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

Title: 多准则优化与决策制定：原理、算法和案例研究

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权衡速度、成本、环境足迹和便利性。 同样，设计一个工业过程必须考虑安全性、环境影响和成本效率。 所有目标都能被最佳满足的理想解决方案很少见；相反，我们寻求良好的折中方案，并努力避免双输的情况。 多标准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。 本读物介绍了这一主题，并基于莱顿大学荷兰莱顿先进计算机科学研究所的硕士课程"多标准优化与决策分析"的修订版编写而成。 该课程由第一作者从2007年到2023年每年教授，作为一学期课程，包括讲座和实践课。 我们的目标是使材料对不以数学为核心专业的硕士生易于理解，在必要时引入基本的数值分析概念，并为有趣的案例提供数值示例。 介绍以作者开发的独特教学方式组织，从线性规划和单点方法等更简单的概念开始，并由此推进到更复杂的概念，如非线性优化的最优性条件和集导向的求解算法。 此外，我们侧重于数学建模和基础，而不是特定的算法，尽管不排除讨论一些求解算法的代表性例子。