In this paper, a hybrid approach organized in four phases is proposed to solve the multi-objective trajectory planning problem for industrial robots. In the first phase, a transcription of the original problem into a standard multi-objective parametric optimization problem is achieved by adopting an adequate parametrization scheme for the continuous robot configuration variables. Then, in the second phase, a global search is performed using a population-based search metaheuristic in order to build a first approximation of the Pareto front (PF). In the third phase, a local search is applied in the neighborhood of each solution of the PF approximation using a deterministic algorithm in order to generate new solutions. Finally, in the fourth phase, results of the global and local searches are gathered and postprocessed using a multi-objective direct search method to enhance the quality of compromise solutions and to converge toward the true optimal PF. By combining different optimization techniques, we intend not only to improve the overall search mechanism of the optimization strategy but also the resulting hybrid algorithm should keep the robustness of the population-based algorithm while enjoying the theoretical properties of convergence of the deterministic component. Also, the proposed approach is modular and flexible, and it can be implemented in different ways according to the applied techniques in the different phases. In this paper, we illustrate the efficiency of the hybrid framework by considering different techniques available in various numerical optimization libraries which are combined judiciously and tested on various case studies.

Coverage path planning (CPP) is a subfield of path planning problems in which free areas of a given domain must be visited by a robot at least once while avoiding obstacles. In some situations, the path may be optimized for one or more criteria such as total distance traveled, number of turns, and total area covered by the robot. Accordingly, the CPP problem has been formulated as a multi-objective optimization (MOO) problem, which turns out to be a challenging discrete optimization problem, hence conventional MOO algorithms like Non-dominated Sorting Genetic Algorithm-2 (NSGA-II) do not work as it is. This study implements a modified NSGA-II to solve the MOO problem of CPP for a mobile robot. In this paper, the proposed method adopted two objective functions: (1) the total distance traveled by the robot and (2) the number of turns taken by the robot. The two objective functions are used to calculate energy consumption. The proposed method is compared to the hybrid genetic algorithm (HGA) and the traditional genetic algorithm (TGA) in a rectilinear environment containing obstacles of various complex shapes. In addition, the results of the proposed algorithm are compared to those generated by HGA, TGA, oriented rectilinear decomposition, and spatial cell diffusion and family of spanning tree coverage in existing research papers. The results of all comparisons indicate that the proposed algorithm outperformed the existing algorithms by reducing energy consumption by 5 to 60%. This paper provides the facility to operate the robot in different modes.

Even the shortest flight through unknown, cluttered environments requires reliable local path planning algorithms to avoid unforeseen obstacles. The algorithm must evaluate alternative flight paths and identify the best path if an obstacle blocks its way. Commonly, weighted sums are used here. This work shows that weighted Chebyshev distances and factorial achievement scalarising functions are suitable alternatives to weighted sums if combined with the 3DVFH* local path planning algorithm. Both methods considerably reduce the failure probability of simulated flights in various environments. The standard 3DVFH* uses a weighted sum and has a failure probability of 50% in the test environments. A factorial achievement scalarising function, which minimises the worst combination of two out of four objective functions, reaches a failure probability of 26%; A weighted Chebyshev distance, which optimises the worst objective, has a failure probability of 30%. These results show promise for further enhancements and to support broader applicability.

This paper focuses on the design, analysis, and multi-objective optimization of a novel 5-degrees of freedom (DOF) double-driven parallel mechanism. A novel 5-DOF parallel mechanism with two double-driven branch chains is proposed, which can serve as a machine tool. By installing two actuators on one branch chain, the proposed parallel mechanism can achieve 5-DOF of the moving platform with only three branch chains. Afterwards, analytical solution for inverse kinematics is derived. The 5$\times$5 homogeneous Jacobian matrix is obtained by transforming actuator velocities into linear velocities at three points on the moving platform. Meanwhile, the workspace, dexterity, and volume are analyzed based on the kinematic model. Ultimately, a stage-by-stage Pareto optimization method is proposed to solve the multi-objective optimization problem of this parallel mechanism. The optimization results show that the workspace, compactness, and dexterity of this mechanism can be improved efficiently.

Electric vehicles (EVs) are very quiet at low speed, which can be hazardous for pedestrians, especially visually impaired people. It is now mandatory (since mid-2019 in Europe) to add external warning sounds, but poor sound design can lead to noise pollution, and consequently annoyance. Moreover, it is possible that EVs are not sufficiently detectable in urban areas because of the masking effect from the background noise. In this paper, we propose a method for the design of warning sounds that takes into account both detectability and unpleasantness. The method implements a multiobjective interactive genetic algorithm (IGA) for the optimisation of the characteristics of synthesised sounds. An experiment is proposed to a first panel of participants in order to define a set of Pareto efficient sounds. At the individual level, sounds obtained with the IGA are compared to different sound design proposals. Results show that the quality of the sounds designed by the IGA method is comparable to those provided by a sound designer. From the sounds of the Pareto set, a design recommendation method based on the probability distributions of the sounds’ characteristics is proposed. An external validation with a second panel of participants shows that these recommended sounds constitute relevant trade-offs when compared to other design proposals.

In the present work, a new hybrid approach combining particle swarm optimization (PSO) algorithm with recurrent dynamic neural network (RDNN), which is described as PSO-RDNN algorithm, is proposed for multi-performance optimization of machining parameters in finish turning of hardened AISI D2. The suggested optimization problem is solved using the weighted sum technique. Process parameters including cutting speed and feed rate are optimized for minimizing operation cost, maximizing tool life, and producing parts with acceptable surface roughness. Based on experimental results, two neural network models were developed for predicting tool flank wear and surface roughness during the machining process. Based on trained neural networks and structured hybrid algorithm, optimum cutting parameters were obtained. The coefficient of determination for trained neural networks was calculated as R2 = 0.9893 and R2 = 0.9879 for predicted flank wear and surface roughness, respectively, which proves the efficiency of trained neural models in real industrial applications. Furthermore, the offered methodology returns a Pareto optimality graph, which represents optimized cutting variables for several various cutting conditions.

We explain some key challenges when dealing with a single- or multi-objective optimization problem in practice. To overcome these challenges, we present a mathematical program that optimizes the Nash social welfare function. We refer to this mathematical program as the Nash social welfare program (NSWP). An interesting property of the NSWP is that it can be constructed for any single- or multi-objective optimization problem. We show that solving the NSWP could result in more desirable solutions in practice than its single- or multi-objective counterpart. We also discuss several promising approaches that could be employed to solve the NSWP in practice.

In product development, user-scenarios are a way of tailoring requirements to defined customer groups. Furthermore, a product design often involves multiple conflicting objectives that are analyzed within an iterative process. The models typically used for the analysis often do not accurately reflect the real-world representation. This can be alleviated by finding robust product designs. While usually uncertainties due to manufacturing tolerances are investigated, we additionally consider uncertainties in the user-scenario. Therefore, we present a robustness evaluation in a multi-objective numerical optimization in product development. For this, we consider manufacturing tolerances using an adjusted Latin Hypercube Sampling as well as deviations in the user-scenario by means of a Gaussian distribution. In the case study, we present the robust development of a customer specific coffee machine, where we show the robustness evaluation and the impact of the proposed adjustments. The advantage of the presented process is a product design tailored to the customer's requirements under specified uncertainties. In addition, this enables a time benefit in the product development due to the automated analysis used in the optimization.

Consensus does not exist for which cost forms (i.e., one accounting solely for explicit cost and the other for both explicit and opportunity costs as in relative opportunity cost) are used in calculating return on investment (ROI) for conservation-related decisions. This research examines how the cost of conservation investment with and without inclusion of the opportunity cost of the protected area results in different solutions in a multi-objective optimization framework at the county level in the Central and Southern Appalachian Region of the USA. We maximize rates of ROI of both forest-dependent biodiversity and economic impact generated by forest-based payments for ecosystem services. We find that the conservation budget is optimally distributed more narrowly among counties that are more likely to be rural when the investment cost measure is relative opportunity cost than when it is explicit cost. We also find that the sacrifice in forest-dependent biodiversity per unit increase in economic impact is higher when investment cost is measured by relative opportunity cost rather than when measured by explicit cost. By understanding the consequences of using one cost measure over the other, a conservation agency can decide on which cost measure is more appropriate for informing the agency’s decision-making process.

This paper deals with the multi-objective optimal design of a novel 6-degree of freedom (DOF) hybrid spray-painting robot. Its kinematic model is obtained by dividing it into serial and parallel parts. The dynamic equation is formulated by virtual work principle. A performance index for evaluating the compactness of robot is presented. Taking compactness, motion/force transmissibility, and energy consumption as performance indices, the optimal geometric parameters of the robot are selected in the Pareto-optimal set by constructing a comprehensive performance index. This paper is very useful for the development of the spray-painting robot.

A trajectory optimisation procedure is addressed to generate a reference trajectory for Satellite Launch Vehicles (SLVs). Using a grid-based discrete scheme, a Modified Minimum Cost Network Flow (MCNF)-based algorithm over a large-scale network is proposed. By using the network grid around the Earth and the discrete dynamic equations of motion, the optimum trajectory from a launch point to the desired orbit is obtained exactly by minimisation of a cost functional subject to the nonlinear dynamics and mission constraints of the SLV. Several objectives such as the flight time and terminal conditions may be assigned to each arc in the network. Simulation results demonstrate the capability of the proposed algorithm to generate an admissible trajectory in the minimum possible time compared with previous works.

Unmanned aerial vehicle (UAV) was introduced for nondeterministic traffic monitoring, and a real-time UAV cruise route planning approach was proposed for road segment surveillance. First, critical road segments are defined so as to identify the visiting and unvisited road segments. Then, a UAV cruise route optimization model is established. Next, a decomposition-based multi-objective evolutionary algorithm (DMEA) is proposed. Furthermore, a case study with two scenarios and algorithm sensitivity analysis are conducted. The analysis result shows that DMEA outperforms other two commonly used algorithms in terms of calculation time and solution quality. Finally, conclusions and recommendations on UAV-based traffic monitoring are presented.

Spray-painting equipments are important for the automatic spraying of long conical objects such as rocket fairing. This paper proposes a spray-painting equipment that consists of a feed worktable, a gantry frame and two serial–parallel mechanisms and investigates the optimal design of PRR–PRR parallel manipulator in serial–parallel mechanisms. Based on the kinematic model of the parallel manipulator, the conditioning performance, workspace and accuracy performance indices are defined. The dynamic model is derived using virtual work principle and dynamic evaluation index is defined. The conditioning performance, workspace, accuracy performance and dynamic performance are involved in multi-objective optimization design to determine the optimal geometrical parameters of the parallel manipulator. Furthermore, the geometrical parameters of the gantry frame are optimized. An example is given to show how to determine these parameters by taking a long object with conical surface as painted object.

This paper proposes a special non-symmetric topology of a 3PRR planar parallel kinematics mechanism, which naturally avoids singularity within the workspace and can be utilized for hybrid kinematics machine tools. Subsequently, single-objective and multi-objective optimizations are conducted to improve the performance. The workspace area and minimum eigenvalue, as well as the condition number of the homogenized Cartesian stiffness matrix across the workspace, have been chosen as the objectives in the optimization based on their relevance to the machining application. The single-objective optimization is conducted by using a single-objective genetic algorithm and a hybrid algorithm, whereas the multi-objective optimization is conducted by using a multi-objective genetic algorithm, a weighted sum single-objective genetic algorithm, and a weighted sum hybrid algorithm. It is shown that the single-objective optimization gives superior value in the optimized objective, while sacrificing the other objectives, whereas the multi-objective optimization compromises the improvement of all objectives by providing non-dominated values. In terms of the algorithms, it is shown that a hybrid algorithm can either verify or refine the optimal value obtained by a genetic algorithm.

In this study MHD flow around and through porous cylinder is numerically investigated. The governing equations are developed in polar coordinate arrangement in both porous and non-porous media on the basis of single-domain technique. The equations are solved numerically based on finite volume method over staggered grid structure. Nusselt number and drag coefficient are selected as two key parameters describing performance of this system. By applying response surface methodology the sensitivity of these parameters to main factors of the problem, including Stuart number, Darcy number and Reynolds number are quantified. RSM is also utilized to perform an optimization process to find the best condition in which the lowest drag force and highest heat transfer rate occur simultaneously. The CFD analysis is carried out for variant Reynolds numbers (10 ≤ Re ≤ 40), Darcy numbers (10-6 ≤ Da ≤ 10-2) and Stuart numbers (2 ≤ N ≤ 10). Streamlines and isotherms are presented to indicate the impacts of such parameters on heat and fluid flow. It can be seen that, Drag coefficient and Nusselt number increase by augmenting magnetic field strength. Beside, Darcy number and Reynolds numbers have a direct and inverse effect on Nuave and Cd, respectively. Results of optimization process show that Nuave and Cd are more sensitive to Reynolds and Stuart numbers, respectively, while they less sensitive to Darcy number. Moreover, it is revealed that the optimum condition occurs at Da = 10-2, Re = 38.1 and N = 4.49.

A new minimally invasive surgical (MIS) robot consisting of a spherical remote center motion (RCM) mechanism with modular design is proposed. A multi-objective dimensional synthesis model is presented to obtain the excellent performance indices. There are four objectives: a global kinematic index, a compactness index, a global comprehensive stiffness index, and a global dynamic index. Other indices characterizing the design requirement, such as workspace, mechanical parameter, and mass, are chosen as constraints. A new decoupled mechanism is raised to solve the coupled motion between the linear platform and the four degrees of freedom (DoF) of surgical instrument as a result of post-driving motors. Another new mechanical decoupled method is proposed to eliminate the coupled motion between the wrist and the forceps, enhance the dexterity of surgical instrument, and improve the independence of each motor. Then, a 7-DoF MIS robotic prototype based on optimization results has been built up. Experiment results validate the effectiveness of the two mechanical decoupled methods. The position change of the RCM point, accuracy, and repeatability of the MIS robot meet the requirements of MIS. Successful animal experiments validate the effectiveness of the novel MIS robot.

With lower turbulence and less rigorous restrictions on noise levels, offshore wind farms provide favourable conditions for the development of high-tip-speed wind turbines. In this study, the multi-objective optimization is presented for a 5MW wind turbine design and the effects of high tip speed on power output, cost and noise are analysed. In order to improve the convergence and efficiency of optimization, a novel type of gradient-based multi-objective evolutionary algorithm is proposed based on uniform decomposition and differential evolution. Optimization examples of the wind turbines indicate that the new algorithm can obtain uniformly distributed optimal solutions and this algorithm outperforms the conventional evolutionary algorithms in convergence and optimization efficiency. For the 5MW wind turbines designed, increasing the tip speed can greatly reduce the cost of energy (COE). When the tip speed increases from 80m/s to 100m/s, under the same annual energy production, the COE decreases by 3.2% in a class I wind farm and by 5.1% in a class III one, respectively, while the sound pressure level increases by a maximum of 4.4dB with the class III wind farm case.

This paper presents a novel reconfigurable parallel mechanism, which can serve as a machine tool. The proposed parallel mechanism can change its structure parameters by driving a bevel gear system fixed in the base platform. First, the forward and inverse kinematics of the proposed mechanism are investigated. Second, the reachable workspace and Jacobian matrix are conducted. Based on the Jacobian matrix, the stiffness model and dexterity of the end effector are developed in detail. Finally, a multi-objective optimization is performed by using the Genetic Algorithm, and the workspace and global performance indexes of stiffness as well as the dexterity are considered as the performance indices to improve the performance of the reconfigurable parallel mechanism. Finally, Pareto frontier figure and several tables are provided to illustrate the results of the optimization. The results showed the proposed method has improved the performance of the reconfigurable machine tool in terms of its stiffness and dexterity.

We assess empirically how agricultural lands should be used to produce the highest valued outputs, which include food, energy, and environmental goods and services. We explore efficiency tradeoffs associated with allocating land between food and bioenergy and use a set of market prices and nonmarket environmental values to value the outputs produced by those crops. We also examine the degree to which using marginal land for energy crops is an approximately optimal rule. Our empirical results for an agricultural watershed in Iowa show that planting energy crops on marginal land is not likely to yield the highest valued output.

This paper proposes a novel three-degrees-of-freedom (3-DOF) hybrid manipulator, 3PU*S-PU, which evolves from the general function (Gf) set theory. After discussing the advantages of this new type of hybrid manipulator, this report analyzes the kinematic and Jacobian matrix of the manipulator. Subsequently, the kinematic performances, including stiffness/compliance, and workspace, undergo analysis, followed by the multi-objective optimization of the compliance and workspace. The Lagrangian method provides the framework for briefly analyzing the dynamics of the proposed manipulator. Finally, the results of this assessment comprise a guideline for controlling the manipulator.