Large-Scale Truss Topology and Sizing Optimization by an Improved Genetic Algorithm with Multipoint Approximation

Truss size and topology optimization problems have recently been solved mainly by many different metaheuristic methods, and these methods usually require a large number of structural analyses due to their mechanism of population evolution. A branched multipoint approximation technique has been introduced to decrease the number of structural analyses by establishing approximate functions instead of the structural analyses in Genetic Algorithm (GA) when GA addresses continuous size variables and discrete topology variables. For large-scale trusses with a large number of design variables, an enormous change in topology variables in the GA causes a loss of approximation accuracy and then makes optimization convergence difficult. In this paper, a technique named the label–clip–splice method is proposed to improve the above hybrid method in regard to the above problem. It reduces the current search domain of GA gradually by clipping and splicing the labeled variables from chromosomes and optimizes the mixed-variables model efficiently with an approximation technique for large-scale trusses. Structural analysis of the proposed method is extremely reduced compared with these single metaheuristic methods. Numerical examples are presented to verify the efficacy and advantages of the proposed technique.

Solving binary programming problems using homotopy theory ideas

PurposeThe aim of the study is to show that merging two areas of mathematics – topology and discrete optimization – could result in a viable option to solve classical or specialized integer problems.Design/methodology/approachIn the paper, discrete topology concepts are applied to propose a metaheuristic algorithm that is capable to solve binary programming problems. Particularly, some of the homotopy for paths principles are used to explore the solution space associated with four well-known NP-hard problems herein considered as follows: knapsack, set covering, bi-level single plant location with order and one-max.FindingsComputational experimentation confirms that the proposed algorithm performs in an effective manner, and it is able to efficiently solve the sets of instances used for the benchmark. Moreover, the performance of the proposed algorithm is compared with a standard genetic algorithm (GA), a scatter search (SS) method and a memetic algorithm (MA). Acceptable results are obtained for all four implemented metaheuristics, but the path homotopy algorithm stands out.Originality/valueA novel metaheuristic is proposed for the first time. It uses topology concepts to design an algorithmic framework to solve binary programming problems in an effective and efficient manner.

Orbitally discrete coarse spaces

<p>Given a coarse space (X, E), we endow X with the discrete topology and denote X ♯ = {p ∈ βG : each member P ∈ p is unbounded }. For p, q ∈ X ♯ , p||q means that there exists an entourage E ∈ E such that E[P] ∈ q for each P ∈ p. We say that (X, E) is orbitally discrete if, for every p ∈ X ♯ , the orbit p = {q ∈ X ♯ : p||q} is discrete in βG. We prove that every orbitally discrete space is almost finitary and scattered.</p>

Exploring 3D printing techniques for the hybrid fabrication of discrete topology optimized structures

The application of topology optimization methods in architecture, while useful for conceptual design explorations, seems to be limited by the practical realization of continuum-type design outcomes. One way to overcome this limitation is setting up design and fabrication techniques, through which continuum domains become discrete structures. This study investigates to which extent discrete optimized systems can be built using a hybrid approach combining 3D printing and analogue fabrication techniques. The procedure is based on an algorithm in Grasshopper (Rhinoceros) that translates continuum topologies obtained in MATLAB into discrete systems, providing alternatives depending on the targeted volume fraction, the intended surface smoothness of the structural components and building material. The study focuses on fabrication aspects and structural performance of discrete structures using 3D printed nodes. Experimental tests evaluate the compressive strength of different types of filaments with varied infill percentages. Final prototypes are fabricated using a hybrid technique involving the use of 3D printed nodes to assemble bar-arrays comprising wooden members. Results provide a critical appraisal of the limitations and potentialities of 3D printing for hybrid fabrication of real scale structures.

On a Topological Space Generated by Monophonic Eccentric Neighborhoods of a Graph

In this paper, we present a way of constructing a topology on a vertex set of a graph using monophonic eccentric neighborhoods of the graph G. In this type of construction, we characterize those graphs that induced the indiscrete topology, the discrete topology, and a particular point topology.

Formation of Millimeter Waves with Electrically Tunable Orbital Angular Momentum

A method for forming electromagnetic waves with a tunable nonzero orbital angular momentum (OAM) is proposed. The approach is based on transforming an incident plane wave into a helical one using an electrically tunable ferroelectric lens. It uses high-resistive thin/thick film electrodes with a special discrete topology. The correlation between film electrodes topology and the highest order of OAM modes that the lens can form is described. A lens prototype based on Ba0.55Sr0.45TiO3 ferroelectric material and operating at a frequency of 60 GHz was designed, manufactured, and tested. The amplitude and phase distribution of the OAM wave with l = +1 formed by prototype were measured to confirm the effectiveness of the proposed method. The proposed lens has a combination of advantages such as low dimensions, electrical control over the OAM modes, and the possibility to operate in the millimeter wavelength range.

Discrete topology and sizing optimization of frame structures with compliance constraints: A semidefinite programming-based approach

The discrete topology and sizing optimization of frame structures with compliance constraints is studied using a novel approach, which is capable of finding the theoretical lower bounds and high-quality discrete solutions in an efficient manner. The proposed approach works by reformulating the discrete problem as a relaxed semidefinite programming (SDP) problem. This reformulation is made possible by a linear relaxation of the original discrete space and the elimination of the nonconvex equilibrium equation using a semidefinite constraint. A continuous global optimum is first derived using existing solvers and then the discrete solution is discovered by the neighborhood search. Numerical examples are presented, including the sizing optimization of 2-Bay 6-Story frame and 3-Bay 10-Story frame, the topology and sizing optimization of 2-Bay 6-Story braced frame. A topology and sizing example with multiple load cases is also provided. The proposed approach and three other metaheuristic algorithms are used to solve these examples. Theoretical lower bounds for these examples can be efficiently discovered by the proposed approach. For the sizing problems, the discrete solutions by the proposed approach are all better than the other algorithms. For the topology and sizing problems, the proposed approach achieves discrete solutions better than genetic algorithm, but worse than the other metaheuristics. The computational superiority of the proposed approach is validated in all the examples.