Efficient hybrid algorithms to solve mixed discrete-continuous optimization problems: A comparative study

Purpose: – In real world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, it is very time-consuming in use of finite element methods. The purpose of this paper is to study the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization, and compares it with the performance of Genetic Algorithms (GA). Design/methodology/approach: – In this paper, the enhanced multipoint approximation method (MAM) is utilized to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the Sequential Quadratic Programming (SQP) technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems. Findings: – The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem and the superiority of the Hooke-Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded. Originality/value: – The authors propose three efficient hybrid algorithms: the rounding-off, the coordinate search, and the Hooke-Jeeves search assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy, and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors φ defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects

Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

A Comparison of the Embedding Method to Multi-Parametric Programming, Mixed-Integer Programming, Gradient-Descent, and Hybrid Minimum Principle Based Methods

In recent years, the embedding approach for solving switched optimal control problems has been developed in a series of papers. However, the embedding approach, which advantageously converts the hybrid optimal control problem to a classical nonlinear optimization, has not been extensively compared to alternative solution approaches. The goal of this paper is thus to compare the embedding approach to multi-parametric programming, mixed-integer programming (e.g., CPLEX), and gradient-descent based methods in the context of five recently published examples: a spring-mass system, moving-target tracking for a mobile robot, two-tank filling, DC-DC boost converter, and skid-steered vehicle. A sixth example, an autonomous switched 11-region linear system, is used to compare a hybrid minimum principle method and traditional numerical programming. For a given performance index for each case, cost and solution times are presented. It is shown that there are numerical advantages of the embedding approach: lower performance index cost (except in some instances when autonomous switches are present), generally faster solution time, and convergence to a solution when other methods may fail. In addition, the embedding method requires no ad hoc assumptions (e.g., predetermined mode sequences) or specialized control models. Theoretical advantages of the embedding approach over the other methods are also described: guaranteed existence of a solution under mild conditions, convexity of the embedded hybrid optimization problem (under the customary conditions on the performance index), solvability with traditional techniques (e.g., sequential quadratic programming) avoiding the combinatorial complexity in the number of modes/discrete variables of mixed-integer programming, applicability to affine nonlinear systems, and no need to explicitly assign discrete/mode variables to autonomous switches.Comment: Accepted to IEEE Transactions on Control Systems Technolog

A Framework for Globally Optimizing Mixed-Integer Signomial Programs

Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York