Selected Benchmark Problems Research Articles

A hierarchical clustering algorithm for addressing multi-modal multi-objective optimization problems

Many evolutionary multi-modal multi-objective algorithms (MMEAs) have been proposed to solve multi-modal multi-objective optimization problems (MMOPs). Unfortunately, the environmental selection process causes many algorithms to place too much emphasis on solution variety in the decision space, which leads to solutions with low convergence quality. As a result, not only are all local Pareto fronts reversed, but objective values are also far lower than the global Pareto Fronts. To tackle these tasks, this paper proposes a hierarchical clustering-based MMOEA_DC_HR model that uses decision space clustering methods to group neighborhood solutions into several local clusters, preserving local Pareto Sets. And secondary clustering is performed in the objective space to select temporary populations from these local clusters to maintain the diversity of the objective space. Additionally, a hierarchical ranking method is introduced to update the convergence archive aiding in maintaining the convergence of the algorithm and controlling the quality of the Pareto Front. The test results show that this novel algorithm exhibits competitive performance in solving selected benchmark problems when compared to other cutting-edge MMEAs.

Punching Shear Response Theory (PSRT) – A two degree of freedom kinematic theory for modeling the entire punching shear vs. deformation response of RC slabs and footings

Punching failures of reinforced concrete flat slabs and footings without shear reinforcement have been responsible for a number of catastrophic collapses. Despite intense scientific efforts in recent decades that have led to failure criteria-based phenomenological models, our current mechanistic understanding is still not sufficiently advanced to fathom the physical background of punching phenomena in RC structures. That is why, this paper proposes a novel two degree of freedom mechanical theory - called Punching Shear Response Theory (PSRT) - that interconnects all relevant effects of punching shear behavior, namely strutting action within a conical concrete shell at the slab-column interface, shear transfer actions elicited along the circumferential punching shear crack, including cohesive fracture process zone behavior, aggregate interlock and dowel action of reinforcement, as well as transfer of normal forces within tangential and radial cracks between slab segments in one all-encompassing algorithm. The PSRT can thoroughly mimic and efficiently reproduce the entire punching failure process of flat slabs and squat members (footings, pile caps, column bases) including prediction of pre- and post-peak punching shear vs. deformation response, quantification of different punching shear contributions and analysis of their evolution and mutual interaction within the failure process. The paper illustrates the analytical development of the PSRT, exemplifies its ability to reproduce the punching shear response of selected benchmark problems, proves its validity by database evaluations (incl. punching strength and deformation capacity) and eventually discloses the physical causalities of punching failures in RC structures.

A comparative study of metaheuristics algorithms based on their performance of complex benchmark problems

Metaheuristic approaches with extremely important improvements are very promising in the solution of intractable optimization problems. The objective of the present study is to test the capability of applications and compare the performance of the four selected algorithms from “classical” (simulated annealing (SA), genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE)) and “new generation” (firefly algorithm (FFA), krill herd (KH), grey wolf optimization (GWO), and symbiotic organism search (SOS)) each by solving selected benchmark problems that are used in the literature for algorithm testing purpose. The selected test problems had very complex objective functions and associated constraints with multiple local optima. Among all selected algorithms, the “new generation” SOS and KH algorithm successfully solved most of all the selected benchmark problems and achieved the best solution for most of them. Among four “classical” algorithms, DE, and PSO effectively attained the optimal solution which was very close to the best one. However, the “new generation” algorithm performed much better than the “classical” one. Therefore, no firm conclusion can be done about the universally best algorithm and their performance may be varied for different benchmark problems. However, in this study for the seven selected test problems, SOS and KH exhibited the most promising result and great potential with respect to execution time also. This study gives some insights to use SOS and KH as the best-performing algorithms to the novice user who can easily get lost in the plethora of large optimization algorithms.

McCARD Criticality Benchmark Analyses with Various Evaluated Nuclear Data Libraries

International Criticality Safety Benchmark Evaluation Project (ICSBEP) criticality analyses were conducted using the McCARD Monte Carlo code for 85 selected benchmark problems with 7 evaluated nuclear data libraries (ENDLs): ENDF/B-VII.1, ENDF/B-VIII.0, JENDL-4.0, JENDL-5.0, JEFF-3.3, TENDL-2021, and CENDL-3.2. Regarding the analyses, it was confirmed that the keff results are sensitive to the ENDL. It is noted that the new-version ENDLs show better performance in the fast benchmark cases, while on the other hand, there are no significant differences in keff among the different ENDLs in the thermal benchmark cases. The sensitivity of the keff results depending on the ENDL may impact nuclear core design parameters such as the shutdown margin, critical boron concentration, and power defects. This study and keff results will be a good reference in the development of new types of nuclear cores or new design codes.

Robust Multiobjective Optimization for Vehicle Routing Problem With Time Windows.

In this article, we focus on the vehicle routing problem (VRP) with time windows under uncertainty. To capture the uncertainty characteristics in a real-life scenario, we design a new form of disturbance on travel time and construct robust multiobjective VRP with the time window, where the perturbation range of travel time is determined by the maximum disturbance degree. Two conflicting objectives include: 1)the minimization of both the total distance and: 2)the number of vehicles. A robust multiobjective particle swarms optimization approach is developed by incorporating an advanced encoding and decoding scheme, a robustness measurement metric, as well as the local search strategy. First, through particle flying in the decision space, the problem space characteristic under deterministic environment is fully exploited to provide guidance for robust optimization. Then, a designed metric is adopted to measure the robustness of solutions and help to search for the robust optimal solutions during the particle flying process. In addition to the updating process of particle, two local search strategies, problem-based local search and route-based local search, are developed for further improving the performance of solutions. For comparison, we develop several robust optimization problems by adding disturbances on selected benchmark problems. The experimental results validate our proposed algorithm has a distinguished ability to generate enough robust solutions and ensure the optimality of these solutions.

W-dominance: Tradeoff-inspired dominance relation for preference-based evolutionary multi-objective optimization

Abstract The paper presents a method of incorporating decision maker preferences into multi-objective meta-heuristics. It is based on tradeoff coefficients and extends their applicability from bi-objective to multi-objective. The method assumes that a decision maker specifies a priori each objective's importance as a weight interval. Based on this, w-dominance relation is introduced, which extends Pareto dominance. By replacing reference points with weight intervals the method eliminates the need for any knowledge concerning expected solutions. Instead, decision maker reflects his context-independent policy regarding objectives. The proposed w-dominance was incorporated into selected multi-objective metaheuristics. Following this, three new metrics were designed. The metrics include prescreening true Pareto Front and final population according to w-dominance relation. Based on preliminary tests, Vector Angle Evolutionary Algorithm (VaEA) was selected as the best match for w-dominance. W-dominance-extended VAEA (wVAEA) was compared in a series of simulations with four state-of-the-art reference point-based multi-objective algorithms. The results show that wVaEA outperforms the four representative algorithms for selected benchmark problems.

A layered genetic algorithm with iterative diversification for optimization of flexible job shop scheduling problems

Flexible job shop scheduling problem (FJSSP) is a further expansion of the classical job shop scheduling problem (JSSP). FJSSP is known to be NP-hard with regards to optimization and hence poses a challenge in finding acceptable solutions. Genetic algorithm (GA) has successfully been applied in this regard since last two decades. This paper provides an insight into the actual complexity of selected benchmark problems through quantitative evaluation of the search space owing to their NP-hard nature. A four-layered genetic algorithm is then proposed and implemented with adaptive parameters of population initialization and operator probabilities to manage intensification and diversification intelligently. The concept of reinitialization is introduced whenever the algorithm is trapped in local minima till predefined number of generations. Results are then compared with various other standalone evolutionary algorithms for selected benchmark problems. It is found that the proposed GA finds better solutions with this technique as compared to solutions produced without this technique. Moreover, the technique helps to overcome the local minima trap. Further comparison and analysis indicate that the proposed algorithm produces comparative and improved solutions with respect to other analogous methodologies owing to the diversification technique.

The Pareto Tracer for General Inequality Constrained Multi-Objective Optimization Problems

Problems where several incommensurable objectives have to be optimized concurrently arise in many engineering and financial applications. Continuation methods for the treatment of such multi-objective optimization methods (MOPs) are very efficient if all objectives are continuous since in that case one can expect that the solution set forms at least locally a manifold. Recently, the Pareto Tracer (PT) has been proposed, which is such a multi-objective continuation method. While the method works reliably for MOPs with box and equality constraints, no strategy has been proposed yet to adequately treat general inequalities, which we address in this work. We formulate the extension of the PT and present numerical results on some selected benchmark problems. The results indicate that the new method can indeed handle general MOPs, which greatly enhances its applicability.

An immersed interface-lattice Boltzmann method for fluid-structure interaction

An immersed interface-lattice Boltzmann method (II-LBM) is developed for modeling fluid-structure systems. The key element of this approach is the determination of the jump conditions that are satisfied by the distribution functions within the framework of the lattice Boltzmann method where forces are imposed along a surface immersed in an incompressible fluid. In this initial II-LBM, the discontinuity related to the normal component of the interfacial force is sharply resolved by imposing the relevant jump conditions using an approach that is analogous to imposing the corresponding pressure discontinuity in the incompressible Navier-Stokes equations. We show that the jump conditions for the distribution functions are the same in both single-relaxation-time and multi-relaxation-time LBM formulations. Tangential forces are treated using the immersed boundary-lattice Boltzmann method (IB-LBM). In our implementation, a level set approach is used to impose jump conditions for rigid-body models. For flexible boundary models, we describe the moving interface by interpolating the positions of marker points that move with the fluid. The II-LBM introduced herein is compared to a direct forcing IB-LBM for rigid-body fluid-structure interaction, and a classical IB-LBM for cases involving elastic interfaces. Higher order accuracy is observed with the II-LBM as compared to the IB-LBM for selected benchmark problems. Although our II-LBM only imposes jump conditions corresponding to the pressure, the error in the velocity field is demonstrated to be much smaller for the II-LBM than the IB-LBM. The II-LBM is also demonstrated to provide superior volume conservation when simulating flexible boundaries.

Shear Crack Propagation Theory (SCPT) – The mechanical solution to the riddle of shear in RC members without shear reinforcement

This paper intends to provide a deeper understanding of shear in beams and slabs without shear reinforcement. To this end, the paper proposes a new theory – called Shear Crack Propagation Theory (SCPT), that interconnects all relevant effects of shear behavior, namely crack localization, crack propagation, cantilever action, shear transfer in the uncracked concrete (compression zone), aggregate interlock, dowel action and crack bridging action in one all-encompassing algorithm. The SCPT represents an artificial reproduction (mechanical twin) of the physical shear problem and allows us to predict the shear crack geometry, the transferred shear force including contributions of all shear transfer actions as well as the corresponding strains and deformations over the entire shear loading process, from crack initiation up to the state of shear failure. The paper illustrates the analytical development of the SCPT, exemplifies its ability to reflect the shear response of selected benchmark problems and eventually delivers a physical explanation for shear failures in members without shear reinforcement.

Assessment of Hamming Distance and Self Organization Map in Solving Cell Formation Problem

The cell formation (CF) problem is considered the most essential issue in cellular manufacturing systems (CMS). CF deals with the arrangement of similar parts into groups known as part families (PFs) and organizes machines also into groups, called machine cells (MCs). In the literature, numerous methods, models and algorithms have been proposed and developed to handle CF problems. However, very few studies have dealt with the assessment and comparison of these methods, to identify the most effective. This has provided strong motivation for the study presented here. The present paper focuses on two methods that are used infrequently to form MCs and PFs, and applies them in three strategies: the first is based on the use of a hamming distance only, while the second uses only a self-organization map (SOM). However, the third method applies a hybrid approach based on SOM and hamming distance. The outputs of the selected methods were compared, to select the best one. A set of five benchmark datasets and three performance measures was used for comparison and evaluation. These performance measures are: percent of the exceptional elements (PE), grouping efficiency (GE), and machine utilization (MU). The results refer to the outperforms of the hamming distance in terms of PE, GE and MU for most of the selected benchmark problems.

Explicit dynamic isogeometric B-Rep analysis of penalty-coupled trimmed NURBS shells

Isogeometric B-Rep Analysis (IBRA) was the first approach that enabled a full integration of Computer Aided Design (CAD) and Computer Aided Engineering (CAE) based on trimmed NURBS B-Rep models ubiquitous in industrial CAD. However, the applicability of IBRA to explicit dynamic problems such as vehicle crash simulations and especially the effect of trimming and penalty coupling on the critical time step were not systematically investigated in the literature. To fill this gap, we developed Explicit IBRA, a combination of the patch coupling capabilities of IBRA with the explicit dynamic features of the FE solver LS-DYNA.For Explicit IBRA, we particularly (i) developed a new penalty-based B-Rep element formulation for the application to a Reissner–Mindlin shell with six degrees of freedom, (ii) formally extended the IBRA theory to explicit time integration schemes, (iii) showed that the common stability criterion and the maximum eigenvalue-based time step estimation from FE still hold, and (iv) used the IBRA exchange format to implement a closed design workflow between the CAD program Rhinoceros and the solver LS-DYNA. We solved selected benchmark problems, from quasi-static linear elastic to highly dynamic elasto-plastic with large deformations, and obtained accurate results with penalty factors that cause no or only a minor decrease in stable time step size. That is, we found that penalty coupling does not have a severe impact on the critical time step in explicit analysis, making Explicit IBRA practically applicable. Finally, we studied an industrial BMW engine bonnet model under dynamic loading and observed good agreement with reference finite element simulations.

Prey-predator algorithm for discrete problems: a case for examinationtimetabling problem

The prey-predator algorithm is a metaheuristic algorithm inspired by the interaction between a predator and its prey. Initial solutions are put into three categories: the better performing solution as the best prey, the worst performing solution as a predator, and the rest as ordinary prey. The best prey totally focuses on exploiting its neighborhood while the predator explores the search space searching for a promising region in the search space. The ordinary prey will be affected by these two extreme search behaviors of exploration and exploitation. The algorithm has been tested and found to be effective in solving different problems arising from different disciplines including engineering, tourism, and management. Originally, the algorithm was designed to deal with continuous problems. However, many problems arising from real aspects are not continuous. Hence, in this paper the prey-predator algorithm will be extended to suit discrete problems. Examination timetabling is used to test the approach. The simulation results with appropriate statistical analysis show that the approach is as good as the cumulative best performance of results recorded in the literature for the selected benchmark problems.

PERFORMANCE EVALUATION OF DIFFERENT LINEAR EQUATION SOLVERS FOR SOLVING NONLINEAR FE PROBLEMS ON MULTICORE ARCHITECTURES

<p>The aim of this paper is to evaluate the performance of existing parallel linear equation solvers to solving large-scale, nonlinear finite element analysis problems on systems with distributed memory. The parallel approach allows us to take an advantage of the distributed memory enabling forming large system matrices and of multiple processing units to achieve significant speedups. Our study is based on comparison of parallel direct solver and parallel iterative solver implemented in SuperLU DIST library from Portable, Extensible Toolkit for Scientific Computation (PETSc). Both considered solvers are designed for distributed system memory model and are based on a Massage Passing Interface (MPI).</p><p>The efficiency of individual solvers is evaluated on a selected benchmark problems, with different solution strategies by comparing computation times and obtained speedups.</p>

The Gradient Subspace Approximation as Local Search Engine within Evolutionary Multi-objective Optimization Algorithms

In this paper, we argue that the gradient subspace approximation (GSA) is a powerful local search tool with in memetic algorithms for the treat mentof multi-objective optimization problems. The GSA utilizes the neighborhood information within the current population in order to compute the best approximation of the gradient at a given candidate solution. The computation of the search direction comes hence for free in terms of additional function evaluations within population based search algorithms such as evolutionary algorithms. Its benefits have recently been discussed in the context of scalar optimization. Here, we discuss and adapt the GSA for the case that multiple objectives have to be considered concurrently. We will further on hybridize line searchers that utilize GSA to obtain the search direction with two different multi-objective evolutionary algorithms. Numerical results on selected bench mark problems indicate thes trength of the GSA-based local search within the evolutionary strategies.

Validation of COMSOL code for analyzing liquid metal magnetohydrodynamic flow

Applicability of COMSOL multiphysics software for analyzing liquid metal MagnetoHydroDynamic (MHD) effect under fusion relevant parameters has been verified. For this purpose, few benchmark problems recommended by fusion MHD community have been simulated. The selected benchmark problems are steady state fully developed MHD duct flow, duct flow under transverse fringed magnetic field and transient phenomenon of natural convection in presence of magnetic field. Apart, from the recommended benchmark problems, an experimental scenario has been simulated having flow geometry with multiple 90° bends. For these simulations, two to three available independent physics modules have been suitably coupled under the single platform of COMSOL. The computed numerical results show good agreement with the available analytical or experimental or reported numerical data in the range of MHD parameters Hartmann number ∼104, Interaction parameter ∼104, wall conductance ratio ∼10−2 & Grasshof number ∼106.

Micro-time variant multi-objective particle swarm optimization (micro-TVMOPSO) of a solar thermal combisystem

Abstract Multi-objective optimization (MOO) algorithms usually require a high number of objective function evaluations to approximate the Pareto-optimal solutions, which can be time-consuming in many engineering applications. To overcome this issue, MOO algorithms using a small population, often referred to as micro-MOO algorithms, aim at approximating the true Pareto front using a smaller number of objective function evaluations. Such algorithms are not common in the evolutionary algorithms literature and their usage in building engineering is seldom. This paper proposes a micro-time variant multi-objective particle swarm optimization (micro-TVMOPSO), which is a revised version of the micro-MOPSO algorithm. First, the proposed algorithm is applied along with eight other MOO algorithms to 24 benchmark problems, and their performance is compared by using two metrics. Although the proposed micro-TVMOPSO algorithm faced difficulties in solving some complicated Pareto fronts, it outperformed the eight optimization algorithms on 10 of the 24 selected benchmark problems. After the comparison of proposed micro-TVMOPSO with several MOO algorithms for different benchmark problems, the micro-TVMOPSO is applied to a case study in engineering: the design optimization of a residential solar thermal combisystem using two conflicting objective functions, the life cycle cost (LCC) and energy use (LCE). Different patterns of variation of the decision variables were observed from the non-dominated solutions found by micro-TVMOPSO, which would have not been possible to notice by performing a single-objective optimization. For instance, the increase of number of solar collectors from 1 to 10 had the impact of increasing the LCC by 84% and decreasing the LCE by 63%. The results indicated that the number of solar thermal collectors is the variable having the most effect on both LCC and LCE. When the number of collectors increases, more energy is harvested, and larger tanks and less auxiliary electric power are needed.

Stability results of a fractional model for unsteady-state fluid flow problem

This paper mainly focuses on a fractional model for unsteady-state fluid flow problem developed based on the meshless local Petrov-Galerkin (MLPG) method with the moving kriging (MK) technique as a background. The contribution of this work is to investigate the stability of a model with fractional order governed by the full Navier-Stokes equations in Cartesian coordinate system both theoretical and numerical aspects. This is examined and discussed in detail by means of matrix method. We show that the scheme is unconditionally stable under the restriction of eigenvalue. The dependence between several of the important parameters that impact on the solution is also studied thoroughly. In discretizing the time domain, an algorithm based on a fixed point method is employed to overcome the nonlinearity. Two selected benchmark problems are provided to validate the stability of the present method, and a very satisfactory agreement with the obtained results can be found.

Dual-horizon peridynamics: A stable solution to varying horizons

In this paper, we present a dual-horizon peridynamics formulation which allows for simulations with dual-horizon with minimal spurious wave reflection. We prove the general dual property for dual-horizon peridynamics, based on which the balance of momentum and angular momentum in PD are naturally satisfied. We also analyze the crack pattern of random point distribution and the multiple materials issue in peridynamics. For selected benchmark problems, we show that DH-PD is less sensitive to the spatial than the original PD formulation.

The domain interface method in non-conforming domain decomposition multifield problems

The Domain Interface Method (DIM) is extended in this contribution for the case of mixed fields as encountered in multiphysics problems. The essence of the non-conforming domain decomposition technique consists in a discretization of a fictitious zero-thickness interface as in the original methodology and continuity of the solution fields across the domains is satisfied by incorporating the corresponding Lagrange Multipliers. The multifield DIM inherits the advantages of its irreducible version in the sense that the connections between non-matching meshes, with possible geometrically non-conforming interfaces, is accounted by the automatic Delaunay interface discretization without considering master and slave surfaces or intermediate surface projections as done in many established techniques, e.g. mortar methods. The multifield enhancement identifies the Lagrange multiplier field and incorporates its contribution in the weak variational form accounting for the corresponding consistent stabilization term based on a Nitsche method. This type of constraint enforcement circumvents the appearance of instabilities when the Ladyzhenskaya–Babuška–Brezzi (LBB) condition is not fulfilled by the chosen discretization. The domain decomposition framework is assessed in a large deformation setting for mixed displacement/pressure formulations and coupled thermomechanical problems. The continuity of the mixed field is studied in well selected benchmark problems for both mixed formulations and the objectivity of the response is compared to reference monolithic solutions. Results suggest that the presented strategy shows sufficient potential to be a valuable tool in situations where the evolving physics at particular domains require the use of different spatial discretizations or field interpolations.