Integrated multiobjective optimization and a priori preferences using genetic algorithms

One of the tasks of decision-making support systems is to develop methods that help the designer select a solution among a set of actions, e.g. by constructing a function expressing his/her preferences over a set of potential solutions. In this paper, a new method to solve multiobjective optimization (MOO) problems is developed in which the user’s information about his/her preferences is taken into account within the search process. Preference functions are built that reflect the decision-maker’s (DM) interests and use meaningful parameters for each objective. The preference functions convert these objective preferences into numbers. Next, a single objective is automatically built and no weight selection is performed. Problems found due to the multimodality nature of a generated single cost index are managed with Genetic Algorithms (GAs). Three examples are given to illustrate the effectiveness of the method.     

Evolutionary multiobjective industrial design: the case of a racing car tire-suspension system

When dealing with multiobjective optimization (MO) of the tire-suspension system of a racing car, a large number of design variables and a large number of objectives have to be taken into account. Two different models have been used, both validated on data coming from an instrumented car, a differential equation-based physical model, and a neural network purely numerical model. Up to 23 objective functions have been defined, at least 14 of which are in strict conflict of each other. The equivalent scalar function based and the objective-as-constraint formulations are intentionally avoided due to their well-known limitations. A fuzzy definition of optima, being a generalization of Pareto optimality, is applied to the problem. The result of such an approach is that subsets of Pareto optimal solutions (on such a problem, a big portion of the entire search space) can be properly selected as a consequence of input from the designer. The obtained optimal solutions are compared with the reference vehicle and with the optima previously obtained with design of experiment techniques and different MO optimization strategies. The proposed strategy improves both the reference (actual) car and previously obtained optima (scalar preference function) in the majority of objectives with technically significant improvements. Moreover, the strategy offers an univoque criterion for the choice among tradeoff solutions in the 14-dimensional objective space. The problem is used as a test of a proposed optimal design strategy for industrial problems, integrating differential equation and neural networks modeling, design of experiments, MO, and fuzzy optimal-based decision making. Such a linked approach gives also a unified view of where to concentrate the computational effort.     

Evolutionary multi-objective optimisation with preferences for multivariable PI controller tuning

Multi-objective optimisation design procedures have shown to be a valuable tool for control engineers. They enable the designer having a close embedment of the tuning process for a wide variety of applications. In such procedures, evolutionary multi-objective optimisation has been extensively used for PI and PID controller tuning; one reason for this is due to their flexibility to include mechanisms in order to enhance convergence and diversity. Although its usability, when dealing with multi-variable processes, the resulting Pareto front approximation might not be useful, due to the number of design objectives stated. That is, a vast region of the objective space might be impractical or useless a priori, due to the strong degradation in some of the design objectives. In this paper preference handling techniques are incorporated into the optimisation process, seeking to improve the pertinency of the approximated Pareto front for multi-variable PI controller tuning. That is, the inclusion of preferences into the optimisation process, in order to seek actively for a pertinent Pareto front approximation. With such approach, it is possible to tune a multi-variable PI controller, fulfilling several design objectives, using previous knowledge from the designer on the expected trade-off performance. This is validated with a well-known benchmark example in multi-variable control. Control tests show the usefulness of the proposed approach when compared with other tuning techniques.     

Control of robust design in multiobjective optimization under uncertainties

In design and optimization problems, a solution is called robust if it is stable enough with respect to perturbation of model input parameters. In engineering design optimization, the designer may prefer a use of robust solution to a more optimal one to set a stable system design. Although in literature there is a handful of methods for obtaining such solutions, they do not provide a designer with a direct and systematic control over a required robustness. In this paper, a new approach to robust design in multiobjective optimization is introduced, which is able to generate robust design with model uncertainties. In addition, it introduces an opportunity to control the extent of robustness by designer preferences. The presented method is different from its other counterparts. For keeping robust design feasible, it does not change any constraint. Conversely, only a special tunable objective function is constructed to incorporate the preferences of the designer related to the robustness. The effectiveness of the method is tested on well known engineering design problems.     

A new graphical visualization of n-dimensional Pareto front for decision-making in multiobjective optimization

New challenges in engineering design lead to multiobjective (multicriteria) problems. In this context, the Pareto front supplies a set of solutions where the designer (decision-maker) has to look for the best choice according to his preferences. Visualization techniques often play a key role in helping decision-makers, but they have important restrictions for more than two-dimensional Pareto fronts. In this work, a new graphical representation, called Level Diagrams, for n-dimensional Pareto front analysis is proposed. Level Diagrams consists of representing each objective and design parameter on separate diagrams. This new technique is based on two key points: classification of Pareto front points according to their proximity to ideal points measured with a specific norm of normalized objectives (several norms can be used); and synchronization of objective and parameter diagrams. Some of the new possibilities for analyzing Pareto fronts are shown. Additionally, in order to introduce designer preferences, Level Diagrams can be coloured, so establishing a visual representation of preferences that can help the decision-maker. Finally, an example of a robust control design is presented - a benchmark proposed at the American Control Conference. This design is set as a six-dimensional multiobjective problem.     

A hypernetwork-based context-aware approach for design lesson-learned knowledge proactive feedback in design for manufacturing

Design lesson-learned knowledge (DLK) clearly describes various design quality problems exposed in past manufacturing stages, solutions and preventive measures. If knowledge management system could proactively feed DLK back into design process, many previous quality problems would be avoided, thus helping designers better implement design for manufacturing (DFM) in a smarter manner. However, since design quality problems are not pointed out in design process, problem-relevant information extracted from design contexts might be inaccurate. In this situation, traditional context-aware approach is prone to acquire design quality problems that designers do not need. Facing these challenges, a hypernetwork-based context-aware DLK proactive feedback approach is proposed to construct hypernetwork-based DLK representation model and predict possible design quality problems in the design process, thus providing corresponding DLK and helping designers reduce the reoccurrence of previous quality problems in DFM. Specifically, hypernetwork-based DLK representation model is first constructed, which consists of designer context network, task context network and DLK network. Based on this model, a context-aware collaborative reason strategy is constructed to predict possible design quality problems according to complex design contexts. To validate the proposed approach, a practical product development case on the shipbuilding design is implemented, and some comparative experiments are conducted. Experiment results show the proposed approach is effective and has a positive performance in DFM. It is anticipated this work opens up a promising way to help designers reuse DLK for reducing the reoccurrence of previous design quality problems in a smarter manner, thus better implementation of DFM.     

Structural optimization of multiple attributes

This paper presents a methodology for structural design optimization of multiple objectives, or attributes. The method represents an improvement over Pareto optimizationbased methods by quantitatively representing trade-offs between conflicting objectives in a single multi-attribute objective function. Classical utility analysis is first used to determine a multi-attribute evaluation function for a particular structure from the designer's viewpoint. This viewpoint takes into account the attribute tradeoffs that are appropriate for a specific project. Since attributes are controlled only indirectly through specification of design decision variables, a new objective function is then formulated which expresses design utility directly in terms of those parameters over which the designer has direct control. A one-bay, three storey steel frame building example demonstrates the methodology for determining the design configuration with the best combination of cost and drift index.     

Divergent exploration in design with a dynamic multiobjective optimization formulation

Formulation space exploration is a new strategy for multiobjective optimization that facilitates both divergent exploration and convergent optimization during the early stages of design. The formulation space is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into the formulation space, the solution to an optimization problem is no longer predefined by any single problem formulation, as it is with traditional optimization methods. Instead, a designer is free to change, modify, and update design objectives, variables, and constraints and explore design alternatives without requiring a concrete understanding of the design problem a priori. To facilitate this process, we introduce a new vector/matrix-based definition for multiobjective optimization problems, which is dynamic in nature and easily modified. Additionally, we provide a set of exploration metrics to help guide designers while exploring the formulation space. Finally, we provide an example to illustrate the use of this new, dynamic approach to multiobjective optimization.     

Integration of design and manufacturing for structural shape optimization

This paper presents an integrated design and manufacturing approach that supports shape optimization of structural components. The approach starts from a primitive concept stage, where boundary and loading conditions of the structural component are given to the designer. Topology optimization is conducted for an initial structural layout. The discretized structural layout is smoothed using parametric B-Spline surfaces. The B-Spline surfaces are imported into a CAD system to construct parametric solid models for shape optimization. Virtual manufacturing (VM) techniques are employed to ensure that the optimized shape can be manufactured at a reasonable cost. The solid freeform fabrication (SFF) system fabricates physical prototypes of the structure for design verification. Finally, a computer numerical control (CNC) machine is employed to fabricate functional parts as well as mold or die for mass production of the structural component. The main contribution of the paper is incorporating manufacturing into the design process, where manufacturing cost is considered for design. In addition, the overall design process starts from a primitive stage and ends with functional parts. A 3D tracked vehicle roadarm is employed throughout this paper to illustrate the overall design process and various techniques involved.     

Optimal synthesis of planar mechanisms via an extensible-link approach

This paper presents a novel approach to optimize the design of planar mechanisms with revolute joints for function generation or path synthesis. The proposed method is based on the use of an extensible-link mechanism model whose strain energy is minimized to find the optimal rigid design. This enables us to get rid of assembly constraints and the use of natural coordinates makes the objective function simpler. Two optimization strategies are developed and then discussed. The first one relies on alternate optimizations of design parameters and point coordinates. The second one uses multiple partial syntheses as starting point for a full synthesis process. The question of finding the global optimum is also addressed and developed. A simple algorithm is proposed to find several local optima among which the designer may choose the best one taking other criteria into account (e.g. stiffness, collision, size,...). Three applications are presented to illustrate the strategies while mentioning their limits.     

A decision support system for material and manufacturing process selection

The material and manufacturing process selection problem is a multi-attribute decision-making problem. These decisions are made during the preliminary design stages in an environment characterized by imprecise and uncertain requirements, parameters, and relationships. Material and process selection decisions must occur before design for manufacturing can begin. This paper describes a prototype material and manufacturing process selection system called MAMPS that integrates a formal multi-attribute decision model with a relational database. The decision model enables the representation of the designer's preferences over the decision factors. A compatibility rating between the product profile requirements and the alternatives stored in the database for each decision criteria is generated using possibility theory. The vector of compatibility ratings are aggregated into a single rating of that alternative's compatibility. A ranked set of compatible material and manufacturing process alternatives is output by the system. This approach has advantages over existing systems that either do not have a decision module or are not integrated with a database.     

Design of heterogeneous turbine blade

Constantly rising operating pressure and temperature in turbine drivers push the material capabilities of turbine blades to the limit. The recent development of heterogeneous objects by layered manufacturing offers new potentials for the turbine blades. In heterogeneous turbine blades, multiple materials can be synthesized to provide better properties than any single material. A critical task of such synthesis in turbine blade design is an effective design method that allows a designer to design geometry and material composition simultaneously.This paper presents a new approach for turbine blade design, which ties B-spline representation of a turbine blade to a physics (diffusion) process. In this approach, designers can control both geometry and material composition. Meanwhile, material properties are directly conceivable to the designers during the design process. The designer's role is enhanced from merely interpreting the optimization result to explicitly controlling both material composition and geometry according to the acquired experience (material property constraints).The mathematical formulation of the approach includes three steps: using B-spline to represent the turbine blade, using diffusion equation to generate material composition variation, using finite element method to solve the constrained diffusion equation. The implementation and examples are presented to validate the effectiveness of this approach for heterogeneous turbine blade design.     

Domain independent shell for DfM and its application to sheet metal forming and injection molding

The objective for this research is to streamline design for manufacturing (DfM) analysis across all manufacturing domains and to provide transparency for DfM measures and evaluation process used. Generic steps are identified for performing manufacturability analysis and the design of a customizable manufacturability evaluation shell is presented. The shell covers several stages of manufacturability analysis (technical, economic) and can perform analyses at different levels of abstraction (qualitative, quantitative). The shell provides feedback to the designer at each level during the design process. By separating domain-specific knowledge from domain independent knowledge and creating an open architecture, the shell can be customized and expanded by the knowledge engineer and the user. The architecture of the shell is presented and its applications to manufacturability analysis for two domains, sheet metal and injection molding, are illustrated.     

Interfacing CAD and CAM—A study in hole design

Computer Aided Design (CAD) and Computer Aided Manufacturing (CAM) are modern tools for both the designer and manufacturing engineer. These two tools, however, are not usually integrated into one system. In this study, an effort has been made to connect design and manufacturing by interfacing them into a unified software system. Through this demonstrative CAD/CAM package, the designer interacts with a graphics terminal to enter hole design details; these, in turn, are sent to a generative automatic process planning routing which defines appropriate process plans. In addition, a cost estimate is given which provides the designer with a measure of the economic effectiveness of his design. In the future, it will be possible to interface such systems with part programming routines to obtain explicit machine control information. Such a system represents a significant step toward making totally automated manufacturing a reality.     

A modified directed search domain algorithm for multiobjective engineering and design optimization

Multiobjective optimization is one of the key challenges in engineering design process. Since the answer to such problem is not unique, a set of evenly distributed solutions is particularly important for a designer. The Directed Search Domain (DSD) method is a numerical optimization approach that has proven to be efficient enough to tackle such optimization problems. In this paper, we propose two modifications to the DSD approach which make the solution algorithm simpler for program implementation. These modifications are related to the control of the search domain and reformulation of the appropriate single objective optimization problem. As a result, the computational efficiency of the method is increased due to the lower number of objective function evaluations. The capabilities of the new approach are demonstrated on a set of test cases.     

Group decision making to better respond customer needs in software development

Quality Function Deployment (QFD) is a well-known planning methodology for translating customer needs into relevant design and production requirements. The intent of applying QFD is to incorporate the voice of the customer into the various phases of the product development cycle for a new product, or a new version of an existing product. The traditional QFD structure requires individuals to express their preferences in a restricted scale without exceptions. In practice, people contributing to the process tend generally to give information about their personal preferences in many different ways, numerically or linguistically, depending on their background. Moreover, collaborative decision-making is not an emphasized issue in QFD even though it requires several people's involvement. In this study, we extend the QFD methodology by introducing a new group decision making approach that takes into account multiple preference formats and fusing different expressions into one uniform group decision by means of fuzzy set theory. An application on software development is supplied to illustrate the approach.     

Facility layout design using a multi‐objective interactive genetic algorithm to support the DM

The unequal area facility layout problem (UA‐FLP) has been addressed by many methods. Most of them only take aspects that can be quantified into account. This contribution presents a novel approach, which considers both quantitative aspects and subjective features. To this end, a multi‐objective interactive genetic algorithm is proposed with the aim of allowing interaction between the algorithm and the human expert designer, normally called the decision maker (DM) in the field of UA‐FLP. The contribution of the DM's knowledge into the approach guides the complex search process, adjusting it to the DM's preferences. The entire population associated to facility layout designs is evaluated by quantitative criteria in combination with an assessment prepared by the DM, who gives a subjective evaluation for a set of representative individuals of the population in each iteration. In order to choose these individuals, a soft computing clustering method is used. Two interesting real‐world data sets are analysed to empirically probe the robustness of these models. The first UA‐FLP case study describes an ovine slaughterhouse plant and the second, a design for recycling carton plant. Relevant results are obtained, and interesting conclusions are drawn from the application of this novel intelligent framework.     

Design of parts for cellular manufacturing using neural network-based approach

A neural network approach is applied to the problem of integrating design and manufacturing engineering. The self organising map (SOM) neural network recognizes products and parts which are modeled as boundary representation (B-rep) solids using a modified face complexity code scheme adopted, and forms the necessary feature families. Based on the part features, machines, tools and fixtures are selected. These information are then fed into a four layer feed-forward neural network that provides a designer with the desired features that meet the current manufacturing constraints for design of a new product or part. The proposed methodology does not involve training of the neural networks used and is seen to be a significant potential for application in concurrent engineering where design and manufacturing are integrated.     

Simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection

Tolerance specification is an important part of mechanical design. Design tolerances strongly influence the functional performance and manufacturing cost of a mechanical product. Tighter tolerances normally produce superior components, better performing mechanical systems and good assemblability with assured exchangeability at the assembly line. However, unnecessarily tight tolerances lead to excessive manufacturing costs for a given application. The balancing of performance and manufacturing cost through identification of optimal design tolerances is a major concern in modern design. Traditionally, design tolerances are specified based on the designer’s experience. Computer-aided (or software-based) tolerance synthesis and alternative manufacturing process selection programs allow a designer to verify the relations between all design tolerances to produce a consistent and feasible design. In this paper, a general new methodology using intelligent algorithms viz., Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi Objective Particle Swarm Optimization (MOPSO) for simultaneous optimal selection of design and manufacturing tolerances with alternative manufacturing process selection is presented. The problem has a multi-criterion character in which 3 objective functions, 3 constraints and 5 variables are considered. The average fitness factor method and normalized weighted objective functions method are separately used to select the best optimal solution from Pareto optimal fronts. Two multi-objective performance measures namely solution spread measure and ratio of non-dominated individuals are used to evaluate the strength of Pareto optimal fronts. Two more multi-objective performance measures namely optimiser overhead and algorithm effort are used to find the computational effort of NSGA-II and MOPSO algorithms. The Pareto optimal fronts and results obtained from various techniques are compared and analysed.     

Designer’s preferences regarding equality constraints in robust design optimization

Robust design optimization (RDO) problems can generally be formulated by appropriately incorporating uncertainty into the corresponding deterministic optimization problems. Equality constraints in the deterministic problem need to be carefully formulated into the RDO problem because of the strictness associated with their feasibility. In this context, equality constraints have been generally classified into two types: (1) those that must be satisfied regardless of uncertainty, examples include physics-based constraints, such as F = ma, and (2) those that cannot be satisfied because of uncertainty, which are typically designer-imposed, such as dimensional constraints. This paper addresses the notion of preferred degree of satisfaction of deterministic equality constraints under uncertainty. Whether or not a particular equality constraint can be exactly satisfied depends on the statistical nature of the design variables that exist in the constraint and on the designer’s preferences. In this context, this paper puts forth three contributions. First, we develop a comprehensive classification of equality constraints in a way that is mutually exclusive and collectively exhaustive. Second, we present a rank-based matrix approach to interactively classify equality constraints, which systematically incorporates the designer’s preferences into the classification process. Third, we present an approach to incorporate the designer’s intra-constraint and inter-constraint preferences for designer-imposed constraints into the RDO formulation. Intra-constraint preference expresses how closely a designer wishes to satisfy a particular constraint; for example, in terms of its mean and standard deviation. A designer may express inter-constraint preference if satisfaction of a particular designer-imposed constraint is more important than that of another. We present an optimization formulation that incorporates the above discussed constraint preferences, which provides the designer with the means to explore design space possibilities. The formulation entails interesting implications in terms of decision making. Two engineering examples are provided to illustrate the practical usefulness of the developments proposed in this paper.