Pareto-optimal Configurations Research Articles

Firefly Algorithm for Finding Optimal Shapes of Electromagnetic Devices

Many real-world optimization problems have to be treated as multi-objective optimization problems. An approach, well established in recent years, is to find Pareto optimal configurations of the trial variables by detecting nondominated solutions with the help of a suitable vector optimization method. Alternatively, relying on scalar optimization methods (both stochastic or deterministic), a suitable objective function taking all objectives into account simultaneously has to be defined. Depending on the number of trial variables, a scalar objective function of that type will exhibit a considerable number of feasible local solutions besides the global one. Therefore, a useful scalar optimization strategy should be able to end up (with a high probability) in the best of all possible solutions in the given search space and additionally detect as many local solutions as possible. Some population-based stochastic methods are implicitly suited for that task; others can be enhanced to fulfill these requirements. Higher order evolution strategies have successfully been tuned for that kind of problem by introducing cluster sensitive recombination [niching higher order evolution strategy (NES)]. The firefly algorithm (FFA) mimics the behavior of fireflies, which use a kind of flashing light to communicate with other members of their species. Since the intensity of the light of a single firefly diminishes with increasing distance, the FFA is implicitly able to detect local solutions on its way to the best solution for a given scalar objective function. The FFA will be applied to the well-known Rastrigin test function and to a shielding/shunting electromagnetic problem with two and three objectives, respectively, and its results will be compared with the ones obtained with an NES.

Combining multi-objective evolutionary algorithms and descriptive analytical modelling in energy scenario design

Environmental and security concerns urge energy planners to design more sustainable energy systems, reducing fossil fuel consumptions in favour of renewable solutions. The proposed scenarios typically rely on a mixing of different energy sources, thereby mitigating the availability and intermittency problems typically related to renewable technologies. Optimizing this combination is of crucial importance to cope with economic, technical, and environmental issues, which typically give rise to multiple contradictory objectives. To this purpose, this article presents a generalized framework coupling EnergyPLAN – a descriptive analytical model for medium/large-scale energy systems – with a multi-objective evolutionary algorithm – a type of optimizer widely used in the context of complex problems. By using this framework, it is possible to automatically identify a set of Pareto-optimal configurations with respect to different competing objectives. As an example, the method is applied to the case of Aalborg municipality, Denmark, by choosing cost and carbon emission minimization as contrasting goals. Results are compared with a manually identified scenario, taken from previous literature. The automatic approach, while confirming that the available manual solution is very close to optimality, yields an entire set of additional optimal solutions, showing its effectiveness in the simultaneous analysis of a wide range of combinations.

Optimal sensor placement under uncertainties using a nondirective movement glowworm swarm optimization algorithm

Optimal sensor placement (OSP) is a critical issue in construction and implementation of a sophisticated structural health monitoring (SHM) system. The uncertainties in the identified structural parameters based on the measured data may dramatically reduce the reliability of the condition evaluation results. In this paper, the information entropy, which provides an uncertainty metric for the identified structural parameters, is adopted as the performance measure for a sensor configuration, and the OSP problem is formulated as the multi-objective optimization problem of extracting the Pareto optimal sensor configurations that simultaneously minimize the appropriately defined information entropy indices. The nondirective movement glowworm swarm optimization (NMGSO) algorithm (based on the basic glowworm swarm optimization (GSO) algorithm) is proposed for identifying the effective Pareto optimal sensor configurations. The one-dimensional binary coding system is introduced to code the glowworms instead of the real vector coding method. The Hamming distance is employed to describe the divergence of different glowworms. The luciferin level of the glowworm is defined as a function of the rank value (RV) and the crowding distance (CD), which are deduced by non-dominated sorting. In addition, nondirective movement is developed to relocate the glowworms. A numerical simulation of a long-span suspension bridge is performed to demonstrate the effectiveness of the NMGSO algorithm. The results indicate that the NMGSO algorithm is capable of capturing the Pareto optimal sensor configurations with high accuracy and efficiency.

Decision support for ranking Pareto optimal process designs under uncertain market conditions

Considering the uncertainty of economic conditions, multi-objective optimisation can be favoured to single-objective optimisation for process design. However, from the Pareto sets generated by multi-objective optimisation it is not obvious to identify the best one, given that each solution is optimal with regard to the selected objectives. A method taking into account the economic parameters uncertainty to support decision making based on the Pareto-optimal solutions is proposed. It uses a Monte-Carlo simulation to define the probability of each of the Pareto optimal configuration to be in the list of the best configurations from the economical point of view. For a given economic context defined the most probable best configurations are identified. The proposed method is applied to two cases: the CO2 capture in power plants and synthetic natural gas production from biomass resources. The results allow to identify the most attractive system designs and give recommendations for the process engineers.

Optimal management of wind and solar energy resources

This paper presents a portfolio-based approach to the harvesting of renewable energy (RE) resources. Our examined problem setting considers the possibility of distributing the total available capacity across an array of heterogeneous RE generation technologies (wind and solar power production units) being dispersed over a large geographical area. We formulate the capacity allocation process as a bi-objective optimization problem, in which the decision maker seeks to increase the mean productivity of the entire array while having control on the variability of the aggregate energy supply. Using large-scale optimization techniques, we are able to calculate – to an arbitrary degree of accuracy – the complete set of Pareto-optimal configurations of power plants, which attain the maximum possible energy delivery for a given level of power supply risk. Experimental results from a reference geographical region show that wind and solar resources are largely complementary. We demonstrate how this feature could help energy policy makers to improve the overall reliability of future RE generation in a properly designed risk management framework.

Robust material handling system design with standard deviation, variance and downside risk as risk measures

The design and planning of major storage systems belong to the class of systems design problems under uncertainty. The overall structure of the system is determined during the design stage while the values of the future conditions and the future planning decisions are not known with certainty. Typically the future uncertainty is modeled through a number of scenarios and each scenario has an individual time-discounted total system cost. The overall performance of the material handling system (MHS) is characterized by the distribution of these scenario costs. The central tendency of the cost distribution is always computed as the expected value of the distribution. Several alternatives for the dispersion of the distribution can be used. In this study the standard deviation, variance, and the downside risk of the cost distribution are investigated as the risk measures of the system. We propose an algorithm to efficiently identify all configurations of the MHS that are Pareto-optimal with respect to the tradeoff between the expected value of the costs and the risk; such Pareto-optimal configurations are also called efficient. Although the MHS model has non-linear constraints, our proposed algorithm can solve such non-linear models taking into account both the expected costs and the risk. The final selection of the storage system for implementation can then be made based on the Pareto graph and other considerations such as the risk preferences of the system owner. The algorithms developed are illustrated through a case study which helps in developing business insights for the warehouse and MHS design planners and decision makers.

Multiobjective Design Optimization in the Lightweight Dataflow for DDDAS Environment (LiD4E) 1

In this paper, we introduce new methods for multiobjective, system-level optimization that have been incorporated into the Lightweight Dataflow for Dynamic Data Driven Application Systems (DDDAS) Environment (LiD4E). LiD4E is a design tool for optimized implementation of dynamic, data-driven stream mining systems using high-level dataflow models of computation. More specifically, we develop in this paper new methods for integrated modeling and optimization of real-time stream mining constraints, multidimensional stream mining performance (precision and recall), and energy efficiency. Using a design methodology centered on data-driven control of and coordination between alternative dataflow subsystems for stream mining (classification modes), we develop systematic methods for exploring complex, multidimensional design spaces associated with dynamic stream mining systems, and deriving sets of Pareto-optimal system configurations that can be switched among based on data characteristics and operating constraints.

Capacity allocation of hybrid solar-wind energy system based on discrete probabilistic method

Complementary renewable energies like wind and solar power may be more sufficient to satisfy reliability requirements. This paper proposes a quantitative capacity allocation method of a hybrid wind and solar energy system. First, discrete probability distributions are established to model the random factors including the volatility of power outputs and the failure of components. Then a multiobjective optimization model is formulated with objectives of minimization of the total investment, the nodal voltages violating limits probability, and power supply inadequacy probability. For the purpose of fast probability computing with a satisfactory precision degree, an innovative probabilistic load flow algorithm is introduced, which deals with means and increments of random variables separately and uses cumulants as well as Gram--Charlier series to obtain probabilistic distributions of state variables. A modified parallel elitist nondominated sorting genetic algorithm II is used to search the Pareto optimal configuration solutions.

Pareto Optimized EDCA Parameter Control for Wireless Local Area Networks

The performance of IEEE 802.11e enhanced distributed channel access (EDCA) is influenced by several interactive parameters that make quality of service (QoS) control complex and difficult. In EDCA, the most critical performance influencing parameters are the arbitration interframe space (AIFS) and contention window size (CW) of each access category (AC). The objective of this paper is to provide a scheme for parameter control such that the throughput per station as well as the overall system throughput of the network is maximized and controllable. For this purpose, a simple and accurate analytical model describing the throughput behavior of EDCA networks is presented in this paper. Based on this model, the paper further provides a scheme in which a Pareto optimal system configuration is obtained via an appropriate CW control for a given AIFS value, which is a different approach compared to relevant papers in the literature that deal with CW control only. The simulation results confirm the effectiveness of the proposed method which shows significant performance improvements compared to other existing algorithms.

Pareto optimal design of sectored toroidal superconducting magnet for SMES

A novel multi-objective optimization design approach for sectored toroidal superconducting magnetic energy storage coil has been developed considering the practical engineering constraints. The objectives include the minimization of necessary superconductor length and torus overall size or volume, which determines a significant part of cost towards realization of SMES. The best trade-off between the necessary conductor length for winding and magnet overall size is achieved in the Pareto-optimal solutions, the compact magnet size leads to increase in required superconducting cable length or vice versa The final choice among Pareto optimal configurations can be done in relation to other issues such as AC loss during transient operation, stray magnetic field at outside the coil assembly, and available discharge period, which is not considered in the optimization process. The proposed design approach is adapted for a 4.5MJ/1MW SMES system using low temperature niobium–titanium based Rutherford type cable. Furthermore, the validity of the representative Pareto solutions is confirmed by finite-element analysis (FEA) with a reasonably acceptable accuracy.

Strategic robust supply chain design based on the Pareto-optimal tradeoff between efficiency and risk

The strategic design of a robust supply chain has to determine the configuration of the supply chain so that its performance remains of a consistently high quality for all possible future conditions. The current modeling techniques often only consider either the efficiency or the risk of the supply chain. Instead, we define the strategic robust supply chain design as the set of all Pareto-optimal configurations considering simultaneously the efficiency and the risk, where the risk is measured by the standard deviation of the efficiency. We model the problem as the Mean–Standard Deviation Robust Design Problem (MSD-RDP). Since the standard deviation has a square root expression, which makes standard maximization algorithms based on mixed-integer linear programming non-applicable, we show the equivalency to the Mean–Variance Robust Design Problem (MV-RDP). The MV-RDP yields an infinite number of mixed-integer programming problems with quadratic objective (MIQO) when considering all possible tradeoff weights. In order to identify all Pareto-optimal configurations efficiently, we extend the branch-and-reduce algorithm by applying optimality cuts and upper bounds to eliminate parts of the infeasible region and the non-Pareto-optimal region. We show that all Pareto-optimal configurations can be found within a prescribed optimality tolerance with a finite number of iterations of solving the MIQO. Numerical experience for a metallurgical case is reported.

A genetic algorithm based optimization framework to visualize, evaluate, and modify 3D space configurations in Desktop VR

This paper presents the design and implementation of a Desktop VR (Virtual Reality) framework for generating and evaluating Pareto-optimal alternate 3D spatial configurations using GA (genetic algorithms). The 3-tier framework involves the generation of the Pareto-optimal plans using GA which are subsequently visualized first using a Java-based 2D Interface and finally in the form of a 3D VR scene. The search spaces (function domains) are extremely large in today’s multifaceted interior design situations, and the optimization procedure involves conflicting objective functions, and limitations in the form of constraint functions. The interior space allocation problem is formulated and implemented as the “optimal configuration of artifacts”. When using GAs, a group of Pareto-optimal solutions (Pareto set) are available for the planners and decision-makers, wherefrom one solution ought to be picked. Therefore, this study applies a tool to not only visually evaluate the plans, but also to interact with those plans to develop them further if needed. Besides enabling the optimal spatial configuration of the scene elements, this framework also facilitates evaluation and interaction via the 3D VR worlds. The framework aids the proactive exploration, analysis, and finalization of design aspects such as color, size, lighting, etc. of the various elements prior to the actual construction. The results demonstrate the robust performance of the GA and the final 3D VR environment with dynamic interactive capabilities. This final interface facilitates “GA-Compliant” transformations and scene modifications thereby facilitating the exploration and examination of alternative scene configurations.

Cooperation policies for efficient in-network caching

Caching is a key component of information-centric networking, but most of the work in the area focuses on simple en-route caching with limited cooperation between the caches. In this paper we model cache cooperation under a game theoretical framework and show how cache cooperation policy can allow the system to converge to a Pareto optimal configuration. Our work shows how cooperation impacts network caching performance and how it takes advantage of the structural properties of the underlying network.

A Method for Shaping the Dynamic Characteristics of Vibration Isolation Systems

In this paper a method for shaping the dynamic characteristics of vibration isolation systems is presented. The multi-criteria optimisation procedure is utilized in order to find the Pareto-optimal system configuration with simultaneous minimization of conflicted optimisation criteria: the isolated body acceleration and suspension travel. As an example of the proposed method, the seat with a pneuma-hydraulic suspension is investigated and its vibro-isolation properties are shaped by an appropriate selection of the system characteristics. The basic findings of the paper consist in the optimisation procedure that takes into account the nonlinear dynamic behaviour of vibration isolation systems.

Trading off Supply Chain Risk and Efficiency through Supply Chain Design

The configuration of complex systems to improve their efficiency (reward), risk, or a combination of both performance measures has long been a goal of systems engineering. This research focuses on designing supply chain systems where a large number of discrete configurations exist. The uncertainty of the future is modeled as a set of scenarios. The risk of the system is modeled as the standard deviation of the profits of the various scenarios, while the efficiency or reward of the system is computed as the expected value of the scenario profits. A configuration for which no other configuration exists that has both higher reward and lower risk is said to be Pareto-optimal. An optimizing algorithm that efficiently identifies all Pareto-optimal configurations of a supply chain is presented. A common risk mitigation strategy for supply chains is to increase the overall capacity of the supply chain by either constructing more facilities or by increasing the capacity of individual facilities. We then show through a numerical example, that this strategy does not always have the desired effect of reducing the risk. This observation is a new and counterintuitive managerial insight.

Designing Robust Routing Algorithms and Mapping Cores in Networks-on-Chip: A Multi-objective Evolutionary-based Approach

Mainstream electronic designs are realized by Systems-on-Chips (SoCs) that push the limits of integration. The advancement of manufacturing technologies in terms of integration leads us to SoCs with many (e.g., 10-1000) digital units (e.g., processor cores, controllers, storage, application-specific units) that need to be intercon- nected in an efficient and reliable way. The Network-on-Chip (NoC) design paradigm emerged recently as a promising alternative to classical bus-based communication ar- chitectures. Aside from better predictability and lower power consumption, the NoC approach offers greater scalability compared to previous solutions for on-chip commu- nication. The design flow of NoCs include several key issues. Among other parameters, the decision of where cores have to be topologically mapped and also the routing algo- rithm represent two highly correlated design problems that must be carefully solved for any given application in order to optimize different performance metrics. The strong correlation between the different parameters often makes that the optimization of a given performance metric has a negative effect on a different performance metric. In this paper we propose a new strategy that simultaneously refines the mapping and the routing function to determine the Pareto optimal configurations which optimize average communication delay and routing robustness. The proposed strategy has been applied on both synthetic and real traffic scenarios. The obtained results show how the solutions found by the proposed approach outperforms those provided by other approaches proposed in literature, in terms of both performance and fault tolerance.

Robust global supply network design

It has been widely documented that disruptions and changes in the environment of manufacturing in a global enterprise impact the performance of the enabling supply network. The need exists for a methodology that can not only provide an objective and transparent evaluation of the efficiency and risks of a supply network configuration but that can also design supply network configurations with provably superior performance. Supply chain engineering SCE fundamentally applies the perspective and methodology of systems engineering to the domain of supply chains. SCE is the integrator of various corporate functions such as purchasing, production, distribution, and sustainment over the total product life cycle from design, through deployment, production, sustainment, and disposal. A supply chain is actually a network that consists of a diverse set of organizational and geographical components that typically change over time. The systematic design and management of such an inherently complex system requires the principles and tools of model-based systems engineering. A comprehensive and integrated model of the structure and the behavior of the supply network of a manufacturing enterprise has been developed. In this model the inherent uncertainty of the future environmental conditions in which the supply network will have to function is captured in a large number of scenarios. The variability of the profits achieved by the supply network for the various scenarios is used as a proxy for the supply network risk. The model allows for the explicit tradeoff of the systems life cycle profit with the variability of this profit. An efficient solution algorithm eliminates the vast majority of feasible supply network configurations from consideration and identifies all the Pareto-optimal configurations. However, the final selection of the network configuration depends on the risk preferences of the designer and the complexity of the enterprise. Selecting the supply network configuration with the appropriate robustness becomes one of the principal risk mitigation policies for the network and, in turn, the enterprise. The combination of the socio designer risk preferences and analysis and technical Pareto-optimization of all feasible supply network configurations creates a transparent engineering design process that finds the supply network configuration best matched to the objectives of the manufacturing enterprise.

Performance analysis of Pareto optimal bearings subject to surface error variations

A Pareto optimization study was carried out on a flat pad aerostatic bearing design. Some of the Pareto optimal configurations were then subjected to surface profiling errors including tilt, concavity, convexity and waviness and key performance parameters such as load capacity, stiffness and flow rate determined. From these studies it was concluded that multi-orifice aerostatic flat pad bearings are highly sensitive to surface profile variations and these surface profile variations are inherent limitations of the current manufacturing techniques. A technique to account for the sensitivity to manufacturing tolerance within air bearing optimization studies is also proposed.

Multiobjective design optimization and Pareto front analysis of a radial eddy current coupler

The paper proposes a multiobjective optimization to design a radial eddy current coupler, where the torque is maximized while the momentum of inertia is minimized to improve the dynamic behavior of the device. An analytical solution of the electromagnetic problem is used to speed up the computation of objectives and an optimization algorithm based on the emulation of the immune system behavior, referred to as Vector Immune System, is adopted to find tradeoff solutions between objectives. The solutions found so far are compared with solutions obtained by a Genetic Algorithm with fuzzy scalarization of objectives. It shows a faster convergence with a better spread of trade-off solutions available for a higher level decision making. A deep analysis of these Pareto optimal configurations is also provided, trying to discover common properties of optimal solutions.

Robust design and optimization for autonomous PV-wind hybrid power systems

This study presents a robust design method for autonomous photovoltaic (PV)-wind hybrid power systems to obtain an optimum system configuration insensitive to design variable variations. This issue has been formulated as a constraint multi-objective optimization problem, which is solved by a multi-objective genetic algorithm, NSGA-II. Monte Carlo Simulation (MCS) method, combined with Latin Hypercube Sampling (LHS), is applied to evaluate the stochastic system performance. The potential of the proposed method has been demonstrated by a conceptual system design. A comparative study between the proposed robust method and the deterministic method presented in literature has been conducted. The results indicate that the proposed method can find a large mount of Pareto optimal system configurations with better compromising performance than the deterministic method. The trade-off information may be derived by a systematical comparison of these configurations. The proposed robust design method should be useful for hybrid power systems that require both optimality and robustness.