Discrete optimization

About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.

Optimal design of steel structures using standard sections

Abstract: The problem of optimal structural design having linked discrete variables is addressed. For such applications, when a discrete value for a variable is selected, values for other variables linked to it must also be selected from a table. The design of steel structures using available sections is a major application area of such problems. Three strategies that combine a continuous variable optimization method with a genetic algorithm, simulated annealing, and branch and bound method are presented and implemented into a computer program for their numerical evaluation. Three structural design problems are solved to study the performance of the proposed methods. CPU times for solution of the problems with discrete variables are large. Strategies are suggested to reduce these times.

Oppositional biogeography-based optimization for combinatorial problems

Abstract: In this paper, we propose a framework for employing opposition-based learning to assist evolutionary algorithms in solving discrete and combinatorial optimization problems. To our knowledge, this is the first attempt to apply opposition to combinatorics. We introduce two different methods of opposition to solve two different type of combinatorial optimization problems. The first technique, open-path opposition, is suited for combinatorial problems where the final node in the graph does not have be connected to the first node, such as the graph-coloring problem. The latter technique, circular opposition, can be employed for problems where the endpoints of a graph are linked, such as the well-known traveling salesman problem (TSP). Both discrete opposition methods have been hybridized with biogeography-based optimization (BBO). Simulations on TSP benchmarks illustrate that incorporating opposition into BBO improves its performance.

A parametric finite element environment tuned for numerical optimization

Abstract: Nowadays, numerical optimization in combination with finite element (FE) analysis plays an important role in the design of electromagnetic devices. To apply any kind of optimization algorithm, a parametric description of the FE problem is required and the optimization task must be formulated. Most optimization tasks described in the literature, feature either specially developed algorithms for a specific optimization task, or extensions to standard finite element packages. Here, a 2D parametric FE environment is presented, which is designed to be best suited for numerical optimization while maintaining its general applicability. Particular attention is paid to the symbolic description of the model, minimized computation time and the user friendly definition of the optimization task.