Algorithms for Locating Constrained Optimal Intervals (original) (raw)
Interval Constraints: Results and Perspectives
Lecture Notes in Computer Science, 2000
Reliably solving non-linear real constraints on computer is a challenging task due to the approximation induced by the resort to floating-point numbers. Interval constraints have consequently gained some interest from the scientific community since they are at the heart of complete algorithms that permit enclosing all solutions with an arbitrary accuracy. Yet, soundness is beyond reach of present-day interval constraint-based solvers, while it is sometimes a strong requirement. What is more, many applications involve constraint systems with some quantified variables these solvers are unable to handle. Basic facts on interval constraints and local consistency algorithms are first surveyed in this paper; then, symbolic and numerical methods used to compute inner approximations of real relations and to solve constraints with quantified variables are briefly presented, and directions for extending interval constraint techniques to solve these problems are pointed out.
A Tabu Search Method for Interval Constraints
Lecture Notes in Computer Science, 2008
This article presents an extension of the Tabu Search (TS) metaheuristic to continuous CSPs, where the domains are represented by floating point-bounded intervals. This leads to redefine the usual TS operators to take into account the special features of interval constraints: real variables encoded in floating points domains, high cardinality of the domains, nature of the CSP where constraints may be partially satisfied.
Soft Computing, 2018
This paper focuses on solving systems of interval linear equations and interval linear programming in a computationally efficient way. Since the computational complexity of most interval enclosure numerical methods is often prohibitive, a procedure to obtain a relaxation of the interval enclosure solution that is computationally tractable is proposed. We show that our approach unifies the four standard interval solutions-the weak, strong, control and tolerance solutions. The interval linear system methods require n • 2 n linear solutions. However, in the case of linear programming problems, we show that this requires just two optimization problem of the size of the problem itself. Numerical examples illustrate our results.
A primal algorithm for interval linear-programming problems
Linear Algebra and its Applications, 1977
An interval linear-programming problem (IP) is Maximize c ?X s.t. b-<Ax< b+. where the matrix A, vectors b-, b + and c are given. In this paper we develop a primal algorithm for solving IP. The algorithm starts with a feasible solution (not necessarily an extreme point) and produces, after finitely many iterations, an optimal solution to an IP.
Exploring the search space with intervals
2008
Institute of Physics, Polish Academy of Sciences, Warsaw, Polandemail: gutow@ifpan.edu.plAbstract. The term global optimization is used in several contexts. Most oftenwe are interested in finding such a point (or points) in many-dimensional searchspace at which the objective function’s value is optimal, i.e. maximal or minimal.Sometimes, however, we are also interested in stability of the solution, that is inits robustness against small perturbations. Here I present the original, interval-analysis-based family of methods designed for exhaustive exploration of the searchspace. The power of intervalmethods makes it possible toreach all mentioned goalswithin a single, unified framework.
Interval Methods for Solving Nonlinear Constraint Satisfaction, Optimization and Similar Problems
Studies in computational intelligence, 2019
The series "Studies in Computational Intelligence" (SCI) publishes new developments and advances in the various areas of computational intelligence-quickly and with a high quality. The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life sciences, as well as the methodologies behind them. The series contains monographs, lecture notes and edited volumes in computational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems, and hybrid intelligent systems. Of particular value to both the contributors and the readership are the short publication timeframe and the worldwide distribution, which enable both wide and rapid dissemination of research output. The books of this series are submitted to indexing to Web of Science, EI-Compendex, DBLP, SCOPUS, Google Scholar and Springerlink.
Interval tools for global optimization
Computers & Mathematics with Applications, 1991
We give ~ short overview of the general ideas involved in solving optimization problems using interval arithmetic. We include a discussion of a few prototype optimization Algorithms.
Solving the interval linear programming problem: A new algorithm for a general case
Expert Systems with Applications, 2018
Based on the binding constraint indices of the optimal solution to the linear programming (LP) model, a feasible system of linear equations can be formed. Because an interval linear programming (ILP) model is the union of numerous LP models, an interval linear equations system (ILES) can be formed, which is the union of these conventional systems. Hence, a new algorithm is introduced in which an arbitrary characteristic model of the ILP model is chosen and solved. The set of indices of its binding constraints is then obtained. This set is used to form and solve an ILES using the enclosure method. If all the components of the interval solutions to this system are strictly non-negative, the optimal solution set (OSS) of the ILP model is determined as the subscription of the zone created by reversing the signs of the binding constraints of the worst model and the binding constraints of the best model. The solutions to several problems obtained by the new algorithm and a Monte Carlo simulation are compared. The proposed algorithm is applicable to large-scale problems. To this end, an ILP model with 270 constraints and 270 variables is solved.
Space-Constrained Interval Selection
Arxiv preprint arXiv:1202.4326, 2012
We study streaming algorithms for the interval selection problem: finding a maximum cardinality subset of disjoint intervals on the line. A deterministic 2-approximation streaming algorithm for this problem is developed, together with an algorithm for the special case of proper intervals, achieving improved approximation ratio of 3/2. We complement these upper bounds by proving that they are essentially best possible in the streaming setting: it is shown that an approximation ratio of 2 − (or 3/2 − for proper intervals) cannot be achieved unless the space is linear in the input size. In passing, we also answer an open question of Adler and Azar [1] regarding the space complexity of constant-competitive randomized preemptive online algorithms for the same problem.