with such properties. Computing [Formula: see text] reduces to solving a semidefinite program whose optimal value also provides a bound on how far f(y) is from the unknown optimal value f*. The size of the semidefinite program can be adapted to the available computational capabilities. Moreover, if one uses the l1-norm, then [Formula: see text] takes a simple and explicit canonical form. Some variations are also discussed.

고립 픽셀 제거 변조부호 선택을 위한 절단평면 알고리즘

In this paper, we introduce a modulation code design problem where best selection of two-dimensional codewords are determined to reduce two-dimensional (2D) Intersymbol Interference (ISI) and Interpage Interference (IPI), while when these codewords are randomly arranged on the storage, isolated pixel cannot be formed. Codeword selection problem and isolated pixel detection problem are formulated as integer program models and we develop a cutting plane algorithm where a valid cut is generated to remove current feasible solution to avoid isolated pixel by solving the isolated pixel detection subproblem. Using the proposed method, 6/8 codewords with non-isolated pixel are found.

A GREEDY ALGORITHM FOR MINIMIZING A SEPARABLE CONVEX FUNCTION OVER A FINITE JUMP SYSTEM

We present a greedy algorithm for minimizing a separable convex function over a finite jump system (E,f), where E is a nonempty finite set and f is a nonempty finite set of integral points in Z^E satisfying a certain exchange axiom. The concept of jump system was introduced by A. Bouchet and W. H. Cunningham. A jump system is a generalization of an integral bisubmodular polyhedron, an integral polymatroid, a (poly-)pseudomatroid and a delta-matroid, and has combinatorially nice properties. The algorithm starts with an arbitrary feasible solution and a current feasible solution incrementally moves toward an optimal one in a greedy way. We also show that the greedy algorithm terminates after changing an initial feasible solution at most[numerical formula] times, where for each e ∈ E [numerical formula].

A Dantzig-Wolfe-Like Variant of Karmarkar's Interior-Point Linear Programming Algorithm

We show that a variant of Karmarkar's projective algorithm for linear programming can be viewed as following the approach of Dantzig-Wolfe decomposition. At each iteration, the current primal feasible solution generates prices which are used to form a simple subproblem. The solution to the subproblem is then incorporated into the current feasible solution. With a suitable choice of stepsize a constant reduction in potential function is achieved at each iteration. We also use our analysis to motivate a new primal simplex pivot rule that is closely related to rules used by E. Klotz and L. Schrage.

A two-segment approximation algorithm for separable convex programming with linear constraints

We discuss a new algorithm for the separable convex programming with linear constraints. This is based on the approximation of the objective function by at most two linear pieces in the neighborhood of the current feasible solution. The two segments will be adaptively defined rather than predecided fixed grids. If3 furthermore, the objective function is differentiable, and one introduces a non-Archimedean infinitesimal, the algorithm generates a sequence of feasible solutions every cluster point of which is an optimal solution. Computational tests on the problem with up to 196 non-linear variables are presented

A New Algorithm for Tree Modification in the Primal Transportation Problem

Primal methods for the transportation problem of linear programming require substantial bookkeeping to deal with constant updating of a tree describing the shipments in the current feasible solution. This paper suggests a new means of bookkeeping which is useful for long narrow problems. The method builds on previous work by the same author which reduces the number of records to be updated. The new methods reduce the number of items which have to be maintained for a replication of the tree and simplify some steps in updating the remaining items.

Improving loops and vanishing variables in long transportation problems

In this paper the following two results are presented: (1)A method which determines the optimal values of certain variables during the iterative solution process. The closer the current primal feasible solution is to the optimal solution, the greater the number of variables which may be determined. (2) For each current feasible solution ( X ij ) of the given m × n transportation problem A, a feasible solution ( X ̄ ij ) of an auxiliary m × m( m −1) transportation problem A ̄ is constructed. Problem A ̄ is shown to be equivalent to an m( m − 1) × m( m − 1) assignment problem with two admissible cells per column. The optimally of ( X ij ) is shown to imply the optimality of ( X ̄ ij ) and conversely. The best “improving loops” (including the improving loops used in MODI) of A ̄ are shown to be the best “improving loops” of A as well.