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The paper aims to unveil the interdependent nature of the studio’s physical settings, the design challenges presented, and the interactions between its inhabitants. This examination seeks to contribute to the enhancement of architectural education by providing insights into the potential improvements in studio-based learning, thereby supporting a more effective and comprehensive educational model in the field of architecture. The scope of this study focuses on three parameters that define the design studio. These are the studio environment, design problems and inhabitants. The study elucidates the significance of these parameters in issuing a case study of a fourth-year architectural studio focusing on historical sites in Izmir, Turkey. The method of the research adopts a co/autoethnographic approach to explore how these elements influence the learning experience and outcome. As a result, this study investigates the dynamics within architectural design studios, emphasizing the symbiotic relationship between the learning environment, the interaction among students and instructors, and the design problem.

The The real world is characterized by deep similarity and interdependence with ill-defined problems, observable in different contexts. Every day, thousands of ill-defined problems are analyzed by people in various sciences, and among the solutions, one is chosen for implementation. Addressing such questions requires a unique ability, and this feature creates a distinction between professionals and beginners in the relevant field. Therefore, the ability to identify such problems is very important, because solving these problems with a limited vision may lead to an inadequate and incomplete solution, which sometimes leads to irreparable consequences in various fields. For this purpose, educational design models were examined in this research. This study was conducted according to the characteristics of the design problem, with the aim of choosing a suitable model to address and solve ill-defined problems in different areas of the real world. [ABSTRACT FROM AUTHOR]

The terms "problem and solution" are omnipresent the world over in various design disciplines and designers often position themselves as problem solvers. Through a rigorous exploration of different perspectives on the problem-solution model and its impact, this article revisits how designers define, perceive, and consequently practice design. It closely explores how frequently propagated terminology and perceptions can impact designers and their work—educationally and professionally. The article also presents alternative approaches to thinking about and practicing design. [ABSTRACT FROM AUTHOR]

The actual energetic situation has several challenges such as pollution, the rarefaction of fossil fuel and the dangers of nuclear. Renewable sources are proposed as a solution and suggested, such as a cost-effectiveness system. The paper deals with the problem of feeding a domestic load with electricity which should respect the ecologies factors, so this work is a design problem of the hybrid renewable energy systems; PV/biomass, PV/diesel/battery, PV/wind/diesel/battery, and wind/diesel/battery to choose the best one of them which feed the load with the lowest cost. The study’s goal is to design a microgrid system by the minimization of the total investment cost with respect to the required technical factor, the minimum allowed renewable energy fraction, and the minimum allowed availability factor. The methodology flowed utilizes frameworks based on a recent algorithm called Movable damped wave algorithm (MDVP). The proposed optimization algorithm is compared with other algorithms to prove its efficacy which are; the artificial electric field algorithm (AEFA), harris hawks optimization (HHO), and the grey wolf optimizer (GWO). The project case study is investigated in Al-Majmaah, Saudi Arabia. The contribution of this work is implementing a recent algorithm that proves its efficacy and finding the best microgrid configuration following many investigations and comparisons. The results confirm that the MDVP is better compared to the other algorithms, its computational time is fast, and its convergence is good; otherwise, the PV/biomass is considered the best configuration in the area of study with a size of 237.698 m2 from PV panel and 954.097 t/year of biomass, which obtained the best Net Present Cost (NPC) of $299504, and a cost of energy (LCOE) assumed as $0.228/kW. A sensitivity analysis is applied to prove the effect of size variation on project factors. The simple observation, by the way, is that any change in the PV size affects the output factors.

Software design patterns have a considerable impact on the software development life cycle. Design pattern (DP) is a reliable and reusable solution provided by software experts to obtain quality software design. However, due to the large number of design patterns, selecting the appropriate one is quite difficult. To overcome this difficulty, several approaches with different methods have been presented to suggest the appropriate DP. Despite conducting a number of studies that have explored some aspects of this field, such as design pattern selection tools and techniques, there is a need for a deeper understanding, analysis, classification, and thorough review of the design pattern selection process. So far, no systematic review of design pattern selection approaches is available. This paper aims to classify existing approaches, provide several criteria for comparing approaches, analyze each one, and identify and analyze the most important elements in this field, including open issues, data sets, and so on. The present investigation paper will help future research to employ the existing approaches taking into account the specification of each one and it also raises awareness about the approaches used in previous research and their potential limitations. [ABSTRACT FROM AUTHOR]

Despite a great deal of effort has been made to present systematic models of design process, in practice, a lot of designs still proceed through unsystematic methods. It seems that the reason for this is too much emphasizing on describing the final design (product) and little attention to the design process; such that, there is no clear method so as to research-based design. This led to illustrate a distinct pattern from configuration of "design protocol" in terms of research-based design process. The aim of this study is to develop a model that can be used in the architecture educational system. So at first step, the readers of this research are architecture students, and designers can also benefit from it in the next steps. So that all the readers of this research using this model, in a logical process, can recognize the right information for design and ultimately achieve an optimal architectural design. In this research, our preferred context is architecture, and the focus is on research-oriented design; therefore, any given example would be in the field of architecture. In this paper, the proposed process is the result of experience gained from five years teaching architectural design (2) in master's degree that includes three milestones as follows: 1) Statement of problem 2) The scheme and 3) Design protocol. "Statement of design problem" is obtained from people's concerns about "design subject" integrated in its "bed". The scheme, itself, constitutes the expectations, goals and mission representing two sets of information (cognitive and distinction) about design that finally leads to establish a "spatial-body program" of the project. As proceeding from the onset of diagram into the end, we passed from "analyze" into "synthesize" phase. In fact, in «analyze» phase, designer decides to collect and analyze information; however, as the process goes forward, he/she combines the information from the previous phase in order to achieve novel findings. Finally, we hope that by taking advantage of the proposed process, designers can find the best way to accomplish their design projects within a defined framework.

Based on a line of inquiry initiated by Dorst, this article explores Foucault's work as a philosophical inspiration for design research and practice. In terms of foucaultian problematization, notions of discourse and problematization— instead of notions of design problems— is an alternative way of dealing with design situations. It is argued that through the problematization of the discourses interwoven in a design project, the designer takes on a critical and political dimension of their own work. In this way, through the project, designers can have the option to critically choose between reinforcing discourses— in case of agreement with them, or subverting discourses— in case of disagreement. [ABSTRACT FROM AUTHOR]

Abstract Background Developers often have to locate design problems in the source code. Several types of design problems may manifest as code smells in the program. A code smell is a source code structure that may reveal a partial hint about the manifestation of a design problem. Recent studies suggest that developers should ignore smells occurring in isolation in a program location. Instead, they should focus on analyzing stinkier code, i.e., program locations—e.g., a class or a hierarchy—affected by multiple smells. There is evidence that the stinkier a program location is, the more likely it contains a design problem. However, there is no empirical evidence on whether developers can effectively identify a design problem in stinkier code. Developers may struggle to make an analysis of inter-related smells affecting the same program location. Besides that, the analysis of stinkier code may require proper tool support due to its analysis complexity. However, there is little knowledge on what are the requirements for a tool that helps developers in revealing stinkier program locations. As a result, developers may not be able to identify design problems due to tool issues. Method To address this matter, we aimed at achieving three goals. In the first case, we proposed Organic—a tool supporting the analysis of stinky code. In the second case, we applied a mixed-method approach to analyze if and how developers can effectively find design problems when reflecting upon stinky code—i.e., a program location affected by multiple smells. We conducted a study with 11 software professionals. Finally, in the third case, we aimed at understanding if Organic could be used by developers to identify design problems. To achieve this goal, we used a method from the Semiotic Engineering theory. This method enabled us to evaluate what are the tool issues that may hinder the identification of design problems in stinky code. Result Our study revealed that only 36.36% of the developers found more design problems when explicitly reasoning about multiple smells as compared to single smells. Moreover, 63.63% of the developers reported much lesser false positives when using the first approach as compared to the latter. The second study, in its turn, showed that most developers may be unable to identify design problems in stinky code without proper tool support. Conclusion Our experiences, in particular the second study, helped us to refine the features of Organic for better supporting developers in reflecting upon stinkier code. For example, analyses of stinky code scattered in class hierarchies or packages is often difficult, time-consuming, and requires proper visualization support. Moreover, without effective support, it remains time-consuming to discard stinky program locations that do not represent design problems.

This article addresses the concept of complexity and its effect on the logic of the design problem. It argues that the competing interpretations of complexity represent a logical antinomy (in the Kantian sense), and that this prevents the concept's further elaboration. It is necessary therefore to address the conditions that have produced this antinomy. Using the Hegelian category of the determination of reflection, complexity is then reconsidered as the effect of the circular logic by which a social system is defined. The complexity of the design problem is then redefined on the basis of this elaboration. [ABSTRACT FROM AUTHOR]

A lesson plan is a design problem for a teacher. The desired solution to this problem is to design an instructional process that can guide students in constructing an understanding of scientific concepts through their own thinking. This article demonstrates a practical approach to designing an effective lesson plan. The approach has five phases: listing the concepts in a lesson, proposing questions that can be answered by each concept, sequencing the questions according to the logic of student cognitive development, selecting resources and designing tasks to create learning situations, and applying knowledge to scientific research and real life. A meiosis lesson from a high school biology course serves as an example for understanding the solutions to problems that may arise in each phase. [ABSTRACT FROM AUTHOR]

Formulating and solving engineering problems and designing solutions that meet the established requirements are important skills that graduating engineering students need to possess. However, there are noticeable gaps in the literature with respect to understanding how the formulation of design problems and establishment of requirements affect the final design solution in undergraduate design education. This paper is an initial step to understand the influence of the content volume of the problem statement and requirements on the content volume of the final solution in capstone design projects. Content volume was used as a measure for this study as it provided a more objective way to measure the relation between problem statement, requirements, and final solutions as compared to other measures such as quality that are more subjective. In doing so, a document analysis of final reports from capstone design class collected over a period of 10 years is conducted. The findings of this research indicate that a low content volume of problem statement and requirements leads to no greater than a medium content volume in the final solution, whereas, a high content volume of final solution is more likely to result from either a high or medium content volume of problem statement and requirements. These findings are used to make several recommendations. Incorporating these recommendations while teaching capstone design classes can help students to improve the content volume of the problem statement and requirements. Thus, this assists in improving students' skills of formulating detailed problem statements and establishing requirements for their projects. [ABSTRACT FROM AUTHOR]

This study investigates the design problem of the linear sliding variable‐based sliding mode controllers of descriptor systems via output information. A generalised regular form, which is the counterpart of that for normal systems, is first recalled. Then a static output feedback sliding mode control strategy is developed to stabilise the descriptor system under consideration and the result is further improved by a reduced‐order observer‐based sliding mode control strategy. Necessary and sufficient conditions are derived such that the resulting sliding motion is regular and asymptotically stable. It is shown that the main merit of the static output feedback sliding mode control method is the simplicity and that of the reduced‐order observer‐based sliding mode control method is the elimination of a restrictive assumption frequently used in the static output feedback sliding mode control method. Finally, two connected one‐mass oscillators model is numerically simulated to testify the validity of the proposed methods. [ABSTRACT FROM AUTHOR]

Highlights • Inverse problems are solved to design the heat flux manipulating devices. • Thermal cloaking and shielding problems are reduced to control problems. • Particle swarm optimization is used to solve control problems. • Optimal solutions give simple rules of designing easily manufactured devices. Abstract Inverse problems associated with designing cylindrical thermal layered shielding and cloaking shells are studied. Using the optimization method these inverse problems are reduced to corresponding control problems. Thermal conductivities of the shell layers play the role of passive controls. A numerical algorithm based on the particle swarm optimization is proposed and the results of numerical experiments are discussed. Important properties of optimal solutions are established. Based on these properties simple design rules are formulated allowing to design cloaking and shielding shells which possess the best cloaking or shielding performance in addition to easy manufacturability. [ABSTRACT FROM AUTHOR]

This study solves a new fault detection strategy for vehicle active suspension systems in finite‐frequency domain. Three fault detection filters are constructed in different finite frequency domains, which ensure that the error between residuals and faults is minimum. The H∞ filter problem is used to figure out the design problem of fault detection. The conditions of residual systems meeting H∞ performance are obtained by considering generalised Kalman–Yakubovich–Popov lemma and stability theory. The problem of filter design is solved by an optimisation algorithm. Illustrative examples are given to show the proposed design method's effectiveness and potential. [ABSTRACT FROM AUTHOR]

The Research Cares With Examining The Nature Of The Architectural Image That Resulting From Contemporary Local Architecture Practice, After Becoming ICT And In Particular (The Internet) Is A Major Source Of The Information Required In Solving Design Problems. The Research Begins Interpretation Of The Origin Of The Design Problem, It Is The Existence Of A Human Need Updated Due To Man's Relationship To Its Environment And Other Individuals Within The Same Temporal And Spatial Environment, The Human Thought As (A Process Mentality To Present Information In Order To Reach The Desired), Represent The Basic Machine In The Production Of Architectural Form. Based On An Pilot Study Conducted By The Researchers, Were Identifier's Dialectical Image Prevalent In Contemporary Analogy, For The Production Of Local Architectural Forms, That Reflect The Demands Of Contemporary Identities, And Here Figured The Research Problem Of As (There Is No Clear Perception Of A Model For The Image Of The Controversy In The Local Thought After The Entry Of Information And Communication Technology As A Main Source Of Architectural Information). The Research Study The Domestic Practices In Order To Establish The First Model To That Image And Then Review The Information Contemporary Studies In Order To Determine The New Image Parameters And Install The Findings And Conclusions, Which Represents The Addition Of Contemporary Local Architectural Knowledge.

The maximum (minimum) effective stiffnesses of a corrugated plate with varying corrugation shape are determined. [ABSTRACT FROM AUTHOR]

This paper explores the optimal design problem of a linear time-invariant control system composed of three different types of linear parallel actuators. The actuators' time constants have been defined to achieve a conflicting behavior among the transient response provided by them. Thus, a novel solution has been proposed to find the best selection of actuators' gains to improve the performance parameters. Such methodology is based on a discrete multiobjective optimization technique. The transfer functions, as well as the transient response, have been derived and evaluated throughout this work. In addition, the stability conditions have been analyzed for a range of closed-loop poles and zeros. The discrete multiobjective optimization problem is formulated with a couple of objective functions: overshoot and settling time of the closed-loop response. A decision-making method has been used to find the best compromise solution from a group of candidate solutions. The results have indicated that a better performance can be achieved with a systematic multiobjective optimization methodology. [ABSTRACT FROM AUTHOR]

The purpose of the present article is to analyse textile teacher students' collaborative designing of a functional 3D textile puzzle for visually impaired children. The data collection took place across three sessions of collaborative designing: defining design constraints, visualization and building a mock-up. Twelve first-year university-level students, training to become textile teachers, participated in the study, working in four teams with three students in each team. We were interested in the nature of their design process and how kernels of design ideas were created and transformed during the collaborative design process. The analysis focused on the teams' design activities and content logs of the video data. The video-recorded data were segmented into two-minute intervals using INTERACT video analysis program. Each segment was classified according to seven observable design activities. This provided a macro level analysis for all design activities during each design session and data for further analysis of different orientations of teams. The results indicated that all teams engaged in progressive design processes and were able to create unique and practical design solutions. The design process turned out to be a problem driven in nature for two teams, whereas the other two teams engaged in a solution-driven design process. [ABSTRACT FROM AUTHOR]

Facility layout presents a complex design challenge. It is particularly regarded as a vital issue in Chinese society and throughout Asian countries where Feng Shui, the ancient and revered Chinese practice governing environmental esthetics, has played and continues to play a vital role in man-made design. In this research, the innovative merger of a fuzzy analytic hierarchy process and a fuzzy technique for order preference by similarity to ideal solution integrating a fuzzy multicriteria decision-making methodology is proposed for solving facility layout design evaluation problems. Our research draws on the traditional analytic methodology of the Feng Shui model and employs the proposed scheme for solving an actual office layout design evaluation problem. In a comparison of the results of our investigations, a positive numerical evaluation demonstrates the feasibility and efficiency of the proposed scheme, and suggests its applicability with other MCDM problems. [ABSTRACT FROM AUTHOR]

Methodology and software for multiversion setting and solution of high dimension design problems was developed. With simple examples, possibility of development of advanced bundled software, which allows updating the spacecraft design in real-time mode, is demonstrated. Mathematical models being in use in aerospace industry were applied. [ABSTRACT FROM AUTHOR]

An analysis of a design rationale focusing on the embodiment design stage is presented through the characterization of information describing design problems, alternative solutions, arguments, explanations and decisions of designers. The characterization of the design questions resulted from empirical research. The findings have been used to describe in detail elements of a design rationale capturing model. The main attributes describe this model during the embodiment phase of the product design, possible relations between the design rationale elements and the definition rules. [ABSTRACT FROM AUTHOR]

The paper focuses on the essentials of psychoanalytic process and change and the question of how the neural correlates and mechanisms of psychodynamic psychotherapy can be investigated. The psychoanalytic approach aims at enabling the patient to remember, repeat and work through concerning explicit memory. Moreover, the relationship between analyst and patient establishes a new affective configuration which enables a reconstruction of the implicit memory. If psychic change can be achieved it corresponds to neuronal transformation.Individualized neuro-imaging requires controlling and measuring of variables that must be defined. Two main methodological problems can be distinguished: The design problem addresses the issue of how to account for functionally related variables in an experimentally independent way. The translation problem raises the question of how to bridge the gaps between different levels of the concepts presupposed in individualized neuro-imaging (e.g. the personal level of the therapist and the client, the neural level of the brain).An overview of individualized paradigms, which have been used until now is given, including Operationalized Psychodynamic Diagnosis (OPD-2) and the Maladaptive Interpersonal Patterns Q-Start (MIPQS). The development of a new paradigm that will be used in fMRI experiments, the Interpersonal Relationship Picture Set (IRPS), is described. Further perspectives and limitations of this new approach concerning the design and the translation problem are discussed.

In the design process of products or systems, a current trend consists in taking into account judgments of users. In this context, a multiobjective optimisation method taking into account judgments of a panel of subjects is proposed. It is aimed at identifying the best trade-offs between quantitative objectives and judgments of users. The method is divided in two steps: (1) judgment data acquisition and (2) integration of the judgment data into the multiobjective optimisation process. The method is based on a stochastic Pareto-based evolutionary algorithm for optimisation and on a multilinear interpolation for judgment modelling. The combination of these techniques makes it possible to solve complex problems, with up to eight decision variables and up to at least eight objectives. Relevant applications of the method include optimisation with judgments about various aspects of the product or system, identification of the best trade-offs satisfying at the same time several groups with different judgments, and analysis of the interest of market segmentation. For illustration purpose, a pilot study about an individual office lighting design problem is processed. [ABSTRACT FROM AUTHOR]

A set of ellipses, with given semi-major and semi-minor axes, is to be cut from a rectangular design plate, while minimizing the area of the design rectangle. The design plate is subject to lower and upper bounds of its widths and lengths; the ellipses are free of any orientation restrictions. We present new mathematical programming formulations for this ellipse cutting problem. The key idea in the developed non-convex nonlinear programming models is to use separating hyperlines to ensure the ellipses do not overlap with each other. For small number of ellipses we compute feasible points which are globally optimal subject to the finite arithmetic of the global solvers at hand. However, for more than 14 ellipses none of the local or global NLP solvers available in GAMS can even compute a feasible point. Therefore, we develop polylithic approaches, in which the ellipses are added sequentially in a strip-packing fashion to the rectangle restricted in width, but unrestricted in length. The rectangle's area is minimized in each step in a greedy fashion. The sequence in which we add the ellipses is random; this adds some GRASP flavor to our approach. The polylithic algorithms allow us to compute good, near optimal solutions for up to 100 ellipses. [ABSTRACT FROM AUTHOR]

The article reports on the algorithm for the designing of led driver on the basis of the use of computer-aided design systems. Topics discussed include radiator projection, calculation of light characteristics, and calculation of transformers. Also discussed are the design problems, light-emitted diode systems, and optimization.

The article describes the lighting equipment design. The algorithmic procedures at all design stages are developed. [ABSTRACT FROM AUTHOR]

The paper focuses on the essentials of psychoanalytic process and change and the question of how the neural correlates and mechanisms of psychodynamic psychotherapy can be investigated. The psychoanalytic approach aims at enabling the patient to "remember, repeat, and work through" concerning explicit memory. Moreover, the relationship between analyst and patient establishes a new affective configuration which enables a reconstruction of the implicit memory. If psychic change can be achieved it corresponds to neuronal transformation. Individualized neuro-imaging requires controlling and measuring of variables that must be defined. Two main methodological problems can be distinguished: the design problem addresses the issue of how to account for functionally related variables in an experimentally independent way. The translation problem raises the question of how to bridge the gaps between different levels of the concepts presupposed in individualized neuro-imaging (e.g., the personal level of the therapist and the client, the neural level of the brain). An overview of individualized paradigms, which have been used until now is given, including Operationalized Psychodynamic Diagnosis (OPD-2) and the Maladaptive Interpersonal Patterns Q-Start (MIPQS). The development of a new paradigm that will be used in fMRI experiments, the "Interpersonal Relationship Picture Set" (IRPS), is described. Further perspectives and limitations of this new approach concerning the design and the translation problem are discussed. [ABSTRACT FROM AUTHOR]

The purposes of this study were two fold. We sought to examine whether the Metacognitive Awareness Inventory (MAI) (Schraw & Dennison, 1994) was able to provide a six factor solution, and to track the shift in metacognition of 294 pre-service teachers in Singapore. We found that undergraduate and graduate pre- service teachers performed significantly different in most of the sub-components of metacognition in the post test. Small incremental changes in these sub-components in terms of pre and post test were highlighted. The implications of these results were discussed. [ABSTRACT FROM AUTHOR]

Abstract: A Cellular Automata approach is introduced in this paper for the optimal design of sewer network problems. The solution of sewer network optimization problems requires the determination of pipe diameters and average pipe cover depths, minimizing the total cost of the sewer network subject to operational constraints. One constraint of the problem, namely, the maximum relative depth of flow, is first used to define the pipe diameters in terms of the pipe slope and, hence, the nodal elevation of the network. As a result, the sewer network optimization problem is redefined, in terms of the network nodal elevations, and the resulting problem is solved using a Cellular Automata (CA) approach. The nodes of the network are used as the CA cell, with the corresponding elevations as CA cell states. The updating rule of the proposed CA is then derived by requiring the stationary total penalized objective function of the problem, with respect to the cell state. The proposed method is used to solve two benchmark examples and the results are compared to those obtained by other methods. The results indicate that the proposed method is highly efficient compared to alternative methods, while producing comparable results. [Copyright &y& Elsevier]

Quantum computing offers new concepts for the simulation of complex physical systems. A quantum computing algorithm for electromagnetic field simulation is presented here. The electromagnetic field simulation is performed on the basis of the Transmission Line Matrix (TLM) method. The Hilbert space formulation of TLM allows us to obtain a time evolution operator for the TLM method, which can then be interpreted as the time evolution operator of a quantum system, thus yielding a quantum computing algorithm. Further, the quantum simulation is done within the framework of the quantum circuit model of computation. Our aim has been to address the design problem in electromagnetics—given an initial condition and a final field distribution, find the structures which satisfy these. Quantum computing offers us the possibility to solve this problem from first principles. Using quantum parallelism we simulate a large number of electromagnetic structures in parallel in time and then try to filter out the ones which have the required field distribution. [ABSTRACT FROM AUTHOR]

In the design of materials for the shielding of electric devices, there is a recent trend to use multilayer compounds due to some restrictions in the making process of the materials but also since they are supposed to have a higher potential to offer “better” characteristics than the related monolayered materials. In this work, we investigate the possible impact of the number of layers in a compound critically. It will turn out that—at least for the general objectives we study here and for conducting polymer composites—multilayered materials are suitable to only a limited extent. To be more precise, when “just” aiming for a high shielding efficiency the task can be accomplished with merely one layer. If in addition the cost of the material comes into play, however, a second layer may be helpful, but further layers do not seem to have a significant impact on the performance of a material. Here we extend an existing multiobjective design problem for the design of shielding materials for our purpose, and attack the resulting multiobjective optimization problem with evolutionary strategies, and finally analyze the results in the viewpoint of the required number of layers within a shielding material. [ABSTRACT FROM AUTHOR]

A set of circles, rectangles, and convex polygons are to be cut from rectangular design plates to be produced, or from a set of stocked rectangles of known geometric dimensions. The objective is to minimize the area of the design rectangles. The design plates are subject to lower and upper bounds of their widths and lengths. The objects are free of any orientation restrictions. If all nested objects fit into one design or stocked plate the problem is formulated and solved as a nonconvex nonlinear programming problem. If the number of objects cannot be cut from a single plate, additional integer variables are needed to represent the allocation problem leading to a nonconvex mixed integer nonlinear optimization problem. This is the first time that circles and arbitrary convex polygons are treated simultaneously in this context. We present exact mathematical programming solutions to both the design and allocation problem. For small number of objects to be cut we compute globally optimal solutions. One key idea in the developed NLP and MINLP models is to use separating hyperplanes to ensure that rectangles and polygons do not overlap with each other or with the circles. Another important idea used when dealing with several resource rectangles is to develop a model formulation which connects the binary variables only to the variables representing the center of the circles or the vertices of the polytopes but not to the non-overlap or shape constraints. We support the solution process by symmetry breaking constraints. In addition we compute lower bounds, which are constructed by a relaxed model in which each polygon is replaced by the largest circle fitting into that polygon. We have successfully applied several solution techniques to solve this problem among them the Branch&Reduce Optimization Navigator ( BARON) and the LindoGlobal solver called from GAMS, and, as described in Rebennack et al. [21], a column enumeration approach in which the columns represent the assignments. Good feasible solutions are computed within seconds or minutes usually during preprocessing. In most cases they turn out to be globally optimal. For up to 10 circles, we prove global optimality up to a gap of the order of 10−8 in short time. Cases with a modest number of objects, for instance, 6 circles and 3 rectangles, are also solved in short time to global optimality. For test instances involving non-rectangular polygons it is difficult to obtain small gaps. In such cases we are content to obtain gaps of the order of 10%. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with the laminated plate design problem formulated as follows: Find all designs giving the plate the required mechanical properties. The paper presents a complete analysis of the main types of design problems for the case when a given set of homogeneous isotropic materials is available to manufacture the plate. Solution of the design problem is obtained using the convex combinations problem technique. [Copyright &y& Elsevier]

The problem of design of laminated plates with specified stiffness and strength characteristics is considered. The starting design problem is reduced to the convex‐combination problems, which is solved by the convolution method. The following design problems are solved: design with allowance for strength, design of a laminated plate of unconstrained thickness, and design for approximately specified characteristics. [ABSTRACT FROM AUTHOR]