Multi-objective Cross Entropy Research Articles

Pareto routing and scheduling of dynamic urban rail transit services with multi-objective cross entropy method

This paper presents a Pareto optimization framework for routing and scheduling dynamic rail transit network services. We first develop an event-based dynamic transit network model that can capture the evolution of passenger demand and service operations with incorporation of passengers’ transfers and recirculation of limited number of train vehicles over different service lines. A multi-objective optimizer is then built upon the transit model which seeks jointly the settings of service lines and schedules that could minimize passengers’ journey times, transfer rates, and operator’s cost. The problem is solved by a cross-entropy method (CEM) which samples potential solutions from statistically tractable distribution models with iterative updates via maximum likelihood. The operational constraints are explicitly incorporated in the solution process which enhances the feasibility of the sampled solutions and hence effectiveness of the computational process compared with other metaheuristics used in the literature. A CEM-based ranking algorithm is further developed for deriving the Pareto-frontiers for the multi-objective transit network routing and scheduling. The proposed framework is applied and tested on the Hong Kong Light Rail Transit (LRT) network using real world scenario data. The results reveal new insights on how the existing operational settings could be improved. The present study contributes to urban transit network service planning with advanced computational techniques.

A Multi-objective Cross Entropy-based algorithm for sustainable global food supply chain with risk considerations: A case study

This paper proposes a sustainable global food supply chain model with risk considerations. Perishable foods begin to deteriorate after were produced. Therefore, without proper maintenance and transportation, the inventories may deteriorate quickly before be used which leads to unavoidable costs. The proposed model has four levels; suppliers, producers, warehouses and demand centers. The sustainable supply chain has three objectives, the first and second one is to reduce economic costs and environmental impacts, respectively and the third one is to maximize the level of employment in the chain. Also, because of nature of the supply chain, several risk factors are investigated in the model including: time delay risk, exchange rate fluctuations, raw material quality and production quality. For solving large instances, a Multi-Objective Cross Entropy (CE) algorithm is introduced. The proposed CE method is efficient in terms of its run time and low difference with the GAMS software. The MID and SM criteria which show the dispersion of the solutions are lower by CE method than the Epsilon constraint method. Also, a robust optimization approach is introduced to overcome the uncertainty. Also, a validation method is performed to evaluate the effectiveness of the robust approach. Then Sensitivity analysis is done to show capability of the model. Finally, the problem is applied for a food company in Iran and the city of Mashhad. The results show the establishment of a new factory in Qazvin lead to increase 2.8% of total costs, whereas decreasing 27.4% of CO2 emissions and increasing 44.2% of social benefits is resulted.

Economic Emission Dispatch Considering Renewable Energy Resources—A Multi-Objective Cross Entropy Optimization Approach

The conventional electrical power system economic dispatch (ED) often only pursues immediate economic benefits but neglects the harmful environment impacts of gas emissions from thermal power plants. To address this shortfall, economic emission dispatch (EED) has drawn a lot of attention in recent years. With the increasing penetration of renewable generation, the intermittence and uncertainty of renewable energy such as solar power and wind power increase the difficulties of power system scheduling. To enhance the dispatch performance with significant penetration of renewable energy, a modified multi-objective cross entropy algorithm (MMOCE) is proposed in this paper. To solve multi-objective optimization problems, a crowding–distance calculation technique and a novel external archive mechanism are introduced into the conventional cross entropy method. Additionally, the population updating process is simplified by introducing a self-adaptive parameter operator that substitutes the smoothing parameters, while the solution diversity and the adaptability in large scale systems are improved by introducing the crossover operator. Finally, a two-stage evolutionary mechanism further enhances the diversity and the rate of convergence. To verify the efficacy of the proposed MMOCE, eight benchmark functions and three different test systems considering different mixes of renewable energy sources are employed. The dispatch results by the proposed MMOCE are compared with other multi-objective cross entropy algorithms and published heuristic methods, confirming the superiority of the proposed MMOCE over other methods in all test systems.

Cross entropy optimization based on decomposition for multi-objective economic emission dispatch considering renewable energy generation uncertainties

Due to the increasing deterioration of environmental problem, combined economic emission dispatch (CEED) problem has become one of the active research areas in recent years. However, with sustained growth of intermittent power supplies connected to power system, their randomness and volatility will pose new challenges to power system optimization dispatch. For dealing with this problem, in this study, a novel Pareto optimization algorithm, called multi-objective cross entropy algorithm based on decomposition (MOCE/D), is proposed to solve a multi-objective optimization model for wind/hydro/thermal/photovoltaic power system by considering the uncertainties of intermittent power supplies and various practical constraints. Then, a hyper-plane-based decision-making strategy is introduced to identify the best compromise solution for the obtained Pareto frontiers. The overall performance of the proposed MOCE/D algorithm have been comprehensively investigated on the modified IEEE 30-bus and 118-bus systems. The statistical simulation results demonstrated that the proposed power system structure effectively reduces the operational cost as well as hazardous emissions; the proposed MOCE/D exhibits more competitive performance than the other state-of-the-art optimization algorithms, and therefore the obtained optimized operation strategy can provide a better trade-off between all objectives considered in this study.

Hybrid Energy Storage System (HESS) optimization enabling very short-term wind power generation scheduling based on output feature extraction

Incorporating Energy Storage System (ESS) with wind farm to establish Wind-Storage Combined Generation System is a promising solution to improve the dependability of integrated wind power. Hybrid Energy Storage System (HESS) is designed based on wind power fluctuation and ESS features. The optimization of system sizing and very short-term generation scheduling are the key points affecting system effectiveness and reliability of wind power. This paper proposes a novel real-time model prediction control (MPC) -multi objective cross entropy (MOCE) based energy management algorithm (MMEMA) to coordinate an HESS based on power output feature extraction. The proposed algorithm includes the SOC regulation strategies considering practical issues including charge/discharge power. Firstly, based on Wavelet Package Decomposition (WPD) and Hilbert Huang Transform (HHT) respectively, the fluctuation feature of real-time wind power output is studied to propose a HESS model aiming to obtain the economic capacity as well as maximum charging/discharging power in every generation scheduling period (10 min). Thus, according to case study, the sizing approach can reduce invest cost by 25.7–47.0%. Then, HESS data is taken as parameters and constraints for the proposed model prediction control (MPC) –multi objective cross entropy (MOCE) algorithm to minimize the deviation between generation scheduling plan and real-time integrated power. The optimization results from case wind farm show that the proposed MMEMA algorithm performs better in smoothing out the fluctuation and managing the SOC of HESS than Non-dominated Sorting Genetic Algorithm II based method (NEMA) by means of evaluating the indexes PD, HSOC and MSE.

Robust multi-objective optimization for energy production scheduling in microgrids

ABSTRACTIn order to achieve better economic and environmental benefits of microgrids (MGs) under multiple uncertainties in renewable energy resources and loads, a novel energy production scheduling method is proposed based on robust multi-objective optimization with minimax criterion. Firstly, a mixed integer minimax multi-objective formulation is developed to capture uncertainties as well as minimize economic and environmental objectives. Secondly, the primal problem is decomposed into a bi-level optimization problem, which attempts to seek robust scheduling scheme set under the worst-case realization of uncertainties in a multi-objective framework. Finally, a hierarchical meta-heuristic solution strategy, including multi-objective cross entropy algorithm and δ+ indicator, is designed to solve the reconstructed problem. Numerical results demonstrate that the proposed scheduling method can effectively attenuate the disturbance of uncertainties as well as reduce energy costs and emissions, as compared with single-objective robust optimization and multi-objective optimization scheduling approaches. This study could offer useful insights which help decision-makers balance robustness and comprehensive benefits in the operation of MGs.

Fault Feature Extraction of Wheel-bearing Based on Multi-objective Cross Entropy Optimization

Fault Feature Extraction of Wheel-bearing Based on Multi-objective Cross Entropy Optimization

Integrated scheduling of energy supply and demand in microgrids under uncertainty: A robust multi-objective optimization approach

As a Demand Response (DR) based working mode, the integrated scheduling of energy supply and demand provides an effective approach to improve economic and environmental benefits for Microgrids (MGs). However, it is still a challenging issue to cover uncertainties caused by intermittent renewable energy and random loads while optimizing multiple objectives in economy and environment. To tackle this issue, an integrated scheduling approach for MGs is proposed based on robust multi-objective optimization. Firstly, load shifting in a finite time is introduced to express an acceptable DR program for industrial customers. A minimax multi-objective optimization model is formulated to seek the minimum operation costs and emissions under the worst-case realization of uncertainties, which are captured by the robust sets with budgets of uncertainty. Secondly, a strong duality based model transformation method is implemented to cope with the strong coupling and nonlinearity in the proposed formulation. Also, Multi-Objective Cross Entropy (MOCE) algorithm is adopted to solve the reconstructed model for simultaneously optimizing all the objectives. Finally, detailed comparative experiments are conducted in problem level, model level and algorithm level. The simulation results show that the proposed scheduling approach can effectively attenuate the disturbances of uncertainties as well as achieve optimal economic and environmental benefits, compared with single-objective robust optimization scheduling approaches and deterministic multi-objective optimization scheduling approaches. Meanwhile, the validity and effectiveness of the robust multi-objective optimization approach for the MG integrated scheduling problem under uncertainty are confirmed.

On Simultaneously Increasing MANET Survivability, Capacity, Power Efficiency and Security

Increasing the capacity, survivability and power efficiency of wireless networks are often seen as competing goals. This paper shows that it is possible to pursue these goals simultaneously in ad hoc networks through the use of a multi-objective cross entropy optimisation operating on the placement of additional nodes and transmission power control. Encouraging results were obtained through simulation, with substantial capacity gains and associated transmission power savings achieved, whilst offering survivability through bi-connected topologies. This paper also discusses how the increase in power efficiency improves the security of the network by reducing the range at which messages within the network can be detected and decoded by eavesdropping nodes. A derivation of the optimal distance required between senders and receivers in the presence of noise is described, and the effects of relaying on overall network capacity and node throughput are discussed.

Multi-objective optimization based on an improved cross-entropy method. A case study of a micro-scale manufacturing process

The strong points of Estimation-of-Distribution algorithms (EDAs) and specifically cross-entropy methods are widely acknowledged. One of the main advantages of EDAs is that the fusion of prior information into the optimization procedure is straightforward, thereby reducing convergence time when such information is available. This study presents the modified Multi-Objective Cross-Entropy (MOCE+) method, based on a new procedure for addressing constraints: (i) the use of variable cutoff values for selecting the elitist population; and, (ii) filtering of the elitist population after each epoch. We study the proposed method in different test suites and compare its performance with some other well-known optimization methods. The comparative study demonstrates the good figures of merit of the MOCE+ method in complex test suites. Finally, the proposed method is applied to the multi-objective optimization of a micro-drilling process. Two conflicting targets are considered: total drilling time and vibrations on the plane that is perpendicular to the drilling axis. The Pareto front, obtained through the optimization process, is analyzed through quality metrics and the available options in the decision-making process. Overall, the quality metrics of the MOCE+ method were better than the metrics of the other optimization methods considered in this work. The reported optimization of the micro-drilling process with the proposed method could potentially have a direct impact on improvements in industrial efficiency.

Large thinned array design based on multi-objective cross entropy algorithm

To consider multi-objective optimization problem with the number of feed array elements and sidelobe level of large antenna array, multi-objective cross entropy (CE) algorithm is proposed by combining fuzzy c-mean clustering algorithm with traditional cross entropy algorithm, and specific program flow of the algorithm is given. Using the algorithm, large thinned array (200 elements) given sidelobe level (−10, −19 and −30 dB) problem is solved successfully. Compared with the traditional statistical algorithms, the optimization results of the algorithm validate that the number of feed array elements reduces by 51%, 11% and 6% respectively. In addition, compared with the particle swarm optimization (PSO) algorithm, the number of feed array elements from the algorithm is more similar, but the algorithm is more efficient.