智能优化是一种利用人工智能技术的优化方法，旨在通过模拟自然界的生物进化、群体行为等现象，采用自适应的算法来解决复杂的优化问题。
其核心思想是通过不断地搜索解空间中的最优解，在不断地迭代过程中寻找最优解，以达到提高效率和降低成本的目的。
智能优化算法具有较强的鲁棒性和全局搜索能力，可以应用于各个领域，如工程优化、金融风险管理、数据挖掘等。
Intelligent Optimization is an optimization method that utilizes artificial intelligence technology, aiming to solve complex optimization problems by simulating natural phenomena such as biological evolution and group behavior, and adopting adaptive algorithms.
The core idea is to continuously search for the optimal solution in the solution space and search for the optimal solution during the iterative process, in order to achieve the goal of improving efficiency and reducing costs.
Intelligent optimization algorithms have strong robustness and global search ability, and can be applied in various fields, such as engineering optimization, financial risk management, data mining, etc.
1. 线性规划：
若优化问题中，目标函数和约束函数f_0,…,f_m都是线性函数，即对任意的x,y∈R^n和α,β∈R,都有：
f_i (αx+βy)=αf_i (x)+βf_i (y),i=0,1,…,m
2. 凸规划：
任意的线性规划问题一定是凸规划。凸规划可看成线性规划的扩展。如果目标函数和约束函数都是凸函数，即对任意的x,y∈R^n和α,β∈R，且满足α+β=1，α≥0，β≥0，下列不等式成立：
f_i (αx+βy)≤αf_i (x)+βf_i (y),i=0,1,…,m
这样的函数即为凸函数。
目标函数和约束函数都是凸函数的问题就是凸规划问题，也叫凸优化问题。
3. 非连续优化问题：
如果可行域是离散的，即为非连续优化问题。（离散问题一般都是困难问题）
4. 单目标问题：
对于多目标问题，比如我们想要优化两个目标函数:
minimize f_1 (x),f_2 (x)
这就是多目标优化问题，否则就是单目标问题。
1. Linear Programming:
If the objective function and constraint functions f_0,…,f_m in an optimization problem are all linear functions, that is, for any x,y∈R^n and α,β∈R:
f_i (αx+βy)=αf_i (x)+βf_i (y),i=0,1,…,m
2. Convex Programming:
Any linear programming problem is necessarily a convex programming problem. Convex programming can be seen as an extension of linear programming. If the objective function and constraint functions are all convex functions, that is, for any x,y∈R^n and α,β∈R satisfying α+β=1，α≥0，β≥0, the following inequality holds:
f_i (αx+βy)≤αf_i (x)+βf_i (y),i=0,1,…,m
Functions that satisfy this inequality are called convex functions. A problem where both the objective function and constraint functions are convex functions is called a convex programming problem, also known as a convex optimization problem. Convex programming has numerous applications in various fields such as machine learning, signal processing, and control theory. Gradient descent and interior-point methods are commonly used to solve convex programming problems.
3. Non-linear Programming:
If the feasible region of an optimization problem is discrete, it is classified as a non-continuous or discrete optimization problem. Discrete optimization problems are typically considered difficult problems, as the feasible solutions are a finite set of discrete points rather than a continuous set. Discrete optimization problems arise in many practical applications in fields such as computer science, engineering, and operations research. Examples of discrete optimization problems include integer programming, combinatorial optimization, and graph optimization. Solving discrete optimization problems typically requires specialized algorithms and techniques that take advantage of the discrete structure of the problem.
4. Single-Objective Optimization:
For multi-objective optimization problems, such as optimizing two objective functions:
Minimize f_1 (x),f_2 (x)
This is a multi-objective optimization problem. Otherwise, it is a single-objective optimization problem.
1.欧洲发电及扩容能源系统模型的研究背景可以追溯到欧洲在能源转型方面的长期努力。欧洲作为世界上最发达的经济体之一，面临着日益增长的能源需求、气候变化、能源安全和可持续发展等问题。为了解决这些问题，欧洲国家已经采取了一系列的政策和措施，包括推动可再生能源的发展、提高能源效率、减少碳排放等。
应用价值有支持能源政策和规划制定、优化能源系统的设计和运营、推动可再生能源的发展、促进能源系统的国际合作。
2.路由优化问题的研究背景可以追溯到计算机网络的发展历程。随着计算机网络规模的不断扩大和网络拓扑结构的日益复杂，如何高效地选择网络中的最佳路径成为了一个重要的问题。路由优化问题的目标是在网络中选择一条最佳路径，以优化网络的性能指标，如延迟、带宽、可靠性等。
应用价值促进网络安全、推动计算机网络的发展。
3. 教育时间表优化问题的研究背景是指如何在给定的时间内，合理安排学校的教学活动、考试和其他活动，以最大程度地提高学校的教育质量和效率的问题。教育时间表优化问题的研究背景可以追溯到学校教育的发展历程。
应用价值提高教学效率、提高教育质量、优化教学资源利用、提高学校管理效率、推动教育改革。
4. 航班调度模型的研究背景是指在航班调度模型的研究中，研究人员需要考虑多种因素，如航班的数量、机型、起降时间、地面服务等。同时，航班调度还需要满足多种约束条件，如机场容量、航班安全等。
应用价值提高乘客的舒适程度、优化航空交通管理、推动航空业的发展。
1. The Research Background of the European power generation and expansion energy system model can be traced back to Europe's long-term efforts in energy transformation. As one of the most developed economies in the world, Europe is facing increasing energy demand, climate change, energy security, and sustainable development issues. In order to address these issues, European countries have adopted a series of policies and measures, including promoting the development of renewable energy, improving energy efficiency, and reducing carbon emissions.
The Application Value includes supporting energy policy and planning formulation, optimizing the design and operation of energy systems, promoting the development of renewable energy, and promoting international cooperation in energy systems.
2. The Research Background of routing optimization problems can be traced back to the development history of computer networks. With the continuous expansion of computer network scale and the increasingly complex network topology, how to efficiently select the best path in the network has become an important issue. The goal of routing optimization problem is to choose the best path in the network to optimize the performance indicators of the network, such as latency, bandwidth, reliability, etc.
The Application Value promotes network security and promotes the development of computer networks.
3. The Research Background of the optimization problem of education schedule refers to how to reasonably arrange teaching activities, exams, and other activities of schools within a given time, in order to maximize the quality and efficiency of education in schools. The research background of optimizing educational schedules can be traced back to the development process of school education.
The Application Value to improve teaching efficiency, improve educational quality, optimize the utilization of teaching resources, improve school management efficiency, and promote educational reform.
4. The Research Background of flight scheduling models refers to the need for researchers to consider various factors in the study of flight scheduling models, such as the number of flights, aircraft types, takeoff and landing times, ground services, etc. At the same time, flight scheduling also needs to meet various constraints, such as airport capacity, flight safety, etc.
The Application Value improves passenger comfort, optimizes air traffic management, and promotes the development of the aviation industry.
AI For Science(人工智能在科学上的应用)对于科学来说是一个集合点。它汇集了人工智能和应用领域的专业知识;将建模知识与工程知识相结合;依赖于合作跨越学科，在人与机器之间。随着技术的进步，该领域的下一波进步将来自于建立一个机器社区学习研究人员、领域专家、公民科学家和工程师一起工作设计和部署有效的人工智能工具。
AI For Science,Artificial Intelligence is a gathering point for science. It brings together professional knowledge in artificial intelligence and application fields; Combining modeling knowledge with engineering knowledge; Relying on collaboration across disciplines, between humans and machines. With the advancement of technology, the next wave of progress in this field will come from establishing a machine community where researchers, domain experts, citizen scientists, and engineers work together to design and deploy effective artificial intelligence tools.
神经下潜（neuro evolution）是一种优化方法，它利用人工神经网络和进化算法相结合的方式来求解问题。基于神经下潜的优化求解可以分为两个阶段：演化阶段和评估阶段。
在演化阶段，首先随机生成一组神经网络，并使用进化算法（如遗传算法或遗传规划）进行优胜劣汰，从而筛选出适应度更高的神经网络。在每一代中，通过交叉、变异等操作对高适应度的神经网络进行操作，产生新的神经网络，以期望在下一代中得到更好的适应度。
在评估阶段，使用所选的神经网络来解决实际问题，例如分类、回归或控制等问题。在评估过程中，需要将神经网络的输出与实际结果进行比较，并计算神经网络的适应度。适应度通常是根据神经网络的性能指标（如分类准确度或均方误差）计算得出的。
通过不断迭代演化和评估过程，神经下潜可以得到越来越适应于特定问题的神经网络。与传统的基于梯度下降的方法相比，神经下潜的优点在于其可以在没有显式目标函数和梯度的情况下进行优化，并且可以处理高维、非线性和复杂的问题。
Neural evolution is an optimization method, which uses the combination of artificial neural network and Evolutionary algorithm to solve problems. The optimization solution based on neural descent can be divided into two stages: the evolution stage and the evaluation stage.
In the evolution stage, a group of neural networks are randomly generated, and Evolutionary algorithm (such as genetic algorithm or genetic programming) is used to select the neural networks with higher fitness. In each generation, high fitness neural networks are manipulated through crossover, mutation, and other operations to generate new neural networks in order to achieve better fitness in the next generation.
During the evaluation phase, use the selected neural network to solve practical problems such as classification, regression, or control. During the evaluation process, it is necessary to compare the output of the neural network with the actual results and calculate the fitness of the neural network. The fitness is usually calculated according to the performance indicators of the neural network (such as classification accuracy or Mean squared error).
Through continuous iterative evolution and evaluation processes, neural networks can be obtained that are increasingly adapted to specific problems. Compared with traditional gradient descent based methods, the advantage of neural descent is that it can optimize without explicit objective functions and gradients, and can handle high-dimensional, nonlinear, and complex problems.
