Design optimization involves the following stages: [1] [2] The formal mathematical (standard form) statement of the design optimization problem is [3]
where The problem formulation stated above is a convention called the negative null form, since all constraint function are expressed as equalities and negative inequalities with zero on the right-hand side.
This convention is used so that numerical algorithms developed to solve design optimization problems can assume a standard expression of the mathematical problem.
to rewrite the above statement in the compact expression
the set or system of (functional) constraints and
When the objective function f is a vector rather than a scalar, the problem becomes a multi-objective optimization one.
If the design optimization problem has more than one mathematical solutions the methods of global optimization are used to identified the global optimum.
Optimization Checklist [2] A detailed and rigorous description of the stages and practical applications with examples can be found in the book Principles of Optimal Design.
Practical design optimization problems are typically solved numerically and many optimization software exist in academic and commercial forms.
Several books, articles and journal publications are listed below for reference.
One modern application of design optimization is structural design optimization (SDO) is in building and construction sector.
SDO emphasizes automating and optimizing structural designs and dimensions to satisfy a variety of performance objectives.
These advancements aim to optimize the configuration and dimensions of structures to optimize augmenting strength, minimize material usage, reduce costs, enhance energy efficiency, improve sustainability, and optimize several other performance criteria.
Concurrently, structural design automation endeavors to streamline the design process, mitigate human errors, and enhance productivity through computer-based tools and optimization algorithms.
Prominent practices and technologies in this domain include the parametric design, generative design, building information modelling (BIM) technology, machine learning (ML), and artificial intelligence (AI), as well as integrating finite element analysis (FEA) with simulation tools.