Trade Studies: the Tug of War Between Competing Objectives

The phrase “you’re the choices you make” is just as relevant in business. There is never a one-size-fits-all solution. In the end, a company must balance competing objectives when finalising a design, in the hope that the decision leads to a profitable outcome. These design choices ultimately define their product’s identity.

In engineering terms, this process is known as a “trade study”. Trade studies can take many forms, from simple Excel spreadsheets and PowerPoint slides to in-depth, marathon-style design reviews. In this article, I’ll explore a more data-driven and robust approach, ideal for tackling challenges in the most competitive and complex industries.

What is Multi-Objective optimisation?

Multi-Objective optimisation (MOO) addresses optimisation problems that involve multiple, often competing, objectives. It provides a mathematical approach to conducting trade studies, enhancing the traditional method of comparing designs against a set of criteria.

Engineers are used to evaluating designs presented in a table, showing each option’s strengths and weaknesses in certain aspects. What MOO adds to this process is the ability to quantify the trade-offs between various objectives. For example, you might discover that through relaxing a safety constraint by just 1% (while still complying with regulations), you could gain a 50% increase in performance!

Instead of yielding a single optimal solution, MOO generates a family of designs known as the Pareto front. Each solution on the Pareto front is nondominated, meaning that no single option is superior across all objectives — they all offer a balanced trade-off between the competing criteria. This is particularly valuable as it allows for more robust decisions to be made later in the process when additional information is available. Executive and commercial teams can also assess each optimal solution more quantitatively, choosing the design that best aligns with their business objectives.

Story Time: Using MOO to Identify the Best Product-Market Fit

In a previous aircraft development project, we faced what seemed like an impossible challenge. Our C-suite decided to target one of the most difficult regions for the aircraft to operate in. Due to the high density altitude in this area, the aircraft needed to operate with a reduced payload to compensate for diminished performance.

In aircraft design, the trade-off between payload and range is often regarded as the “grandfather” of all trade studies. To meet the demands of operating in this challenging region, we had two primary options: compromise on payload to maintain range or increase the design payload with a reduction in range. Additionally, we had to consider that designing an aircraft optimized for the most demanding environment might result in a less attractive product for other markets. Therefore, we needed to remain flexible and consider the possibility of relaxing this requirement if necessary.

Evaluating all these options fairly and robustly is challenging when information is disorganised and scattered across qualitative assessments and charts that capture only part of the picture. This is where Multi-Objective Optimisation becomes essential. By framing this challenge as an MOO problem, we could visualise the markets that different aircraft designs could capture, quantify the trade-offs required to meet these goals, and assess the compromises needed to succeed in the most challenging regions.

MOO provided invaluable design insights, leading to a more informed decision-making process. This approach allowed the company to develop a strategy for releasing their aircraft that would ensure long-term growth and profitability.

MOO — A Practical Implementation Guide

While a traditional trade study might involve manually comparing a handful of options, Multi-Objective optimisation can simultaneously evaluate hundreds or even thousands of alternatives, presenting a family of optimal solutions. This empowers decision-makers to identify the best possible trade-offs and select the design that aligns most closely with their objectives.

With that in mind, let’s dive into the practical implementation of MOO in industry, exploring state-of-the-art algorithms, its integration with Model-Based Systems Engineering and synergy with Business Intelligence tools.

State-of-the-Art Algorithms

One of the most straightforward algorithms to solve a Multi-Objective optimisation problem is the Epsilon-Constraint method. This approach optimizes one objective while treating the others as fixed constraints. In a two-objective scenario, this can be visualised as introducing a vertical line that represents a constraint on the first objective, 𝑓₁, and then optimizing the second objective, 𝑓₂. The result is a single point on the Pareto set. By gradually moving this vertical line across the solution space, the entire Pareto set can be mapped out.

However, a limitation of the Epsilon-Constraint method is that adjusting the fixed constraint by a set amount in each iteration often results in a non-uniformly spaced Pareto front. This uneven granularity can be problematic, particularly in areas of the solution space that are of high interest. To overcome this, the Normal Boundary Intersection (NBI) method offers an alternative by searching the solution space starting from a line that connects the optima of each objective. The rationale is that even spacing along this line is more likely to produce an evenly spaced Pareto front.

Both methods ultimately reduce the MOO problem to a series of single-objective optimisation tasks, where techniques from Multidisciplinary Design optimisation (MDO) can be applied — especially in the development of complex systems.

Want to learn more about Multidisciplinary Design optimisation? Check out our previous article here.

Another widely used approach involves Evolutionary Algorithms (EA), such as Genetic Algorithms (GA). These algorithms are inspired by the process of natural selection and evolution. They typically start with a population of potential designs, from which parents are selected based on their ranks in the objectives. New generations of designs are then created through recombination of parent pairs, with occasional random mutations to maintain diversity within the population. This iterative process continues until a predefined stopping criterion is met, progressively refining the solutions to approach the optimal set.

Bridging the Gap with Model-Based Systems Engineering

The importance of an effective and sustainable workflow in product optimisation cannot be overstated. That’s why we believe Model-Based Systems Engineering is crucial for successfully implementing Multi-Objective optimisation in the development of complex systems.

Even in the most advanced organisations, design optimisation activities are often carried out in an ad-hoc manner or confined to specific subsystems. MBSE facilitates MOO and Multidisciplinary Design optimisation by ensuring the traceability of top-level objectives down to the most detailed design decisions. When design optimisation is integrated into the systems engineering processes, the optimal design becomes adaptable to evolving requirements and changing needs.

At OptimiSE, we specialise in helping organisations establish the methodologies and toolchains necessary to integrate design optimisation with MBSE. If this resonates with your needs, feel free to book a free initial consultation with us!

Closing the Loop with Business Intelligence Tools

As highlighted by the above personal story, very often the identity of the product is heavily influenced by the top-level stakeholders. However, the engineering and business domains can become out of sync when engineers present highly technical data to executives, or when executives provide engineers with ambiguous requirements.

To bridge this gap, integrating Business Intelligence (BI) tools can be highly effective. By establishing a data lake that pulls trade study data from the MBSE environment, you can present information in clear, concise dashboards stripped of low-level technical details. This enables executives to focus on selecting the solution that best aligns with their objectives. As design data remains synchronised throughout the development process, stakeholders can drill down into each subsystem or component at any stage to understand its contribution to the overall product. This approach fosters a collaborative environment, ensuring a streamlined and effective development process that includes all parties.

Conclusion

The process of navigating trade studies is a fundamental aspect of engineering and business decision-making. Each decision shapes the final product and its success in the market. Multi-Objective optimisation elevates traditional trade studies by offering a data-driven approach that quantifies trade-offs and presents a range of optimal solutions. This enables more informed and robust decision-making, especially in complex systems where the stakes are high.

The integration of MOO with Model-Based Systems Engineering and Business Intelligence tools further enhances this process, ensuring that the design optimisation is not only thorough but also aligned with evolving business objectives. MBSE provides the necessary traceability and adaptability in the design process, while BI tools bridge the gap between engineers and business stakeholders, fostering collaboration across all domains.

As design challenges continue to emerge, the ability to balance competing objectives through informed trade studies will remain a critical determinant of success. What are your experiences in trade study analysis, and what common pitfalls have you encountered? Share your thoughts with us below!