active constraint

简明释义

起作用的约束

英英释义

例句

1.Time was an active constraint 活跃约束 in the project timeline, forcing the team to prioritize tasks.

时间是项目时间表中的一个 活跃约束 active constraint，迫使团队优先处理任务。

2.In the optimization problem, the budget acted as an active constraint 活跃约束 that could not be exceeded.

在优化问题中，预算作为一个 活跃约束 active constraint，不能被超越。

3.The environmental regulations imposed an active constraint 活跃约束 on the emissions produced by the factory.

环境法规对工厂产生的排放施加了一个 活跃约束 active constraint。

4.The client's requirements included an active constraint 活跃约束 regarding the maximum weight of the product.

客户的要求包括一个关于产品最大重量的 活跃约束 active constraint。

5.The design team faced an active constraint 活跃约束 that limited the materials they could use for the project.

设计团队面临一个 活跃约束 active constraint，限制了他们在项目中可以使用的材料。

作文

In the realm of mathematics and optimization, the term active constraint refers to a condition or limitation that is currently influencing the outcome of a problem. Specifically, it describes a constraint that is 'active' at a given point in the solution space, meaning that if this constraint were relaxed, the optimal solution would change. Understanding active constraint is essential for anyone involved in mathematical modeling, economics, engineering, or any field that requires optimization. To illustrate this concept, consider a simple example involving a factory that produces two types of products: A and B. The factory has a limited amount of resources, such as raw materials and labor hours. The objective is to maximize profit while adhering to these resource limitations. Let's say the factory can produce up to 100 units of product A and 50 units of product B with the available resources. The constraints in this scenario include the maximum production limits for both products. Now, suppose the factory is currently producing 80 units of product A and 30 units of product B. At this production level, the constraints on product A (the limit of 100 units) are not affecting the solution because there is still capacity to produce more. However, the constraint on product B (the limit of 50 units) is active constraint, as the factory is close to reaching its maximum production limit for this product. If the factory wanted to increase the total profit by producing more product B, it would be unable to do so without violating the constraint. Therefore, in this scenario, the active constraint is the limitation on product B's production.In optimization problems, identifying active constraints helps in determining which constraints are critical for achieving the best solution. By focusing on these active constraints, decision-makers can prioritize their efforts in resource allocation and strategic planning. For instance, if the factory managers realize that the demand for product A is declining while the demand for product B is increasing, they might consider adjusting their production strategy to focus more on product B. This adjustment would involve re-evaluating the active constraint related to product B and possibly finding ways to relax it, such as investing in additional resources or improving operational efficiency.Moreover, the concept of active constraints extends beyond simple production scenarios. In economics, for example, individuals may face budget constraints that limit their consumption choices. These budget constraints can be viewed as active constraints when individuals are making decisions about how to allocate their limited resources among various goods and services. Understanding which constraints are active can lead to better decision-making and resource management.In conclusion, the concept of active constraint is pivotal in various fields that involve optimization and resource allocation. By identifying and analyzing these constraints, individuals and organizations can make informed decisions that lead to improved outcomes. Whether in manufacturing, economics, or any other domain, recognizing the role of active constraints allows for a deeper understanding of the factors that influence decision-making processes and ultimately drive success.

在数学和优化领域，术语active constraint指的是当前影响问题结果的条件或限制。具体而言，它描述了在给定解空间中处于“活动”状态的约束，这意味着如果放宽此约束，最优解将会改变。理解active constraint对于任何参与数学建模、经济学、工程学或任何需要优化的领域的人来说都是至关重要的。为了说明这个概念，我们考虑一个简单的例子，涉及一家生产两种类型产品（A和B）的工厂。该工厂的资源有限，例如原材料和劳动时间。目标是在遵守这些资源限制的同时最大化利润。假设工厂可以在可用资源下最多生产100个单位的产品A和50个单位的产品B。在这种情况下，约束条件包括两个产品的最大生产限制。现在，假设工厂目前正在生产80个单位的产品A和30个单位的产品B。在这一生产水平下，产品A的约束（最大100个单位）并未影响解决方案，因为仍然有能力生产更多。然而，产品B的约束（最大50个单位）是active constraint，因为工厂接近达到该产品的最大生产限制。如果工厂希望通过生产更多的产品B来增加总利润，就无法做到这一点，而不违反该约束。因此，在这种情况下，active constraint是与产品B生产相关的限制。在优化问题中，识别active constraints有助于确定哪些约束对实现最佳解决方案至关重要。通过关注这些活动约束，决策者可以优先考虑资源分配和战略规划中的努力。例如，如果工厂管理者意识到产品A的需求正在下降，而产品B的需求正在上升，他们可能会考虑调整生产策略，更加专注于产品B。这一调整将涉及重新评估与产品B相关的active constraint，并可能找到放宽它的方法，例如投资额外资源或提高运营效率。此外，active constraints的概念超越了简单的生产场景。在经济学中，例如，个人可能面临预算约束，这限制了他们的消费选择。当个人在决定如何在各种商品和服务之间分配有限资源时，这些预算约束可以被视为active constraints。理解哪些约束是活动的，可以导致更好的决策和资源管理。总结来说，active constraint的概念在涉及优化和资源分配的各个领域中都是关键的。通过识别和分析这些约束，个人和组织可以做出明智的决策，从而改善结果。无论是在制造业、经济学还是任何其他领域，认识到active constraints的作用都能让人们更深入地理解影响决策过程的因素，并最终推动成功。