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    What is Multi-Objective Optimization?

    In the ever-evolving landscape of engineering and design, finding the perfect balance between conflicting objectives is often a challenging task. Traditional optimization techniques might struggle to cope with the complexity of real-world problems that involve multiple conflicting goals. However, with the advent of Multi-Objective Optimization (MOO) and cloud-based simulation tools like SimScale, engineers and designers now have a powerful combination at their disposal to streamline the design process and achieve remarkable shape optimization results.

    What is the Multi-Objective Optimization Method?

    Multi-Objective Optimization (MOO) is an optimization technique used to optimize designs when multiple objectives are involved. In engineering scenarios, it is quite common to have more than one simultaneous objective, such as minimizing weight, maximizing performance, and reducing costs. Unlike single-objective optimization, which aims to find a single optimal solution, MOO aims to identify a set of solutions, known as the Pareto front.

    In Figure 1, the Pareto front is displayed for an optimization of a Tesla valve with Optimus, an Automation and Optimization tool by Noesis Solutions, and SimScale as the simulation tool.

    Watch the on-demand webinar for this application here: Tesla Valve Design Optimization in SimScale.

    The baseline design highlighted at the base of the arrows was improved upon for the pressure loss in both directions, and the plotted line shows the Pareto front with the non-dominated boundary points highlighted. The design cannot be improved beyond those points within the constraints used in the optimization.

    A graph showing the Pareto front for the optimization of a Tesla valve
    Figure 1: A Pareto front from Optimus from Noesis Solutions for the optimization of a Tesla valve (See the corresponding on-demand webinar with SimScale)

    Multi-Objective Optimization vs. Many-Objective Optimization?

    Though the terms might sound similar, there is a notable distinction between multi-objective optimization and many-objective optimization. While both involve dealing with multiple objectives, multi-objective optimization describes scenarios with two or three objectives. On the other hand, many-objective optimization refers to scenarios where the number of objectives is relatively large, often in the range of four or more.

    Handling many-objective optimization becomes significantly more complex due to the increased size of the Pareto front and the need for sophisticated visualization and decision-making techniques.

    The Pareto Front – The Trade-offs

    The Pareto front represents a unique concept in Multi-Objective Optimization, and knowing how to leverage the Pareto front is a crucial part of designing with Multi-Objective Optimization. The Pareto front is a collection of solutions where no improvement in one objective can be made without causing a deterioration in at least one other objective. In simpler terms, these solutions are considered non-dominated, as there is no single “best” solution but a range of compromises between objectives. Engineers and designers can then select the most suitable design from this Pareto front based on their specific requirements and preferences.

    Pareto optimization lies at the core of MOO, as it seeks to explore and identify solutions on the Pareto front. This process involves using sophisticated algorithms to analyze a vast number of design alternatives, producing a diverse range of optimal solutions.

    One of the key challenges in Pareto optimization is striking the right balance between the objectives, as enhancing one may negatively impact another. However, cloud-based simulation tools and optimization software have revolutionized this process, enabling engineers to efficiently compute the Pareto front and make informed decisions much more quickly and easily than ever before.

    Optimization Algorithms: Powering the Pursuit of Perfection

    To achieve MOO efficiently, powerful optimization algorithms are employed. These algorithms intelligently navigate the vast design space, searching for solutions that closely approximate the Pareto front. Several state-of-the-art optimization algorithms are commonly used, including:

    • Genetic Algorithms: Inspired by natural selection, genetic algorithms involve the use of mutation, crossover, and selection to evolve a population of potential solutions over generations.
    • Particle Swarm Optimization: This algorithm is inspired by the social behavior of birds flocking or fish schooling. Particles iteratively adjust their positions based on their own experience and the experience of their neighbors.
    • NSGA-II (Non-dominated Sorting Genetic Algorithm II): A popular algorithm that sorts the population into different “fronts” based on their dominance relationships, allowing for a diverse and evenly distributed set of solutions.

    Shape Optimization: Sculpting Designs for Maximum Performance

    Shape optimization is a specific application of MOO that focuses on altering the shape of a design to achieve desired objectives. Whether it is optimizing the aerodynamics of an aircraft wing, reducing drag in a car’s body, or minimizing the pressure drop through a valve, shape optimization plays a crucial role in enhancing overall performance.

    By leveraging cloud-based simulation tools like SimScale and automated shape optimization tools like Friendship Systems CAESES® and Optimus from Noesis Solutions, engineers can iterate through design variations rapidly and efficiently, leading to breakthroughs in product development.

    Figure 2: Shape optimization project on a GEMÜ 534 globe valve using Friendship Systems CAESES® and SimScale.

    How to set up a Multi-Objective Shape Optimization

    There are some prerequisites for setting up a MOO, including:

    • A robust method of parameterizing and driving the CAD model that can be achieved using Friendship Systems CAESES®, Noesis Optimus®, or other optimization software solutions
    • A simulation platform that can compute how well the different shapes meet the objectives and provide the performance values for the Pareto Front; a cloud simulation platform such as SimScale can increase the speed of optimization by parallelizing the simulations.
    • An analysis tool for creating the workflow and plotting the Pareto Front

    Once the prerequisites are met, a MOO is typically conducted as follows:

    • It starts with a Design-of-Experiments (DoE) to broadly map the available design space for the geometry and the other variables.
    • The database that is obtained from the DoE can then be used to generate the surrogate model (response surface) for the optimization model.
    • Simulations can then be performed and compared iteratively to check the predictions that are made by the surrogate model, thus augmenting its precision.
    • For a single MOO, multiple optimization studies can be performed to explore different objectives and positions on the Pareto Front.

    An example of a workflow with CAESES and SimScale can be seen in Figures 3 and 4.

    Schematic of a workflow using Friendship Systems CAESES and SimScale to optimize pump performance
    Figure 3: Example Friendship Systems CAESES® and SimScale workflow to optimize the performance of a KSB high-efficiency Calio pump.
    Figure 4: Example parameterization of the number of blades for a KSB high-efficiency Calio pump, parameterized in Friendship Systems CAESES®

    Benefits of Multi-Objective Optimization

    Comprehensive Decision-Making:

    MOO provides engineers with a holistic view of the design space, revealing the trade-offs between different objectives. This empowers them to make informed decisions that align with project goals, customer requirements, and budget constraints.

    Time and Cost Efficiency:

    Cloud-based simulation tools, combined with MOO algorithms, significantly reduce the time and resources required for design iterations. Engineers can explore a vast range of design alternatives in parallel, leading to quicker convergence on optimal solutions.

    Innovation and Creativity:

    By unlocking the potential of the Pareto front, MOO encourages innovative thinking and creativity. Engineers can explore unconventional design ideas and push the boundaries of what’s possible to discover breakthrough solutions.

    The Power of Cloud-Based Simulation Tools in MOO

    Scalability and Flexibility:

    SimScale offers unparalleled scalability, allowing engineers to access vast computational resources on demand. This means simulations can be run in parallel, significantly reducing the time required for optimization tasks and enabling the exploration of more design alternatives.


    Traditional on-premises simulation setups can be expensive to maintain and upgrade. SimScale eliminates the need for expensive hardware investments, allowing companies to pay only for the computing resources they use.

    Collaboration and Accessibility:

    SimScale promotes collaboration among team members regardless of their physical location. Designers, engineers, and stakeholders can access simulation data and optimization results from anywhere with an internet connection, streamlining the communication and decision-making processes.

    Automated Workflows and API capability:

    SimScale’s API connections mean that the whole process can be automated, enabling engineers to set up complex simulations and optimization workflows with ease. This automation reduces manual intervention, minimizes errors, and accelerates the entire design process.

    Integration with Design Software:

    SimScale integrates seamlessly with popular Computer-Aided Design (CAD) and optimization software. This allows engineers to easily transfer and modify design geometries for simulations, saving time and effort during the optimization process.


    As the field of engineering continues to evolve, the importance of Multi-Objective Optimization and shape optimization cannot be overstated. These cutting-edge techniques, powered by advanced optimization algorithms like Friendship Systems CAESES and Optimus from Noesis Solutions, along with cloud-based simulation tools like SimScale, empower engineers and designers to achieve optimal designs, striking the perfect balance between conflicting objectives. Embracing these methodologies opens new possibilities, driving innovation and efficiency in product development while meeting the diverse needs of consumers in a rapidly changing world.

    By leveraging the concepts of the Pareto front, Pareto optimization, optimization algorithms, and shape optimization, engineers can navigate the intricate trade-offs between competing objectives efficiently. These methodologies empower innovation, creativity, and robust decision-making, leading to groundbreaking designs.

    Set up your own cloud-native simulation via the web in minutes by creating an account on the SimScale platform. No installation, special hardware, or credit card is required.

    Last updated: August 25th, 2023

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