Mixed-integer Global Optimization Research Articles

Insights into Optimal Schemes of Radial Network Arch Pedestrian Bridge

The main objective of the article is to find the optimal ranges of the cardinal topological, shape, and dimensional parameters that fully describe the constructional scheme of pedestrian radial network arch bridges of moderate spans. This task is solved by formulating the global optimization problem and seeking the minimum mass of the whole bridge structure. An optimal bridge scheme was obtained by tuning a large set of interdependent design parameters of diverse character: the topological parameters–the type of hanger arrangement, and the number of hangers; the shape parameters–hanger spread and central section angles, the alteration of these angles, and the arch rise; and the sizing parameters–all cross‐sectional dimensions of structural members. Mathematically, this is a constrained mixed‐integer global optimization problem solved by a stochastic evolutionary algorithm. Plane light‐deck bridges of typical moderate 30, 45, 60, 75, and 90 m spans were optimized. Decisive design parameters and their rational ranges for all spans were revealed. In addition, the effects of some simplifications of the general bridge scheme were shown: using the constant spread and central section angles; imposing certain values on the ratio arch rise/bridge span; bounding the hanger diameters to a given value; and so on. Obtained results clearly indicate that the design recommendations for the lightweight network arch bridges should differ from the recommendations for similar automotive and railway bridges. Our findings are: the optimal ratio of arch rise to the bridge span is 0.20–0.30, the number of hangers is >40 even for the shortest spans, the spread angle between hangers is 30°–40°, and the girder mass amounts to ∼30% of the total bridge mass, while the mass of hangers amounts up to 20% and increases when imposing constraints on the minimal radius at the expense of diminishing arch mass.

Parallel Global Search Algorithm with Local Tuning for Solving Mixed-Integer Global Optimization Problems

Parallel Global Search Algorithm with Local Tuning for Solving Mixed-Integer Global Optimization Problems

An efficient modified differential evolution algorithm for solving constrained non-linear integer and mixed-integer global optimization problems

In this paper, an efficient modified Differential Evolution algorithm, named EMDE, is proposed for solving constrained non-linear integer and mixed-integer global optimization problems. In the proposed algorithm, new triangular mutation rule based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best,better and the worst individuals among the three randomly selected vectors is introduced. The proposed novel approach to mutation operator is shown to enhance the global and local search capabilities and to increase the convergence speed of the new algorithm compared with basic DE. EMDE uses Deb’s constraint handling technique based on feasibility and the sum of constraints violations without any additional parameters. In order to evaluate and analyze the performance of EMDE, Numerical experiments on a set of 18 test problems with different features, including a comparison with basic DE and four state-of-the-art evolutionary algorithms are executed. Experimental results indicate that in terms of robustness, stability and efficiency, EMDE is significantly better than other five algorithms in solving these test problems. Furthermore, EMDE exhibits good performance in solving two high-dimensional problems, and it finds better solutions than the known ones. Hence, EMDE is superior to the compared algorithms.

Global Methods for Dynamic Optimization and Mixed-Integer Dynamic Optimization

An overview of global methods for dynamic optimization and mixed-integer dynamic optimization (MIDO) is presented, with emphasis placed on the control parametrization approach. These methods consist of extending existing continuous and mixed-integer global optimization algorithms to encompass solution of problems with ODEs embedded. A prerequisite for so doing is a convexity theory for dynamic optimization as well as the ability to build valid convex relaxations for Bolza-type functionals. For solving dynamic optimization problems globally, our focus is on the use of branch-and-bound algorithms; on the other hand, MIDO problems are handled by adapting the outer-approximation algorithm originally developed for mixed-integer nonlinear problems (MINLPs) to optimization problems embedding ODEs. Each of these algorithms is thoroughly discussed and illustrated. Future directions for research are also discussed, including the recent developments of general, convex, and concave relaxations for the solutions of nonlinear ODEs.

A parametric mixed-integer global optimization framework for the solution of process engineering problems under uncertainty

This paper presents two algorithms for the global solution of parametric mixed-integer nonlinear programming problems. The basic idea of both the algorithms is to create parametric convex underestimators and overestimators of the nonconvex functions, which converge to the global solution by using branch and bound techniques on the space of continuous variables. However, the proposed algorithms differ from each other in the way the integer solutions are obtained. While the first algorithm is based upon a branch and bound framework, the second algorithm relies on introducing cuts.

A Controlled Random Search Technique Incorporating the Simulated Annealing Concept for Solving Integer and Mixed Integer Global Optimization Problems

In this paper, a computational algorithm, named RST2ANU algorithm, has been developed for solving integer and mixed integer global optimization problems. This algorithm, which primarily is based on the original controlled random search approach of Price [22i], incorporates a simulated annealing type acceptance criterion in its working so that not only downhill moves but also occasional uphill moves can be accepted. In its working it employs a special truncation procedure which not only ensures that the integer restrictions imposed on the decision variables are satisfied, but also creates greater possibilities for the search leading to a global optimal solution. The reliability and efficiency of the proposed RST2ANU algorithm has been demonstrated on thirty integer and mixed integer optimization problems taken from the literature. The performance of the algorithm has been compared with the performance of the corresponding purely controlled random search based algorithm as well as the standard simulated annealing algorithm. The performance of the method on mathematical models of three realistic problems has also been demonstrated.