Optimisation of road vehicle passive suspension systems. Part 2. Qualification and case study

As an aid during the concept design phase, the two-dimensional vehicle simulation programme Vehsim2d has been developed (see part 1 of this paper for the vehicle model). The leap-frog optimisation algorithm for constrained problems (LFOPC) has been linked to the multi-body dynamics simulation code (Vehsim2d) to enable the computationally economic optimisation of certain vehicle and suspension design variables. This paper describes the simulation programme, the qualification of the programme, and gives an example of the application of the Vehsim2d/LFOPC system. In particular it is used to optimise the damper characteristics of an existing 22 ton three axle vehicle, over a typical terrain and at a representative speed. By using this system the optimised damper characteristics with respect to ride comfort for the vehicle are computed. The optimum damper characteristics give a 28.5% improvement in the ride comfort of the vehicle over the specified terrain and prescribed speed. Further optimisation runs were performed considering other terrain and different speed values. From these results final damper characteristics for the vehicle are proposed. Using the proposed characteristics, simulations were performed with the more advanced and proven DADS programme. The results show that the damper suggested by the optimisation study is indeed likely to improve the suspension of the vehicle. This study proves that the Vehsim2d/LFOPC vehicle modelling and optimisation system is indeed a valuable tool for a vehicle design team.     

Gradient-based approximation methods applied to the optimal design of vehicle suspension systems using computational models with severe inherent noise

The principal aim of this paper is to evaluate the feasibility of using gradient-based approximation methods for the optimisation of the spring and damper characteristics of an off-road vehicle, for both ride comfort and handling. The Sequential Quadratic Programming algorithm and the relatively new Dynamic-Q method are the two successive approximation methods used for the optimisation. The determination of the objective function value is performed using computationally expensive numerical simulations that exhibit severe inherent numerical noise. The use of forward finite differences and central finite differences for the determination of the gradients of the objective function within Dynamic-Q is also investigated. This is done in investigating methods for overcoming the difficulties associated with the optimisation of noisy objective functions.A recreational off-road vehicle is modelled in ADAMS, and coupled to MATLAB for the execution of the optimisation process. The full vehicle ADAMS model includes suspension kinematics, a load-dependent tyre model, as well as non-linear springs and dampers. Up to four design variables are considered in modelling the suspension characteristics.It is found that both algorithms perform well in optimising handling. However, difficulties are encountered in obtaining improvements in the design process when ride comfort is considered. Nevertheless, meaningful design configurations are still achievable through the proposed optimisation process, at a relatively low cost in terms of the number of simulations that have to be performed.     

Optimisation of pneumatic circuit aimed at improving the vibro-isolation properties of seat suspension

The object of a numerical simulation and optimisation is the seat with a visco-elastic passive suspension, with improved vibro-isolation properties by means the multi-criteria optimisation. Basing on the verified passive seat suspension model, a modification of the pneumatic circuit in order to help the working machines operators against vibration is considered. The root mean square (RMS) acceleration measured at the seat and the maximum relative displacement of the seat suspension are minimised as the chosen vibro-isolation criteria. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Efficient optimisation of a vehicle suspension system, using a gradient-based approximation method, Part 1: Mathematical modelling

A methodology is proposed for the efficient determination of gradient information, when performing gradient based optimisation of an off-road vehicle’s suspension system. The methodology is applied to a computationally expensive, non-linear vehicle model, that exhibits severe numerical noise. A recreational off-road vehicle is modelled in MSC.ADAMS, and coupled to MATLAB for the execution of the optimisation. The successive approximation method, Dynamic-Q, is used for the optimisation of the spring and damper characteristics. Optimisation is performed for both ride comfort and handling. The determination of the objective function value is performed using computationally expensive numerical simulations.This paper proposes a non-linear pitch-plane model, to be used for the gradient information, when optimising ride comfort. When optimising for handling, a non-linear four wheel model, that includes roll, is used. The gradients of the objective function and constraint functions are obtained through the use of central finite differences, within Dynamic-Q, via numerical simulation using the proposed simplified models. The importance of correctly scaling these simplified models is emphasised. The models are validated against experimental results. The simplified vehicle models exhibit significantly less numerical noise than the full vehicle simulation model, and solve in significantly less computational time.     

Design and validation of an unmanned surface vehicle simulation model

In this paper we present a multiphysics simulation model of Halcyon, an autonomous unmanned surface vehicle (USV). The simulation model presented in this paper has been developed to rapidly progress the design, development and validation of Halcyon’s autonomy management system, particularly in challenging sea conditions. Using simulation for this purpose enables extensive testing across the full environmental operating envelope of the vessel, hence greatly reducing the need for real-world sea-trials. The simulator is comprised of a novel and comprehensive sea-surface wave environment model, a six degree of freedom nonlinear unified seakeeping and manoeuvring boat dynamics model, an actuation dynamics model, an autopilot and an interface with an autonomy management system. Results are presented that show good agreement between real-world and simulated sea-trials data.     

A hybrid differential evolution algorithm to vehicle routing problem with fuzzy demands

In this paper, the vehicle routing problem with fuzzy demands (VRPFD) is considered, and a fuzzy chance constrained program model is designed, based on fuzzy credibility theory. Then stochastic simulation and differential evolution algorithm are integrated to design a hybrid intelligent algorithm to solve the fuzzy chance constrained program model. Moreover, the influence of the dispatcher preference index on the final objective of the problem is discussed using stochastic simulation, and the best value of the dispatcher preference index is obtained.     

The multi-trip vehicle routing problem

The basic vehicle routing problem is concerned with the design of a set of routes to serve a given number of customers, minimising the total distance travelled. In that problem, each vehicle is assumed to be used only once during a planning period, which is typically a day, and therefore is unrepresentative of many practical situations, where a vehicle makes several journeys during a day. The present authors have previously published an algorithm which outperformed an experienced load planner working on the complex, real-life problems of Burton's Biscuits, where vehicles make more than one trip each day. This present paper uses a simplified version of that general algorithm, in order to compare it with a recently published heuristic specially designed for the theoretical multi-trip vehicle routing problem.     

Optimisation of Structures with Inelastic Deformations

In context of design optimisation, the treatment of inelastic, path-dependent materials is a topic of interest. As opposed to purely elastic materials, it is necessary to store and analyse the deformation history in order to appropriately describe inelastic material behaviour. For design optimisation of structures sensitivities of all quantities of influence have to be computed so as to use gradient based optimisation algorithms. Considering path-dependent materials the sensitivities of internal variables that represent the deformation history have to be additionally calculated. A numerical effective way of determining sensitivities is the variational sensitivity analysis. This approach is applied to develop a powerful and effective algorithm to compute sensitivities of the structural response with respect to their geometric design. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Economic lot sizes and vehicle scheduling

In this paper a relationship between the vehicle scheduling problem and the dynamic lot size problem is considered. For the latter problem we assume that order quantities for different products can be determined separately. Demand is known over our n-period production planning horizon. For a certain product our task is to decide for each period if it should be produced or not. If it is produced, what is its economic lot size? Our aim here is to minimize the combined set-up and inventory holding costs. The optimal solution of this problem is given by the well-known Wagner-Whitin dynamic lot size algorithm. Also many heuristics for solving this problem have been presented. In this article we point out the analogy of the dynamic lot size problem to a certain vehicle scheduling problem. For solving vehicle scheduling problems the heuristic algorithm developed by Clark and Wright in very often used. Applying this algorithm to the equivalent vehicle scheduling problem we obtain by analogy a simple heuristic algorithm for the dynamic lot size problem. Numerical results indicate that computation time is reduced by about 50% compared to the Wagner-Whitin algorithm. The average cost appears to be approximately 0.8% higher than optimum.     

A General Meta-Heuristic Based Solver for Combinatorial Optimisation Problems

In recent years, there have been many studies in which tailored heuristics and meta-heuristics have been applied to specific optimisation problems. These codes can be extremely efficient, but may also lack generality. In contrast, this research focuses on building a general-purpose combinatorial optimisation problem solver using a variety of meta-heuristic algorithms including Simulated Annealing and Tabu Search. The system is novel because it uses a modelling environment in which the solution is stored in dense dynamic list structures, unlike a more conventional sparse vector notation. Because of this, it incorporates a number of neighbourhood search operators that are normally only found in tailored codes and it performs well on a range of problems. The general nature of the system allows a model developer to rapidly prototype different problems. The new solver is applied across a range of traditional combinatorial optimisation problems. The results indicate that the system achieves good performance in terms of solution quality and runtime.     

BIANCA: a genetic algorithm to solve hard combinatorial optimisation problems in engineering

The genetic algorithm BIANCA, developed for design and optimisation of composite laminates, is a multi-population genetic algorithm, capable to deal with unconstrained and constrained hard combinatorial optimisation problems in engineering. The effectiveness and robustness of BIANCA rely on the great generality and richness in the representation of the information, i.e. the structure of populations and individuals in BIANCA, and on the way the information is extensively exploited during genetic operations. Moreover, we developed proper and original strategies to treat constrained optimisation problems through the generalisation of penalisation methods. BIANCA can also treat constrained multi-objective problems based on the construction of the Pareto frontier. Therefore, BIANCA allows us to approach very general design problems for composite laminates, but also to make a step forward to the treatment of more general problems of optimisation of materials and structures. In this paper, we describe specifically the case of optimal design of composite laminates, concerning both the theoretical formulation and the numeric resolution.     

An interval uncertain optimization method for vehicle suspensions using Chebyshev metamodels

This paper proposes a new design optimization framework for suspension systems considering the kinematic characteristics, such as the camber angle, caster angle, kingpin inclination angle, and toe angle in the presence of uncertainties. The coordinates of rear inner hardpoints of upper control arm and lower control arm of double wishbone suspension are considered as the design variables, as well as the uncertain parameters. In this way, the actual values of the design variables will vary surrounding their nominal values. The variations result in uncertainties that are described as interval variables with lower and upper bounds. The kinematic model of the suspension is developed in software ADAMS. A high-order response surface model using the zeros of Chebyshev polynomials as sampling points is established, termed as Chebyshev metamodel, to approximate the kinematic model. The Chebyshev meta-model is expected to provide higher approximation accuracy. Interval uncertain optimization problems usually involve a nested computationally expensive double-loop optimization process, in which the inner loop optimization is to calculate the bounds of the interval design functions, while the outer loop is to search the optimum for the deterministic optimization problem. To reduce the computational cost, the interval arithmetic is introduced in the inner loop to improve computational efficiency without compromising numerical accuracy. The numerical results show the effectiveness of the proposed design method.     

Covariance analysis for active vehicle suspensions

In this paper the covariance analysis will be extended to active suspension systems with skyhook dampers. The covariance matrix of the entire vehicle system follows from an algebraic equation, the so-called Ljapunov matrix equation, and no integrations are required. An essential prerequisite of the covariance analysis is a white noise input process. This can always be provided by modelling the random vehicle excitation by means of a shape filter. Performance criteria are presented and appropriate design parameters are found by optimization. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimal location of dwell points in a single loop AGV system with time restrictions on vehicle availability

Since the workload of a manufacturing system changes over time, the material handling equipment used in the facility will be idle at certain time intervals to avoid system overload. In this context, a relevant control problem in operating an automated guided vehicle (AGV) system is where to locate idle vehicles. These locations, called dwell points, establish the response times for AVG requests. In this article, a dynamic programming algorithm to solve idle vehicle positioning problems in unidirectional single loop systems is developed to minimize the maximum response time considering restrictions on vehicle time available to travel and load/unload requests. This polynomial time algorithm finds optimal dwell points when all requests from a given pick-up station are handled by a single AGV. The proposed algorithm is used to study the change in maximum response time as a function of the number of vehicles in the system.     

Solving multiobjective vehicle routing problem with stochastic demand via evolutionary computation

This paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer. The solution to this vehicle routing problem with stochastic demand (VRPSD) involves the optimization of complete routing schedules with minimum travel distance, driver remuneration, and number of vehicles, subject to a number of constraints such as time windows and vehicle capacity. To solve such a multiobjective and multi-modal combinatorial optimization problem, this paper presents a multiobjective evolutionary algorithm that incorporates two VRPSD-specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions. A new way of assessing the quality of solutions to the VRPSD on top of comparing their expected costs is also proposed. It is shown that the algorithm is capable of finding useful tradeoff solutions for the VRPSD and the solutions are robust to the stochastic nature of the problem. The developed algorithm is further validated on a few VRPSD instances adapted from Solomon’s vehicle routing problem with time windows (VRPTW) benchmark problems.     

Hybrid modeling approach for vehicle frame coupled with nonlinear dampers

The vehicle frame system comprises frame structure and nonlinear dampers. In order to investigate the effects of frame flexibility and nonlinear hysteresis, a hybrid modeling approach for vehicle frame coupled with nonlinear dampers will be proposed. Before that, a complex model for nonlinear damper is developed consisting of knowledge-based model and support vector machine (SVM) model. The frame structure is modeled by FEM where the SVM complex model of damper is embedded in. Thus a hybrid model for vehicle frame system is established and successfully validated via a dummy vehicle riding in different conditions. The results show that the hybrid model can capture the nonlinear dynamic characteristics accurately. The hybrid model can also provide a basis for structural design with the existing of FEM model.     

Computational fluid dynamics applied to the aerodynamic design of a land‐based supersonic vehicle

The BLOODHOUND SSC project was publicly announced in October 2008, with a primary engineering objective of designing, constructing and running a vehicle capable of achieving a speed of 1000 mph on land. The aerodynamic design of this vehicle is to be accomplished using computational simulation only and this paper describes the development and application of the approach adopted. The computational model employs a cell vertex finite volume algorithm for the solution of compressible viscous flow problems on unstructured hybrid meshes. A one equation turbulence model is adopted and the solution of the steady flow equations is obtained by explicit relaxation. For the combination of high Mach number, complex geometry and complex boundary conditions, involving rotating surfaces and a rolling ground, a consistent HLLC numerical flux function is adopted to ensure a stable procedure. To illustrate the impact of the approach upon the final configuration, a number of simulations undertaken to aid the aerodynamic design are described. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Ant Colony Optimisation for Machine Layout Problems

Flexible machine layout problems describe the dynamic arrangement of machines to optimise the trade-off between material handling and rearrangement costs under changing and uncertain production environments. A previous study used integer-programming techniques to solve heuristically reduced versions of the problem. As an alternative, this paper introduces an ant colony optimisation (ACO) algorithm to generate good solutions. Experimental results are presented, with ACO obtaining better solutions than the reduction heuristic.     

A tabu search algorithm for the periodic vehicle routing problem with multiple vehicle trips and accessibility restrictions

In this paper, we consider a periodic vehicle routing problem that includes, in addition to the classical constraints, the possibility of a vehicle doing more than one route per day, as long as the maximum daily operation time for the vehicle is not exceeded. In addition, some constraints relating to accessibility of the vehicles to the customers, in the sense that not every vehicle can visit every customer, must be observed. We refer to the problem we consider here as the site-dependent multi-trip periodic vehicle routing problem. An algorithm based on tabu search is presented for the problem and computational results presented on randomly generated test problems that are made publicly available. Our algorithm is also tested on a number of routing problems from the literature that constitute particular cases of the proposed problem. Specifically we consider the periodic vehicle routing problem; the site-dependent vehicle routing problem; the multi-trip vehicle routing problem; and the classical vehicle routing problem. Computational results for our tabu search algorithm on test problems taken from the literature for all of these problems are presented.     

Lexicographic optimisation in generalised network flow problems

In this paper the lexicographic optimisation of the multiobjective generalised network flow problem is considered. Optimality conditions are proved on the basis of the equivalence of this problem and a weighted generalised network flow problem. These conditions are used to develop a network-based algorithm which properly modifies primal-dual algorithms for minimum cost generalised network flow problems. Computational results indicate that this algorithm is faster than general-purpose algorithms for linear lexicographic optimisation. Besides, this model is used for approaching a water resource system design problem.