Title: Multicriteria Optimization and Decision Making: Principles, Algorithms and Case Studies Show Chinese title

Title: 多准则优化与决策：原理、算法及案例研究

Abstract: Real-world decision and optimization problems, often involve constraints and conflicting criteria. For example, choosing a travel method must balance speed, cost, environmental footprint, and convenience. Similarly, designing an industrial process must consider safety, environmental impact, and cost efficiency. Ideal solutions where all objectives are optimally met are rare; instead, we seek good compromises and aim to avoid lose-lose scenarios. Multicriteria optimization offers computational techniques to compute Pareto optimal solutions, aiding decision analysis and decision making. This reader offers an introduction to this topic and has been developed on the basis of the revised edition of the reader for the MSc computer science course "Multicriteria Optimization and Decision Analysis" at the Leiden Institute of Advanced Computer Science, Leiden University, The Netherlands. This course was taught annually by the first author from 2007 to 2023 as a single semester course with lectures and practicals. Our aim was to make the material accessible to MSc students who do not study mathematics as their core discipline by introducing basic numerical analysis concepts when necessary and providing numerical examples for interesting cases. The introduction is organized in a unique didactic manner developed by the authors, starting from more simple concepts such as linear programming and single-point methods, and advancing from these to more difficult concepts such as optimality conditions for nonlinear optimization and set-oriented solution algorithms. Besides, we focus on the mathematical modeling and foundations rather than on specific algorithms, though not excluding the discussion of some representative examples of solution algorithms. Show Chinese abstract

Abstract: 现实世界中的决策和优化问题通常涉及约束条件和相互冲突的标准。例如，选择一种出行方式必须平衡速度、成本、环境影响和便利性。同样地，工业过程的设计必须考虑安全、环境影响和成本效率。完全满足所有目标的理想解非常罕见；相反，我们寻求良好的折衷方案，并力求避免双输的局面。多准则优化提供了计算帕累托最优解的计算技术，有助于决策分析和决策制定。 本读者介绍了这一主题，并基于莱顿大学莱顿高级计算机科学研究所“多准则优化与决策分析”课程修订版的读者发展而成。自2007年至2023年，第一作者每年以单学期课程的形式讲授这门课，包括讲座和实践环节。我们的目标是通过在必要时引入基本数值分析概念并提供有趣的案例数值实例，使材料易于被非数学核心学科的硕士学生理解。介绍部分按照作者开发的独特教学方法组织，从更简单的概念如线性规划和单点法开始，逐步过渡到更复杂的概念如非线性优化的最优性条件和集值解算法。此外，我们侧重于数学建模和基础理论，而不是特定算法，尽管并不排除讨论一些代表性解算算法的例子。