Optimisation in Product Design Engineering

What is optimisation?

The optimisation is a wide concept, which the most people understand it intuitively but cannot explain it so easily. To define what is optimisation and how to get it, we will restrict this concept only for design and engineering of tangibles products with the aim to go to the market.

In this universe, there are several metrics to be considerate, where these are chosen at initial steps of the product development, coming from various strategies such as Design Thinking, Double Diamond, Product Design Specification, Total Design Methodology etc. In this step are defined which of metrics have more importance or weight, according to of the design targets chosen. Most of metrics exist due that our real world has restrictions such as cost, energy, material, time, environment etc. In a competitive market, continuous endeavour to make better and cheaper products is the only way to survive through the time. Another advantage of optimising products is that less material and energy are used to make or use them (less weight or less maintenance for instance), and this is good for the environment by the time that a change in production paradigm with reduction of resources is coming (Capra, 1982). To get better, competitive and eco-friendly products is necessary to look for an optimised design. 

In sum, in this case, optimisation can be understood as the best solution possible that will satisfy all metrics selected for making a specific product design respecting the priority of these metrics.

Problem Optimisation Approach

Once known the metrics to be considered for the product design (more about design metrics will be discussed in a future post here), the second step is how to equation it to find the best region to work. This step is not an easy task in the case which there are several variables in the project. Traditional methods like try and faults or trust on designer/engineer experience, supported by empiric or parametric processes, is not enough to solve complex problems, and several amounts of time and resources could be lost. The ideal approach should equation the problem in an analytical function, but in the most of engineering problems, it is no possible to be described, being necessary a numerical approach supported by computerised routine and software (Paredes, 2016). This condition, in which several quantities of variables and interactions are required, forces us to look for computational algorithms as a tool to supporting us in the search for the best solution in less time and resources. Numerous outputs values can be generated for each alteration in input values, creating a conjunct of possible solutions to be analysed. To support the search for the solution, it is essential to convert the problem into mathematical language. The formal description of an optimisation problem is Maximise (or Minimise) desired functions and minimised (or Maximise) undesired functions. In a mathematical description it is:

Where f_m(x) are objective functions, that are project goals in which if want to minimise or maximise. If m=1, the problem is mono-objective, if m≥2 the problem is multi-objective. g(x) and h(x) are constraint functions, and x is a vector of n decisions variables. This last one is the restrict conjunct, called Variables Limits, where there are all possible solutions, that to be valid, must respect all restrictions g(x) and h(x). It is bounded by limits values x_k^min (lower) and x_k^max (higher) that establish the decision space.

Examples of an objective function are efficiency, cost, thermal exchange, friction, stress, natural frequency and another. Inputs variables are all parameters that we have the freedom to change from objective function, for instance: materials, dimensions and form, operations conditions and another. Examples of constraints are standards, manufacturing, mass or volume, displacement, Tensile Yield Strength and another. 

In a multi-objective optimisation problem (MOOP), each function has the objective to minimise or maximise and in general, there is not only one solution that is optimum for all goals, once usually objectives are conflicting. In this case, increase the resolution of a function will necessarily decrease the resolution of other function (Pareto´s Optimal Boundary). The most of real-life problems are MOOP and to solve it, there is a conjunct of possible solutions. 

In literature, there are several techniques to solve mono and multi-objective optimisation problems. As is not the goal of this dissertation discussing them in depth, we will just list some of the most commons techniques.

Some commons techniques solutions of optimisation problems:

• Ant Colony Optimisation
• Direct-Search
• Elitist Non-Dominated Sorting Genetic Algorithms
• Genetic or Evolutionary Algorithm
• Gradient Methods
• Heuristics
• Interactive Optimisation
• Lagrangian Relaxation
• Meta-Heuristics
• Mono/Multi-objective Particle Swarm Optimisation
• Neural Networks
• Pareto Optimal Boundary
• Swarm Intelligence

Structural Optimisation

Currently, is common to divide structural optimisation into four types: Parametric or Dimensional Optimisation, Shape Optimisation, Topology Optimisation and Topographic Optimisation.

• Parametric or Sizing Optimisation: Do not change the structural form, but only its dimensions (Figure 1).

Figure 1 - Illustration of sizing optimisation.

• Shape Optimisation: The external shape is altered. More possibilities are made than parametric optimisation (Figure 2). 

Figure 2 - Illustration of shape optimisation.

• Topology Optimisation: The material is distributed for each domain point, changing internal and boundary geometry. This method is that can remove more material and make more possibilities (Figure 3).

Figure 3 - Illustration of topology optimisation.

• Topographic Optimisation: Applied to shell structures. It works mixing the concepts of parametric and topology optimisation (Figure 4).

Figure 4 - Example of topography optimisation (FONT: Altair).

Bibliography:

Capra, F. (1982). The turning point: Science, society, and the rising culture. New York: Simon and Schuster.

Paredes, B. (2016). OTIMIZAÇÃO EM ENGENHARIA. Retrieved March 11, 2018, from https://www.esss.co/blog/otimizacao-em-engenharia/