Tohid Erfani

Directed search domain: a method for even generation of the Pareto frontier in multiobjective optimization

Optimization is one of the most important and challenging parts of any engineering design. In real-world design, multiobjective optimization with constraints has to be considered. The optimal solution in this case is not unique because the objectives can contradict each other. Therefore, a set of optimal solutions, which forms the Pareto frontier, should be considered. There are many algorithms to generate a Pareto set. However, only a few of them are potentially capable of providing an evenly distributed set of solutions. This property is especially important in real-life design because a decision maker is usually able to analyse only a very limited number of solutions. The main objective of this article is to develop and give detailed description of an algorithm that is able to generate an evenly distributed Pareto set in a general formulation. The approach is based on shrinking a search domain to generate a Pareto optimal solution in a selected area on the Pareto frontier. The effectiveness of the algorithm is demonstrated by a number of challenging test cases. For the first time, some of these test cases are successfully solved via a classical approach.

Simulating water markets with transaction costs

This paper presents an optimization model to simulate short-term pair-wise spot-market trading of surface water abstraction licenses (water rights). The approach uses a node-arc multicommodity formulation that tracks individual supplier-receiver transactions in a water resource network. This enables accounting for transaction costs between individual buyer-seller pairs and abstractor-specific rules and behaviors using constraints. Trades are driven by economic demand curves that represent each abstractors time-varying water demand. The purpose of the proposed model is to assess potential hydrologic and economic outcomes of water markets and aid policy makers in designing water market regulations. The model is applied to the Great Ouse River basin in Eastern England. The model assesses the potential weekly water trades and abstractions that could occur in a normal and a dry year. Four sectors (public water supply, energy, agriculture, and industrial) are included in the 94 active licensed water diversions. Each licenses unique environmental restrictions are represented and weekly economic water demand curves are estimated. Rules encoded as constraints represent current water management realities and plausible stakeholder-informed water market behaviors. Results show buyers favor sellers who can supply large volumes to minimize transactions. The energy plant cooling and agricultural licenses, often restricted from obtaining water at times when it generates benefits, benefit most from trades. Assumptions and model limitations are discussed. Key Points Transaction tracking hydro-economic optimization models simulate water markets Proposed model formulation incorporates transaction costs and trading behavior Water markets benefit users with the most restricted water access

Towards fully automatic reliable 3D acquisition

This paper describes a novel system for accurate 3D digitization of complex objects. Its main novelties can be seen in the new approach, which brings together different systems and tools in a unique platform capable of automatically generating an accurate and complete model for an object of interest. This is performed through generating an approximate model of the object, designing a stereo imaging network for the object with this model and capturing the images at the designed postures through exploiting an inverse kinematics method for a non-standard six degree of freedom robot. The images are then used for accurate and dense 3D reconstruction using photogrammetric multi-view stereo method in two modes, including resolving scale with baseline and with control points. The results confirm the feasibility of using Particle Swarm Optimization in solving inverse kinematics for this non-standard robot. The system provides this opportunity to test the effect of incidence angle on imaging network design and shows that the matching algorithms work effectively for incidence angle of 10?. The accuracy of the final point cloud generated with the system was tested in two modes through a comparison with a dataset generated with a close range 3D colour laser scanner. We designed a 6-DOF robot for accurate and dense 3D reconstruction using images.Particle Swarm Optimization was evaluated for inverse kinematic of the robot.A software package, Imaging Network Designer, was tested for this robot.The accuracy of the robot for 3D reconstruction is around 200 µ m .

An evolutionary approach to solve a system of multiple interrelated agent problems

Graphical abstractDisplay Omitted HighlightsWe develop an evolutionary approach to solve interrelated optimisation problems.Multiple agents autonomously deal with their own problems and react to the others.Test problems in water pollution and aerospace modelling demonstrate the algorithm.Experiments on scalability and convergence of the algorithm show promising results. Deterministic approaches to simultaneously solve different interrelated optimisation problems lead to a general class of nonlinear complementarity problem (NCP). Due to differentiability and convexity requirements of the problems, sophisticated algorithms are introduced in literature. This paper develops an evolutionary algorithm to solve the NCPs. The proposed approach is a parallel search in which multiple populations representing different agents evolve simultaneously whilst in contact with each other. In this context, each agent autonomously solves its optimisation programme while sharing its decisions with the neighbouring agents and, hence, it affects their actions. The framework is applied to an environmental and an aerospace application where the obtained results are compared with those found in literature. The convergence and scalability of the approach is tested and its search algorithm performance is analysed. Results encourage the application of such an evolutionary based algorithm for complementarity problems and future work should investigate its development as well as its performance improvements.

Fair Resource Allocation Using Multi-population Evolutionary Algorithm

Resource allocation between selfish agents are performed under centralised and/or distributed mechanisms. However, there are issues in both cases. In centralised solution, although the resources are allocated in an efficient way, the allocation decisions may not be acceptable for some selfish agents making them reluctant to cooperation. In decentralised solution, although the problem is solved from each agent’s perspective, the allocation leads to an inefficient usage of provided resources. For example, such an issue is evident in a water network distribution system where different agents share the river water and a central planner (CP) maximises the social welfare to the whole system. Issue arises when the CP solution is not acceptable by some agents. Therefore, a mechanism should be devised to encourage each agent to accept the CP decision. This paper introduces a mechanism in re-distributing the CP revenue value amongst the competing agents based on their contribution to the CP value. To find each user’s contribution, this paper develops a parallel evolutionary search algorithm which enables the agents to autonomously solve their local optimisation problem whilst interacting with the other agents and the whole system. The search evolves towards a solution which is used as an incentive for calculating a fair revenue for each agent. The framework is applied to a river reach with five competitive users. Results show decentralised coupled centralised approaches has the potential to represent mechanisms for a fair resource allocation among competing self-interested agents.

A webcam photogrammetric method for robot calibration

This paper describes a strategy for accurate robot calibration using close range photogrammetry. A 5-DoF robot has been designed for placement of two web cameras relative to an object. To ensure correct camera positioning, the robot is calibrated using the following strategy. First, a Denavit-Hartenberg method is used to generate a general kinematic robot model. A set of reference frames are defined relative to each joint and each of the cameras, transformation matrices are then produced to represent change in position and orientation between frames in terms of joint positions and unknown parameters. The complete model is extracted by multiplying these matrices. Second, photogrammetry is used to estimate the postures of both cameras. A set of images are captured of a calibration fixture from different robot poses. The camera postures are then estimated using bundle adjustment. Third, the kinematic parameters are estimated using weighted least squares. For each pose a set of equations are extracted from the model and the unknown parameters are estimated in an iterative procedure. Finally these values are substituted back into the original model. This final model is tested using forward kinematics by comparing the model’s predicted camera postures for given joint positions to the values obtained through photogrammetry. Inverse kinematics is performed using both least squares and particle swarm optimisation and these techniques are contrasted. Results demonstrate that this photogrammetry approach produces a reliable and accurate model of the robot that can be used with both least squares and particle swarm optimisation for robot control.

Optimization of Induced Velocity for Plasma Actuator with Multiple Encapsulated Electrodes using Response Surface Methodology

In design problem such as a new configuration of plasma actuator for maximizing the velocity of the airflow, experimental setup is done by an ad-hoc procedure. This provides the researcher with a relationship of the input parameters (width of the electrode, distance of the electrodes, the voltage and etc) and the velocity. As the experiments are time consuming and expensive in most of the cases, the above method is not always a reasonable approach in finding the optimal plasma configuration. In this paper response surface methodology, a surrogate modelling approach, is used to allow a systematic investigation in setting the experiments and finding the optimal plasma configuration. This allows the researcher to consider the uncertainty in observation and find a reliable approximate model for the induced velocity. Furthermore, the velocity of the airflow is modelled with small while enough number of experimental setups. The model is validated with the experimental data.

Generation of pareto frontier via a modified directed search domain method

Multiobjective optimization is one of the key challenges in engineering design process. Due to the non-uniqueness of the solution in this context, a set of evenly distributed solutions is particularly important for the designer. Directed Search Domain (DSD) method is proved to be efficient enough to tackle such a problem. In this paper, we introduce two main modifications of the DSD to make the algorithm simpler for application. They are related to the conduct of the search domain and reformulation of the appropriate single objective optimization problem. The proposed modifications increase the efficiency of the method in computational time with lower number of objective evaluations. A set of test cases demonstrates the capabilities of the new approach.

Real‐Options Water Supply Planning: Multistage Scenario Trees for Adaptive and Flexible Capacity Expansion Under Probabilistic Climate Change Uncertainty

Planning water supply infrastructure includes identifying interventions that cost‐effectively secure an acceptably reliable water supply. Climate change is a source of uncertainty for water supply developments as its impact on source yields is uncertain. Adaptability to changing future conditions is increasingly viewed as a valuable design principle of strategic water planning. Because present decisions impact a systems ability to adapt to future needs, flexibility in activating, delaying, and replacing engineering projects should be considered in least‐cost water supply intervention scheduling. This is a principle of Real Options Analysis, which this paper applies to least‐cost capacity expansion scheduling via multistage stochastic mathematical programming. We apply the proposed model to a real‐world utility with many investment decision stages using a generalized scenario tree construction algorithm to efficiently approximate the probabilistic uncertainty. To evaluate the implementation of Real Options Analysis, the use of two metrics is proposed: the value of the stochastic solution and the expected value of perfect information that quantify the value of adopting adaptive and flexible plans, respectively. An application to Londons water system demonstrates the generalized approach. The investment decisions results are a mixture of long‐term and contingency schemes that are optimally chosen considering different futures. The value of the stochastic solution shows that by considering uncertainty, adaptive investment decisions avoid £100 million net present value (NPV) cost, 15% of the total NPV. The expected value of perfect information demonstrates that optimal delay and early decisions have £50 million NPV, 6% of total NPV. Sensitivity of results to the characteristics of the scenario tree and uncertainty set is assessed.

Approximation of the pareto surface via a hybrid of scalarization method and evolutionary algorithm

© 2015, American Institute of Aeronautics and Astronautics Inc. All Rights Reserved.In engineering design process, multiobjective optimization plays an important role. Since the solution to the problem is not unique, the designer requires a set of evenly distributed solutions for trade-off analysis. Classical gradient based algorithms and evo- lutionary approaches have shown their capability on producing such a set. This paper introduces a hybrid method which exploits a classical scalarization approach to partition the solution space into different and distinct local search spaces. The sub-problems in each local search domain are then solved by evolutionary strategies in parallel by using the neighboring population information. The fitness function is constructed to handle the problem constraints and meanwhile minimize the distance of the solution to the true opti- mum frontier. The algorithm behavior is studied on different numerical test cases as well as an engineering aerodynamic problem. The results are compared in both convergence and diversity to those of another well known approach to demonstrate the efficacy of the proposed method. It is concluded that scalarization increases the convergence speed while maintaining a well spread set of solutions.