Multi-Objective Optimization Techniques

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What is an approach to tackle constraints in optimization?

Use of barrier functions with an additional parameter µ that is continuously shrinked to reach zero

Use of dynamic programming

Use of Lagrange multipliers

Use of penalties, i.e., assign a sufficiently large value to the objective function (correct)

What is the main idea behind interior methods in optimization with restrictions?

Use the fulfillment of the constraints as additional objective function building a so-called penalty function

Use the constraints to modify the objective function

Make sure not to leave the feasible region (correct)

Use the constraints to reduce the search space

What is the Pareto frontier in multi-objective optimization?

A technique to reduce the number of objectives

A method to combine multiple objectives into a single objective

A set of optimal solutions that represent the best trade-off between different objectives (correct)

A single optimal solution that satisfies all objectives

What is the main advantage of using evolutionary methods in multi-objective optimization?

They can approximate the Pareto frontier in parallel Signup and view all the answers

What is the main idea behind VEGA, a multi-objective evolutionary algorithm?

Select parts of the mating parents according to each objective function Signup and view all the answers

What is the main idea behind NSGA, a multi-objective evolutionary algorithm?

Sort individuals according to their dominance Signup and view all the answers

What is the main idea behind MSGA, a multi-objective evolutionary algorithm?

Mark individuals as belonging to a certain objective function Signup and view all the answers

What is the main challenge in solving TSP with time windows?

The problem is NP-hard Signup and view all the answers

What is the goal of multi-objective optimization when a single point that minimizes all functions cannot be found?

Locating a Pareto-optimal solution Signup and view all the answers

Which term refers to solutions where every component in a local neighborhood is worse or equal in multi-objective optimization?

Pareto optimal (local) Signup and view all the answers

In the context of a Pareto front, what describes the trade-off between different objectives?

Pareto frontier Signup and view all the answers

How is the search space X related to multi-objective optimization?

It is where the optimization is performed Signup and view all the answers

Which technique involves computing the entire Pareto frontier using a population-based algorithm?

Homotopic techniques Signup and view all the answers

What is a dominant point in the context of Pareto optimization?

A point where all other components are worse Signup and view all the answers

Which method is used for combining different objectives into a single solution in multi-objective optimization?

Convex combination Signup and view all the answers

Which region contains the solutions that cannot be improved without worsening another according to the Pareto front?

Non-dominated region Signup and view all the answers

What is the main idea behind goal programming in multi-objective optimization?

Minimizing the distance of objectives to predefined goals Signup and view all the answers

Which method involves fixing thresholds for all but one objective function beforehand and optimizing the most important one?

Priority optimization Signup and view all the answers

What is the purpose of exploring the coefficient space of the convex combination in multi-objective optimization?

To obtain the Pareto frontier Signup and view all the answers

Which programming optimizes according to a predefined ordering of objective functions?

Prioritization programming Signup and view all the answers

What happens if points arise in the search space that are unfeasible during optimization with constraints?

Objective function values cannot be computed at all Signup and view all the answers

Which constraints limit the optimization process in many applications?

Inequality constraints, equality constraints, and box constraints Signup and view all the answers

What characterizes a fixed trade-off in multi-objective optimization?

Finding the point in the Pareto front tangent to a hyperplane Signup and view all the answers

Which type of constraints might arise in the optimization process and can be either linear or non-linear?

Equality and inequality constraints Signup and view all the answers