Lecture

Optimization and Simulation

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Description

This lecture covers the concepts of transformations into single-objective functions, lexicographic rules, constrained optimization, and heuristics in optimization and simulation. It explains the weighted sum method, goal programming, and lexicographic optimization, providing examples and practical applications. The instructor discusses how to define ideal objectives, sort objectives, and formulate constraints to achieve optimal solutions.

Official source

Related concepts (28)

Multi-objective optimization

Multi-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.

Mathematical optimization

Mathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.

Convex optimization

Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.

Constrained optimization

In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized.

Simulation

A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.

Related lectures (54)

Optimization and Simulation

Covers the general framework of optimization and simulation, including deterministic control and the optimization problem.

Optimization and Simulation

Explores optimization, simulation, heuristics, and Pareto solutions in multi-objective problems.

Optimization and Simulation: Heuristics Intensification

Explores optimization and simulation techniques, emphasizing heuristics intensification for efficient solution finding.

Optimization Methods: Theory Discussion

Explores optimization methods, including unconstrained problems, linear programming, and heuristic approaches.

Thermodynamic Properties: Equations and Models

Explains thermodynamic properties, equations of state, and mixture rules for energy systems modeling.

Related concepts (28)

Multi-objective optimization

Mathematical optimization

Convex optimization

Constrained optimization

Simulation