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The purpose of this paper is to review, evaluate and classify the academic research that has been published in facility layout problems (FLPs) and to analyse how researches and practices on FLPs are.

The review is based on 166 papers published from 1953 to 2021 in international peer-reviewed journals. The literature review on FLPs is presented under broader headings of discrete space and continuous space FLPs. The important formulations of FLPs under static and dynamic environments represented in the discrete and continuous space are presented. The articles reported in the literature on various representations of facilities for the continuous space Unequal Area Facility Layout Problems (UA-FLPs) are summarized. Discussed and commented on adaptive and robust approaches for dynamic environment FLPs. Highlighted the application of meta-heuristic solution methods for FLPs of a larger size.

It is found that most of the earlier research adopted the discrete space for the formulation of FLPs. This type of space representation for FLPs mostly assumes an equal area for all facilities. UA-FLPs represented in discrete space yield irregular shape facilities. It is also observed that the recent works consider the UA-FLPs in continuous space. The solution of continuous space UA-FLPs is more accurate and realistic. Some of the recent works on UA-FLPs consider the flexible bay structure (FBS) due to its advantages over the other representations. FBS helps the proper design of aisle structure in the detailed layout plan. Further, the recent articles reported in the literature consider the dynamic environment for both equal and unequal area FLPs to cope with the changing market environment. It is also found that FLPs are Non-deterministic Polynomial-complete problems, and hence, they set the challenges to researchers to develop efficient meta-heuristic methods to solve the bigger size FLPs in a reasonable time.

Due to the extremely large number of papers on FLPs, a few papers may have inadvertently been missed. The facility layout design research domain is extremely vast which covers other areas such as cellular layouts, pick and drop points and aisle structure design. This research review on FLPs did not consider the papers published on cellular layouts, pick and drop points and aisle structure design. Despite the possibility of not being all-inclusive, the authors firmly believe that most of the papers published on FLPs are covered and the general picture presented on various approaches and parameters of FLPs in this paper are precise and trustworthy.

To the best of the authors’ knowledge, this paper reviews and classifies the literature on FLPs for the first time under the broader headings of discrete space and continuous space representations. Many important formulations of FLPs under static and dynamic environments represented in the discrete and continuous space are presented. This paper also provides the observations from the literature review and identifies the prospective future directions.

The purpose of this study is the application of the following concepts to the time discrete form. Variational Calculus, potential and kinetic energies, velocity proportional Rayleigh dissipation function, the Lagrange and Hamilton formalisms, extended Hamiltonians and Poisson brackets are all defined and applied for time-continuous physical processes. Such processes are not always time-continuously observable; they are also sometimes time-discrete.

The classical approach is developed with the benefit of giving only a short table on charge and flux formulation, as they are similar to the classical case just like all other formulation types. Moreover, an electromechanical example is represented as well.

Lagrange and Hamilton formalisms together with the velocity proportional (Rayleigh) dissipation function can also be used in the discrete time case, and as a result, dissipative equations of generalized motion and dissipative canonical equations in the discrete time case are obtained. The discrete formalisms are optimal approaches especially to analyze a coupled physical system which cannot be observed continuously. In addition, the method makes it unnecessary to convert the quantities to the other. The numerical solutions of equations of dissipative generalized motion of an electromechanical (coupled) system in continuous and discrete time cases are presented.

The formalisms and the velocity proportional (Rayleigh) dissipation function aforementioned are used and applied to a coupled physical system in time-discrete case for the first time to the best of the author’s knowledge, and systems of difference equations are obtained depending on formulation type.

The purpose of this paper is to study algebraic structures that underlie the geometric approaches. The structures and their properties are analyzed to address how to systematically pose a class of boundary value problems in a pair of interlocked complexes.

The work utilizes concepts of algebraic topology to have a solid framework for the analysis. The algebraic structures constitute a set of requirements and guidelines that are adhered to in the analysis.

A precise notion of “relative dual complex”, and certain necessary requirements for discrete Hodge‐operators are found.

The paper includes a set of prerequisites, especially for discrete Hodge‐operators. The prerequisites aid, for example, in verifying new computational methods and algorithms.

The paper gives an overall view of the algebraic structures and their role in the geometric approaches. The paper establishes a set of prerequisites that are inherent in the geometric approaches.

An abstract lattice of empty set cells is shown to be able to account for a primary substrate in a physical space. Space‐time is represented by ordered sequences of topologically closed Poincaré sections of this primary space. These mappings are constrained to provide homeomorphic structures serving as frames of reference in order to account for the successive positions of any objects present in the system. Mappings from one section to the next involve morphisms of the general structures, representing a continuous reference frame, and morphisms of objects present in the various parts of this structure. The combination of these morphisms provides space‐time with the features of a non‐linear generalized convolution. Discrete properties of the lattice allow the prediction of scales at which microscopic to cosmic structures should occur. Deformations of primary cells by exchange of empty set cells allow a cell to be mapped into an image cell in the next section as far as the mapped cells remain homeomorphic. However, if a deformation involves a fractal transformation to objects, there occurs a change in the dimension of the cell and the homeomorphism is not conserved. Then, the fractal kernel stands for a “particle” and the reduction of its volume (together with an increase in its area up to infinity) is compensated by morphic changes of a finite number of surrounding cells. Quanta of distances and quanta of fractality are demonstrated. The interactions of a moving particle‐like deformation with the surrounding lattice involves a fractal decomposition process, which supports the existence and properties of previously postulated inerton clouds as associated to particles. Experimental evidence of the existence of inertons is reviewed and further possibilities of experimental proofs proposed.

To provide a discrete‐time nonlinear model for surface permanent‐magnet synchronous machines (SPMSMs) in order to discuss the stability of such machines.

Through differencing the co‐energy, obtained from a finite element method, the main flux path can be described by a complex reluctance. Furthermore, for a SPMSM, an equivalent circuit is presented that includes the eddy‐current losses and the voltage drops across stator resistance and leakage inductance. The model is transformed to a discrete‐time state‐space model by using a forward rectangular rule. By using a root locus technique, the stability of the new model is discussed.

From the calculated root locus it is concluded that the stability of a SPMSM is only guaranteed for certain values of the open loop gain. Moreover, by using the forward rectangular rule, it is concluded that a well‐considered time step has to be chosen.

The model considers the fundamental space harmonic components only. Moreover, the saturation of the leakage flux path is neglected.

As the model is formulated in discrete time, it can be used in modern drives where a digital controller is used.

This paper presents an equivalent electrical circuit for SPMSMs that takes into account the saturation of the magnetizing flux paths as well as the magnetic interaction between the two orthogonal magnetic axes.

To discuss a new parallel algorithmic platform (minlp_machine) for complex mixed‐integer non‐linear programming (MINLP) problems.

The platform combines features from classical non‐linear optimization methodology with novel innovations in computational techniques. The system constructs discrete search zones around noninteger discrete‐valued variables at local solutions, which simplifies the local optimization problems and reduces the search process significantly. In complicated problems fast feasibility restoration may be achieved through concentrated Hessians. The system is programmed in strict ANSI C and can be run either stand alone or as a support library for other programs. File I/O is designed to recognize possible usage in both single and parallel processor environments. The system has been tested on Alpha, Sun and Linux mainframes and parallel IBM and Cray XT4 supercomputer environments. The constrained problem can, for example, be solved through a sequence of first order Taylor approximations of the non‐linear constraints and feasibility restoration utilizing Hessian information of the Lagrangian of the MINLP problem, or by invoking a nonlinear solver like SQP directly in the branch and bound tree. minlp_machine( ) has been tested as a support library to genetic hybrid algorithm (GHA). The GHA(minlp_machine) platform can be used to accelerate the performance of any linear or non‐linear node solver. The paper introduces a novel multicomputer partitioning of the discrete search space of genuine MINLP‐problems.

The system is successfully tested on a small sample of representative MINLP problems. The paper demonstrates that – through concurrent nonlinear branch and bound search – minlp_machine( ) outperforms some recent competing approaches with respect to the number of nodes in the branch and bound tree. Through parallel processing, the computational complexity of the local optimization problems is reduced considerably, an important aspect for practical applications.

This paper shows that binary‐valued MINLP‐problems will reduce to a vector of ordinary non‐linear programming on a suitably sized mesh. Correspondingly, INLP‐ and ILP‐problems will require no quasi‐Newton steps or simplex iterations on a compatible mesh.

The purpose of this paper is to investigate a control engineering-based system model that allows for any value of production delay for a three-tier supply chain with information delays between tiers or systems with epos.

A discrete z transform model of automatic pipeline, variable inventory and order based production control system three-tier supply chain is obtained using a state-space model using a reachable control formulation. This model provides a discrete time state-space model conversion using an exponential production delay with no loss of generality.

This work allows a three-tier supply chain model to be computed via a spreadsheet using any production delay and can be modified to include different sales smoothing procedures. The model is fully controllable and observable. Stability of these models is obtained from the system eigenvalues and agrees with our previously published stability boundaries.

The system is described by a linear control model of the production process and does not include production limits or other resource limitations, including history of sales demand and response.

This present model is an extension of the model devised by White and Censlive, in that it allows accurate modelling of multi-tier inventory production systems by permitting flexible selection of delay parameter values for real systems.

The purpose of this paper is to present a new computational framework to address future preliminary design needs for aircraft subsystems. The ability to investigate multiple candidate technologies forming subsystem architectures is enabled with the provision of automated architecture generation, analysis and optimization. Main focus lies with a demonstration of the frameworks workings, as well as the optimizers performance with a typical form of application problem.

The core aspects involve a functional decomposition, coupled with a synergistic mission performance analysis on the aircraft, architecture and component levels. This may be followed by a complete enumeration of architectures, combined with a user defined technology filtering and concept ranking procedure. In addition, a hybrid heuristic optimizer, based on ant systems optimization and a genetic algorithm, is employed to produce optimal architectures in both component composition and design parameters. The optimizer is tested on a generic architecture design problem combined with modified Griewank and parabolic functions for the continuous space.

Insights from the generalized application problem show consistent rediscovery of the optimal architectures with the optimizer, as compared to a full problem enumeration. In addition multi-objective optimization reveals a Pareto front with differences in component composition as well as continuous parameters.

This paper demonstrates the frameworks application on a generalized test problem only. Further publication will consider real engineering design problems.

The paper addresses the need for future conceptual design methods of complex systems to consider a mixed concept space of both discrete and continuous nature via automated methods.

This study aims to propose an enhanced eco-driving strategy based on reinforcement learning (RL) to alleviate the mileage anxiety of electric vehicles (EVs) in the connected environment.

In this paper, an enhanced eco-driving control strategy based on an advanced RL algorithm in hybrid action space (EEDC-HRL) is proposed for connected EVs. The EEDC-HRL simultaneously controls longitudinal velocity and lateral lane-changing maneuvers to achieve more potential eco-driving. Moreover, this study redesigns an all-purpose and efficient-training reward function with the aim to achieve energy-saving on the premise of ensuring other driving performance.

To illustrate the performance for the EEDC-HRL, the controlled EV was trained and tested in various traffic flow states. The experimental results demonstrate that the proposed technique can effectively improve energy efficiency, without sacrificing travel efficiency, comfort, safety and lane-changing performance in different traffic flow states.

In light of the aforementioned discussion, the contributions of this paper are two-fold. An enhanced eco-driving strategy based an advanced RL algorithm in hybrid action space (EEDC-HRL) is proposed to jointly optimize longitudinal velocity and lateral lane-changing for connected EVs. A full-scale reward function consisting of multiple sub-rewards with a safety control constraint is redesigned to achieve eco-driving while ensuring other driving performance.

New applications of solid freeform fabrication (SFF) are arising, such as functional rapid prototyping and in situ fabrication, which push SFF to its limits in terms of geometrical fidelity due to the applications' inherent process uncertainties. Current closed‐loop feedback control schemes monitor and manipulate SFF techniques at the process level, e.g. envelope temperature, feed rate. “Closing the loop” on the process level, instead of the overall part geometry level, leads to limitations in the types of errors that can be detected and corrected. The purpose of this paper is to propose a technique called greedy geometric feedback (GGF) control which “closes the loop” on the overall part geometry level.

The overall part geometry is monitored throughout the print and, using a greedy algorithm, real‐time decisions are made to serially determine the locations of subsequent droplets, i.e. overall part geometry is directly manipulated. A computer simulator and a physical experimental platform were developed to compare the performance of GGF to an open‐loop control scheme. Root mean square surface height errors were measured under controlled uncertainties in droplet height, droplet radius of curvature, droplet positioning and mid‐print part deformations.

The GGF technique outperformed open‐loop control under process uncertainties in droplet shape, droplet placement and mid‐print part deformations. The disparity between performances is dependant on the nature and extent of the imposed process uncertainties.

Future research will focus on improving the performance of GGF for specific cases by designing more complex greedy algorithmic scoring heuristics. Also, the technique will be generalized beyond heightmap representations of 3D spaces.

The GGF technique is the first to “close the loop” on the overall part geometry level. GGF, therefore, can compensate for a broader range of errors than existing closed‐loop feedback control schemes. Also, since the technique only requires the real‐time update of a very limited set of heights, the technique is computationally inexpensive and widely applicable. By developing a closed‐loop feedback scheme that addressed part geometry‐level errors, SFF can be applied to more challenging in situ fabrication scenarios with less conventional materials.