A Branch-and-Estimate Heuristic Procedure for Solving Nonconvex Integer Optimization Problems

2015 ◽  
Author(s):  
Prashant Palkar ◽  
Ashutosh Mahajan
Keyword(s):  
Optimization Problems ◽  
Heuristic Procedure ◽  
Integer Optimization

scholarly journals Partially distributed outer approximation

2021 ◽  
Author(s):  
Alexander Murray ◽  
Timm Faulwasser ◽  
Veit Hagenmeyer ◽  
Mario E. Villanueva ◽  
Boris Houska
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Outer Approximation ◽  
Mixed Integer ◽  
Global Optimality ◽  
Integer Optimization ◽  
Global Minimizers ◽  
Outer Approximation Method ◽  
Coupling Constraints ◽  
Outer Approximation Algorithm

AbstractThis paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization problems with separable convex objective functions, affine coupling constraints, and compact domain. PaDOA proceeds by alternating between solving large-scale structured mixed-integer linear programming problems and partially decoupled mixed-integer nonlinear programming subproblems that comprise much fewer integer variables. We establish conditions under which PaDOA converges to global minimizers after a finite number of iterations and verify these properties with an application to thermostatically controlled loads and to mixed-integer regression.

Afterword

2010 ◽  
pp. 269-272
Author(s):  
E. Parsopoulos Konstantinos ◽  
N. Vrahatis Michael
Keyword(s):  
Optimization Problems ◽  
Optimization Methods ◽  
Special Structure ◽  
Integer Optimization ◽  
Hybrid Schemes ◽  
Research Results ◽  
Global Minimizers ◽  
Classical Optimization

In the previous chapters, we presented the fundamental concepts and variants of PSO, as along with a multitude of recent research results. The reported results suggest that PSO can be a very useful tool for solving optimization problems from different scientific and technological fields, especially in cases where classical optimization methods perform poorly or their application involves formidable technical difficulties due to the problem’s special structure or nature. PSO was capable of addressing continuous and integer optimization problems, handling noisy and multiobjective cases, and producing efficient hybrid schemes in combination with specialized techniques or other algorithms in order to detect multiple (local or global) minimizers or control its own parameters.

A Mixed-Integer Memetic Algorithm Applied to Batch Process Optimization

2013 ◽  
Vol 300-301 ◽  
pp. 645-648 ◽  
Author(s):  
Yung Chien Lin
Keyword(s):  
Memetic Algorithm ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Space ◽  
Memetic Algorithms ◽  
Batch Processes ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Genetic Operators ◽  
Search Methods

Evolutionary algorithms (EAs) are population-based global search methods. Memetic Algorithms (MAs) are hybrid EAs that combine genetic operators with local search methods. With global exploration and local exploitation in search space, MAs are capable of obtaining more high-quality solutions. On the other hand, mixed-integer hybrid differential evolution (MIHDE), as an EA-based search algorithm, has been successfully applied to many mixed-integer optimization problems. In this paper, a mixed-integer memetic algorithm based on MIHDE is developed for solving mixed-integer constrained optimization problems. The proposed algorithm is implemented and applied to the optimal design of batch processes. Experimental results show that the proposed algorithm can find a better optimal solution compared with some other search algorithms.

scholarly journals About stability of mixed integer optimization problems under perturbations of input data of vector criterion

2021 ◽  
pp. 7-11
Author(s):  
Tetiana Lebedeva ◽  
Natalia Semenova ◽  
Tetiana Sergienko
Keyword(s):  
Initial Data ◽  
Input Data ◽  
Optimization Problems ◽  
Point Of View ◽  
Mixed Integer ◽  
Stability Of Solutions ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Small Perturbations ◽  
Vector Criterion

The article is devoted to the study of the influence of uncertainty in initial data on the solutions of mixed integer optimization vector problems. In the optimization problems, including problems with vector criterion, small perturbations in initial data can result in solutions strongly different from the true ones. The problem of stability of the indicated tasks is studied from the point of view of direct coupled with her question in relation to stability of solutions belonging to some subsets of feasible set.

scholarly journals Benchmarks for Current Linear and Mixed Integer Optimization Solvers

2015 ◽  
Vol 63 (6) ◽  
pp. 1923-1928 ◽  
Author(s):  
Josef Jablonský
Keyword(s):  
Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Large Scale ◽  
Optimization Problems ◽  
Academic Research ◽  
Mixed Integer ◽  
Important Class ◽  
Integer Optimization ◽  
Computational Performance ◽  
Optimization Solvers

Linear programming (LP) and mixed integer linear programming (MILP) problems belong among very important class of problems that find their applications in various managerial consequences. The aim of the paper is to discuss computational performance of current optimization packages for solving large scale LP and MILP optimization problems. Current market with LP and MILP solvers is quite extensive. Probably among the most powerful solvers GUROBI 6.0, IBM ILOG CPLEX 12.6.1, and XPRESS Optimizer 27.01 belong. Their attractiveness for academic research is given, except their computational performance, by their free availability for academic purposes. The solvers are tested on the set of selected problems from MIPLIB 2010 library that contains 361 test instances of different hardness (easy, hard, and not solved).

scholarly journals Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

2022 ◽  
Author(s):  
Merve Bodur ◽  
Timothy C. Y. Chan ◽  
Ian Yihang Zhu
Keyword(s):  
Optimization Problems ◽  
Linear Optimization ◽  
Trust Region ◽  
Inverse Optimization ◽  
Mixed Integer ◽  
Integer Optimization ◽  
Solution Algorithms ◽  
Linear Optimization Problems ◽  
Mixed Integer Linear Optimization ◽  
Plane Solution

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.

Introduction

1995 ◽  
Author(s):  
Christodoulos A. Floudas
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Optimization Problems ◽  
Batch Process ◽  
Mixed Integer ◽  
Optimization Models ◽  
Integer Optimization ◽  
Mixed Integer Optimization ◽  
Location Allocation ◽  
Primary Focus

This chapter introduces the reader to elementary concepts of modeling, generic formulations for nonlinear and mixed integer optimization models, and provides some illustrative applications. Section 1.1 presents the definition and key elements of mathematical models and discusses the characteristics of optimization models. Section 1.2 outlines the mathematical structure of nonlinear and mixed integer optimization problems which represent the primary focus in this book. Section 1.3 illustrates applications of nonlinear and mixed integer optimization that arise in chemical process design of separation systems, batch process operations, and facility location/allocation problems of operations research. Finally, section 1.4 provides an outline of the three main parts of this book. A plethora of applications in all areas of science and engineering employ mathematical models. A mathematical model of a system is a set of mathematical relationships (e.g., equalities, inequalities, logical conditions) which represent an abstraction of the real world system under consideration. Mathematical models can be developed using (i) fundamental approaches, (ii) empirical methods, and (iii) methods based on analogy. In (i), accepted theories of sciences are used to derive the equations (e.g., Newton’s Law). In (ii), input-output data are employed in tandem with statistical analysis principles so as to generate empirical or “black box” models. In (iii), analogy is employed in determining the essential features of the system of interest by studying a similar, well understood system. The variables can take different values and their specifications define different states of the system. They can be continuous, integer, or a mixed set of continuous and integer. The parameters are fixed to one or multiple specific values, and each fixation defines a different model. The constants are fixed quantities by the model statement. The mathematical model relations can be classified as equalities, inequalities, and logical conditions. The model equalities are usually composed of mass balances, energy balances, equilibrium relations, physical property calculations, and engineering design relations which describe the physical phenomena of the system. The model inequalities often consist of allowable operating regimes, specifications on qualities, feasibility of heat and mass transfer, performance requirements, and bounds on availabilities and demands. The logical conditions provide the connection between the continuous and integer variables.

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