Stack- and Queue-like Dynamics in Recurrent Neural Networks

What dynamics do simple recurrent networks (SRNs) develop to represent stack-like and queue-like memories? SRNs have been widely used as models in cognitive science. However, they are interesting in their own right as non-symbolic computing devices from the viewpoints of analogue computing and dynamical systems theory. In this paper, SRNs are trained oil two prototypical formal languages with recursive structures that need stack-like or queue-like memories for processing, respectively. The evolved dynamics are analysed, then interpreted in terms of simple dynamical systems, and the different ease with which SRNs aquire them is related to the properties of these simple dynamical Within the dynamical systems framework, it is concluded that the stack-like language is simpler than the queue-like language, without making use of arguments from symbolic computation theory

Train Scheduling and Rescheduling in the UK with a Modified Shifting Bottleneck Procedure

This paper introduces a modified shifting bottleneck approach to solve train scheduling and rescheduling problems. The problem is formulated as a job shop scheduling model and a mixed integer linear programming model is also presented. The shifting bottleneck procedure is a well-established heuristic method for obtaining solutions to the job shop and other machine scheduling problems. We modify the classical shifting bottleneck approach to make it suitable for the types of job shop problem that arises in train scheduling. The method decomposes the problem into several single machine problems. Different variations of the method are considered with regard to solving the single machine problems. We compare and report the performance of the algorithms for a case study based on part of the UK railway network

A genetic algorithm for two-dimensional bin packing with due dates

This paper considers a new variant of the two-dimensional bin packing problem where each rectangle is assigned a due date and each bin has a fixed processing time. Hence the objective is not only to minimize the number of bins, but also to minimize the maximum lateness of the rectangles. This problem is motivated by the cutting of stock sheets and the potential increased efficiency that might be gained by drawing on a larger pool of demand pieces by mixing orders, while also aiming to ensure a certain level of customer service. We propose a genetic algorithm for searching the solution space, which uses a new placement heuristic for decoding the gene based on the best fit heuristic designed for the strip packing problems. The genetic algorithm employs an innovative crossover operator that considers several different children from each pair of parents. Further, the dual objective is optimized hierarchically with the primary objective periodically alternating between maximum lateness and number of bins. As a result, the approach produces several non-dominated solutions with different trade-offs. Two further approaches are implemented. One is based on a previous Unified Tabu Search, suitably modified to tackle this revised problem. The other is randomized descent and serves as a benchmark for comparing the results. Comprehensive computational results are presented, which show that the Unified Tabu Search still works well in minimizing the bins, but the genetic algorithm performs slightly better. When also considering maximum lateness, the genetic algorithm is considerably better

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

Local search framework for irregular shaped stock-cutting

Constructive algorithms have been shown to be an effective solution approach. However, decoding the representation as a permutation of pieces and the layout of the solution is not a 1-1 mapping Hypothesis: there exists significant redundancy in the search algorithm as a result of reproducing the same solution from a different representatio

Column generation and sequential heuristic procedure for solving an irregular shape cutting stock problem

The research addressing two-dimensional (2D) irregular shape packing has largely focused on the strip packing variant of the problem. However, it can be argued that this is a simplification. The materials from which pieces are required to be cut will ultimately have a fixed length either due to the physical dimensions of the material or through constraints on the cutting machinery. Hence, in order to cut all the pieces, multiple sheets may be required. From this scenario arises the 2D irregular shape cutting stock problem. In this paper, we will present implementations of cutting stock approaches adapted to handle irregular shapes, including two approaches based on column generation (CG) and a sequential heuristic procedure. In many applications, setup costs can be reduced if the same pattern layout is cut from multiple sheets; hence there is a trade-off between material waste and number of patterns. Therefore, we describe the formulation and implementation of an adaptation of the CG method to control the number of different patterns. CG is a common method for the cutting stock problem; however, when the pieces are irregular the sub-problem cannot be solved optimally. Hence we implement CG and solve the subproblem using the beam search heuristic. Further, we introduce a version of CG for instances where the number of rows is less than the number of columns

Construction heuristics for two-dimensional irregular shape bin packing with guillotine constraints

The paper examines a new problem in the irregular packingliterature that has existed in industry for decades;two-dimensional irregular (convex) bin packing with guillotineconstraints. Due to the cutting process of certain materials, cutsare restricted to extend from one edge of the stock-sheet toanother, called guillotine cutting. This constraint is commonplace in glass cutting and is an important constraints intwo-dimensional cutting and packing problems. In the literature,various exact and approximate algorithms exist for finding the twodimensional cutting patterns that satisfy the guillotine cuttingconstraint. However, to the best of our knowledge, all of thealgorithms are designed for solving rectangular cutting where cutsare orthogonal with the edges of the stock-sheet. In order tosatisfy the guillotine cutting constraint using these approaches,when the pieces are non-rectangular, practitioners implement a twostage approach. First, pieces are enclosed within rectangle shapesand then the rectangles are packed. Clearly, imposing this condition is likely to lead to additional waste. Thispaper aims to generate guillotine-cutting layouts of irregularshapes using a number of strategies. The investigation comparestwo two-stage approaches; one approximates pieces by rectangles,the other approximates pairs of pieces by rectangles usingphi-functions for optimal clustering. Both these approaches usestate of the art rectangle bin packing with guillotineconstraints. Further, we design and implement a one-stage approachusing a self-adapted forest search algorithm. Experimental resultsshow the one-stage strategy to produce good solutions in less timeover the two-stage approach

An improved TOPOS constructive algorithm for nesting problems

A constructive approach for nesting problems based on the TOPOS algorithm is presented and improved via a more powerful nofit polygon generator that can efficiently represent holes in the partial solution. Hence the solution quality is less dependent on the placement order and new "best fit" criteria can be utilised