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A Novel Decomposition Solution Approach for the Restoration Problem in Distribution Networks
Related concepts (33)
Linear programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
Cutting-plane method
In mathematical optimization, the cutting-plane method is any of a variety of optimization methods that iteratively refine a feasible set or objective function by means of linear inequalities, termed cuts. Such procedures are commonly used to find integer solutions to mixed integer linear programming (MILP) problems, as well as to solve general, not necessarily differentiable convex optimization problems. The use of cutting planes to solve MILP was introduced by Ralph E. Gomory.
Integer programming
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
Travelling salesman problem
The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP.
Branch and bound
Branch and bound (BB, B&B, or BnB) is a method for solving optimization problems by breaking them down into smaller sub-problems and using a bounding function to eliminate sub-problems that cannot contain the optimal solution. It is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root.
Branch and cut
Branch and cut is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values. Branch and cut involves running a branch and bound algorithm and using cutting planes to tighten the linear programming relaxations. Note that if cuts are only used to tighten the initial LP relaxation, the algorithm is called cut and branch. This description assumes the ILP is a maximization problem.
Nonlinear programming
In mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.
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.
Power system simulation
Electrical power system simulation involves power system modeling and network simulation in order to analyze electrical power systems using design/offline or real-time data. Power system simulation software's are a class of computer simulation programs that focus on the operation of electrical power systems. These types of computer programs are used in a wide range of planning and operational situations for electric power systems.
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z or blackboard bold . The set of natural numbers is a subset of , which in turn is a subset of the set of all rational numbers , itself a subset of the real numbers . Like the natural numbers, is countably infinite.