scholarly journals On decomposition and multiobjective-based column and disjunctive cut generation for MINLP

2020 ◽  
Author(s):  
Pavlo Muts ◽  
Ivo Nowak ◽  
Eligius M. T. Hendrix
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Resource Constrained ◽  
Linear Coupling ◽  
Integer Nonlinear Programming ◽  
Coupling Constraints ◽  
Cut Generation ◽  
Low Dimensional ◽  
Industrial Optimization

Abstract Most industrial optimization problems are sparse and can be formulated as block-separable mixed-integer nonlinear programming (MINLP) problems, defined by linking low-dimensional sub-problems by (linear) coupling constraints. This paper investigates the potential of using decomposition and a novel multiobjective-based column and cut generation approach for solving nonconvex block-separable MINLPs, based on the so-called resource-constrained reformulation. Based on this approach, two decomposition-based inner- and outer-refinement algorithms are presented and preliminary numerical results with nonconvex MINLP instances are reported.

scholarly journals A Review of Deterministic Optimization Methods in Engineering and Management

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Hua Lin ◽  
Jung-Fa Tsai ◽  
Chian-Son Yu
Keyword(s):  
Nonlinear Programming ◽  
Optimization Problems ◽  
Optimization Methods ◽  
Mixed Integer Nonlinear Programming ◽  
Mixed Integer ◽  
Deterministic Optimization ◽  
Practical Applications ◽  
Signomial Programming ◽  
Deterministic Methods ◽  
Integer Nonlinear Programming

With the increasing reliance on modeling optimization problems in practical applications, a number of theoretical and algorithmic contributions of optimization have been proposed. The approaches developed for treating optimization problems can be classified into deterministic and heuristic. This paper aims to introduce recent advances in deterministic methods for solving signomial programming problems and mixed-integer nonlinear programming problems. A number of important applications in engineering and management are also reviewed to reveal the usefulness of the optimization methods.

Cost optimization of project schedules under constrained resources and alternative production processes by mixed-integer nonlinear programming

2019 ◽  
Vol 26 (10) ◽  
pp. 2474-2508 ◽  
Author(s):  
Rok Cajzek ◽  
Uroš Klanšek
Keyword(s):  
Nonlinear Programming ◽  
Production Process ◽  
Cost Optimization ◽  
Mixed Integer ◽  
Time Constraints ◽  
Resource Constrained ◽  
Content Type ◽  
Production Processes ◽  
Proposed Model ◽  
Integer Nonlinear Programming

Purpose The purpose of this paper is cost optimization of project schedules under constrained resources and alternative production processes (APPs). Design/methodology/approach The model contains a cost objective function, generalized precedence relationship constraints, activity duration and start time constraints, lag/lead time constraints, execution mode (EM) constraints, project duration constraints, working time unit assignment constraints and resource constraints. The mixed-integer nonlinear programming (MINLP) superstructure of discrete solutions covers time–cost–resource options related to various EMs for project activities as well as variants for production process implementation. Findings The proposed model provides the exact optimal output data for project management, such as network diagrams, Gantt charts, histograms and S-curves. In contrast to classic scheduling approaches, here the optimal project structure is obtained as a model-endogenous decision. The project planner is thus enabled to achieve optimization of the production process simultaneously with resource-constrained scheduling of activities in discrete time units and at a minimum total cost. Practical implications A set of application examples are addressed on an actual construction project to display the advantages of proposed model. Originality/value The unique value this paper contributes to the body of knowledge reflects through the proposed MINLP model, which is capable of performing the exact cost optimization of production process (where presence and number of activities including their mutual relations are dealt as feasible alternatives, meaning not as fixed parameters) simultaneously with the associated resource-constrained project scheduling, whereby that is achieved within a uniform procedure.

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.

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