Multi-objective Self-adaptive Differential Evolution Research Articles

A Chaotic Sobol Sequence-based multi-objective evolutionary algorithm for optimal design and expansion of water networks

The design of a water distribution network (WDN) is an optimization problem that is computationally challenging with conflicting objectives. This study offers an enhanced Chaotic Sobol Sequence-based Multi-Objective Self-Adaptive Differential Evolution (CS-MOSADE) algorithm for multi-objective WDN design. The CS-MOSADE algorithm was tested on two benchmark WDNs, and a real WDN. Optimization results indicate that the CS-MOSADE algorithm converged two to three times faster than the MOSADE and NSGA-IIalgorithms and led to better output in terms of even distribution of solutions and convergence towards the true Pareto-optimal front. Smaller spacing metric indicated better uniformity in the obtained solutions; and larger hyper-area and coverage function values depicted better convergence towards the true Pareto-optimal front for the CS-MOSADE algorithm compared to the other algorithms. The CS-MOSADE algorithm was then applied to solve a WDN expansion problem for optimal pump scheduling and minimization of Life Cycle Cost, maximization of reliability and minimization of Green House Gas (GHG) emissions. A significant reduction in GHG emissions of 2.17 x 106 kg was achieved at an additional cost of $0.55 x 107 when optimal pump scheduling was incorporated in the model of the real WDN over service life of 50 years.

A Self-Adaptive Multiobjective Differential Evolution Algorithm for the Unrelated Parallel Batch Processing Machine Scheduling Problem

In this paper, the unrelated parallel batch processing machine (UPBPM) scheduling problem is addressed to minimize the total energy consumption (TEC) and makespan. Firstly, a mixed-integer line programming model (MILP) of the UPBPM scheduling problem is presented. Secondly, a self-adaptive multiobjective differential evolution (AMODE) algorithm is put forward. Since the parameter value can affect the performance of the algorithm greatly, an adaptive parameter control method is proposed according to the convergence index of the individual and the evolution degree of the population to improve the exploitation and exploration ability of the algorithm. Meanwhile, an adaptive mutation strategy is proposed to improve the algorithm’s convergence and the solutions’ diversity. Finally, to verify the effectiveness of the algorithm, comparative experiments are carried out on 20 instances with 5 different scales. Numerical comparisons indicate that the proposed method can achieve high comprehensive performance.

Improved MOSADE algorithm incorporating Sobol sequences for multi-objective design of Water Distribution Networks

Design of Water Distribution Networks (WDNs) is a tremendously hard optimization problem, and consideration of reliability further adds to the complexity, which may involve huge computational effort. As several past studies stressed that Evolutionary Algorithms (EAs) could be efficient tools for WDN design, so this study, presents an effective methodology, Multi-Objective Self Adaptive Differential Evolution (MOSADE) algorithm using Sobol sequences for random number generation, termed as (S-MOSADE) for WDN design. The efficacy of the S-MOSADE framework is evaluated by application on a few benchmark WDNs, by considering cost minimization and mechanical reliability maximization and comparing the results with that of NSGA-II algorithm. The results illustrated that S-MOSADE algorithm leads to a better Pareto-optimal front than NSGA-II with respect to uniformly spaced and wide range of non-dominated solutions, and converges faster as compared to other algorithms. To further reduce the computational burden, minimizing the cost and maximizing the network resilience is carried out to generate the initial population for S-MOSADE algorithm. This has reduced the computational burden by almost three times as compared to random initialization of population, thus saving a lot of computational time. The study concludes that the proposed S-MOSADE algorithm with the strategy of solutions initialized with minimum cost and maximum network resilience could be used effectively for speeding-up the multi-objective design of WDNs.

A Self-Adaptive Multi-Objective Differential Evolution Algorithm Applied to the Styrene Reactor Optimization

A Self-Adaptive Multi-Objective Differential Evolution Algorithm Applied to the Styrene Reactor Optimization

Self-adaptive multi-objective differential evolution algorithm with first front elitism for optimizing network usage in networked control systems

In networked control systems, by means of event-triggered transmission, it is possible to reduce the network usage, keeping the control system performance at satisfactory levels. There are several schemes for event-triggered transmission. In this study, we propose a multi-objective optimization problem to tune the event-triggered mechanisms. On solving the proposed problem by means of multi-objective evolutionary optimization, a set of efficient solutions is generated with different tradeoffs between control system performance and the number of transmissions. To solve the proposed problem, we also developed an improved multi-objective differential evolution algorithm that includes a self-adaptive mechanism, dynamic crowding distance operator, and novel elitism of the first front. The proposed method is applied to tune decentralized event-triggered mechanisms for a controller given a priori, considering random network-induced delays and packet loss. Two case studies are present ed, comparing the performance of eight different decentralized event-triggered schemes, analyzing the selection of the sampling period, and demonstrating the efficacy of the proposed tuning method.

Performance-based multi-objective design and expansion of water distribution networks considering life cycle costs and future demands

Abstract Designing the Water Distribution Networks (WDNs) consists of finding out pipe sizes such that the demands are satisfied and the desired performance levels are achieved at minimum cost. However, WDNs are subject to many future changes such as an increase (or decrease) in demand due to population change and migration, changes in water availability due to seasonal and climatic change, etc. Thus, the capacity expansion of WDNs needs to be performed such that the cost of interventions made is minimum while satisfying the demand and performance requirements at various time periods. Therefore, the current study proposed a Dynamic Programming (DP) framework for capacity expansion of WDNs and solved using Multi-Objective Self Adaptive Differential Evolution (MOSADE). The methodology is tested on three benchmark WDNs, namely Two-loop (TL), GoYang, and Blacksburg (BLA) WDNs, and applied to a real case study of the Badlapur region, Maharashtra, India. The results show that the proposed methodology leads to effective Pareto optimal fronts, making it an efficient method for solving WDN expansion problems. Subsequently, an Analytical Hierarchy Process (AHP) based multi-criteria decision-making (MCDM) analysis was performed on the obtained Pareto-optimal solutions to determine the most suitable solution based on three criteria: Life Cycle Cost (LCC) of expansions, hydraulic reliability, and mechanical reliability. The main advantage of the proposed methodology is its capability to consider hydraulic performance as well as structural integrity and demand satisfaction in the face of hydraulic and mechanical failures.

Multi-performance based computational model for the cuboid open traveling salesman problem in a smart floating city

The term “smart city” has been emerged as a novel solution to uphold the useless urban areas and the term has taken the advantage of sustainable and environmental resources. On the other hand, the term “floating city” has been studied for just only a few years as alternative living spaces for humanity across the world since land scarcity has already begun. Therefore, in this research, we propose multi-objective optimization algorithms to obtain the Pareto front solutions for the cuboid open traveling salesman problem (COTSP) in a “smart floating city” context. Given n nodes and the distances between each pair of nodes, the COTSP in this paper aims to find the shortest possible tour with a traveling distance that starts from the depot (i.e., node 1) and visits each node exactly once without needing to return to the depot. As known, a cuboid has height, length, and depth and the COTSP defines its x, y, z coordinates as a cuboid corresponding to height, length, and depth. In addition to the traveling distance, the platform (building breakwaters) cost is measured by the z coordinates (depths) of the nodes/platforms that represent both the platforms below the sea level. Note that unlike the traditional TSP, it has a variable seed number and a variable number of nodes/platforms in each solution. The paper aims to find the Pareto front solutions by minimizing the traveling distance and platform cost of the infrastructures below the sea level simultaneously. We develop a multi-objective self-adaptive differential evolution (MOJDE) algorithm, a nondominated sorting genetic algorithm (NSGAII), and a harmony search (MOHS) algorithm to solve the problem in such a way that we minimize the traveling distance while minimizing the platform cost simultaneously. All algorithms are compared to each other. The computational results show that the MOJDE and NSGAII algorithms outperform the MOHS algorithm in terms of commonly used performance measures from the literature.

Evaluation of Lung Involvement in Patients with Coronavirus Disease from Chest CT Images Using Multi-Objective Self-Adaptive Differential Evolution Approach

Evaluation of Lung Involvement in Patients with Coronavirus Disease from Chest CT Images Using Multi-Objective Self-Adaptive Differential Evolution Approach

Aero-mechanical multidisciplinary optimization of a high speed centrifugal impeller

An aero-mechanical multidisciplinary optimization was carried out for a high-speed centrifugal impeller, SRV2-O, by integrating a Self-adaptive Multi-Objective Differential Evolution (SMODE) algorithm, RANS solver technique, Finite Element Method (FEM), and data mining technique of analysis of variance (ANOVA). Specifically, the optimization of the impeller was conducted for the maximization of isentropic efficiency and the minimization of maximum stress. During optimization, constraints were imposed on the total pressure ratio at the optimization point and the mass flow rate at the choked point as well. Where, the former constraint intends to guarantee the working capability of the impeller while the latter tries to fix the working range. After optimization, six optimal Pareto solutions are finally obtained. The isentropic efficiency of the optimal solutions is increased by 2.07% at most while the maximum stress is decreased by 6.36% at most among the Pareto solutions. The better performance of optimal designs was demonstrated through detailed aerodynamic and mechanical analysis. Then, the ANOVA is used to explore the effects of variables on performance function in design space, it is found that, the design variables located at the meridian channel and the leading edge of the full blade have significant effect on aerodynamic performance. These variables are crucial to reduce the loss caused by shock wave at impeller inlet and the leakage flow at blade tip. Meanwhile, the design variables located near the leading edge of full blade root section have great effect on strength performance, as they are effective to decrease the bend of blades and thus reduce the maximum stress. Thereby, the better aeromechanical performance can be achieved by dedicated adjustment on the curves of both the shroud of meridional channel and leading edge of full blade. The results of ANOVA are consistent with the aero-mechanical analysis. Therefore, the effectiveness of aero-mechanical optimization and data mining framework is demonstrated.

A Modified Multiobjective Self-Adaptive Differential Evolution Algorithm and Its Application on Optimization Design of the Nuclear Power System

A modified multiobjective self-adaptive differential evolution algorithm (MMOSADE) is presented in this paper to improve the accuracy of multiobjective optimization design in the nuclear power system. The performance of the MMOSADE is tested by the ZDT test function set and compared with classical evolutionary algorithms. The results indicate that MMOSADE has a better performance in convergence and diversity. Based on the MMOSADE, a multiobjective optimization design platform for the nuclear power system is proposed, and the application of which is carried out. The evaluation program of the PRHR-HX in AP1000 is developed, and its reliability is verified. The optimal design schemes of PHHR-HX are obtained by utilizing the multiobjective optimization design platform. The results show that the optimal design schemes can envelop the prototype design scheme. This conclusion proves that the optimization design platform proposed in this paper is effective and feasible.

A multi-stage stochastic programming approach for blood supply chain planning

Abstract Perishability of blood products and uncertainty in donation and demand sizes complicate the blood supply chain planning. This paper presents a novel bi-objective mixed-integer model for integrated collection, production/screening, distribution and routing planning of blood products, and seeks to simultaneously optimize the total cost and freshness of transported blood products to hospitals. To cope with inherent uncertainty of input data, a multi-stage stochastic programming approach with a combined scenario tree is presented. Due to the high complexity of the problem, a novel hybrid multi-objective self-adaptive differential evolution algorithm is developed, which benefits from the variable neighborhood search with fuzzy dominance sorting (hereafter it is briefly called MSDV). MSDV is validated through comparing its performance with two of the most common multi-objective evolutionary algorithms (i.e. MOICA and NSGA-II). Applicability of the proposed decision model is also tested through a real case study. Our results show that the solution efficiency of a network can be balanced with its effectiveness through customer satisfaction. Further, several sensitivity analyses are carried out to provide valuable managerial insights.

Optimal sizing of PV/wind/diesel hybrid microgrid system using multi-objective self-adaptive differential evolution algorithm

Abstract Microgrid systems, such as solar photovoltaic (PV) power and wind energy, integrated with diesel generators are promising energy supplies and are economically feasible for current and future use in relation to increased demands for energy and depletion of conventional sources. It is thus important to optimize the size of hybrid microgrid system (HMS) components, including storage, to determine system cost and reliability. In this paper, optimal sizing of a PV/wind/diesel HMS with battery storage is conducted using the Multi-Objective Self-Adaptive Differential Evolution (MOSaDE) algorithm for the city of Yanbu, Saudi Arabia. Using the multi-objective optimization approach, the objectives are treated simultaneously and independently, thereby leading to a reduction in computational time. One of the main criteria to consider when designing and optimizing the HMS is the energy management strategy, which is required to coordinate the different units comprising the HMS. The multi-objective optimization approach is then used to analyze the Loss of Power Supply Probability (LPSP), the Cost of Electricity (COE), and the Renewable Factor (RF) in relation to HMS cost and reliability and is tested using three case studies involving differing house numbers. Results verify its application in optimizing the HMS and in its practical implementation. In addition, optimization results using the proposed approach provided a set of design solutions for the HMS, which will assist researchers and practitioners in selecting the optimal HMS configuration. Moreover, it is important to select optimally sized HMS components to ensure that all load demands are met at the minimum energy cost and high reliability.

Stochastic Fractal Based Multiobjective Fruit Fly Optimization

Abstract The fruit fly optimization algorithm (FOA) is a global optimization algorithm inspired by the foraging behavior of a fruit fly swarm. In this study, a novel stochastic fractal model based fruit fly optimization algorithm is proposed for multiobjective optimization. A food source generating method based on a stochastic fractal with an adaptive parameter updating strategy is introduced to improve the convergence performance of the fruit fly optimization algorithm. To deal with multiobjective optimization problems, the Pareto domination concept is integrated into the selection process of fruit fly optimization and a novel multiobjective fruit fly optimization algorithm is then developed. Similarly to most of other multiobjective evolutionary algorithms (MOEAs), an external elitist archive is utilized to preserve the nondominated solutions found so far during the evolution, and a normalized nearest neighbor distance based density estimation strategy is adopted to keep the diversity of the external elitist archive. Eighteen benchmarks are used to test the performance of the stochastic fractal based multiobjective fruit fly optimization algorithm (SFMOFOA). Numerical results show that the SFMOFOA is able to well converge to the Pareto fronts of the test benchmarks with good distributions. Compared with four state-of-the-art methods, namely, the non-dominated sorting generic algorithm (NSGA-II), the strength Pareto evolutionary algorithm (SPEA2), multi-objective particle swarm optimization (MOPSO), and multiobjective self-adaptive differential evolution (MOSADE), the proposed SFMOFOA has better or competitive multiobjective optimization performance.

Multi-objective optimization of p -xylene oxidation process using an improved self-adaptive differential evolution algorithm

Abstract The rise in the use of global polyester fiber contributed to strong demand of the Terephthalic acid (TPA). The liquid-phase catalytic oxidation of p -xylene (PX) to TPA is regarded as a critical and efficient chemical process in industry [1] . PX oxidation reaction involves many complex side reactions, among which acetic acid combustion and PX combustion are the most important. As the target product of this oxidation process, the quality and yield of TPA are of great concern. However, the improvement of the qualified product yield can bring about the high energy consumption, which means that the economic objectives of this process cannot be achieved simultaneously because the two objectives are in conflict with each other. In this paper, an improved self-adaptive multi-objective differential evolution algorithm was proposed to handle the multi-objective optimization problems. The immune concept is introduced to the self-adaptive multi-objective differential evolution algorithm (SADE) to strengthen the local search ability and optimization accuracy. The proposed algorithm is successfully tested on several benchmark test problems, and the performance measures such as convergence and divergence metrics are calculated. Subsequently, the multi-objective optimization of an industrial PX oxidation process is carried out using the proposed immune self-adaptive multi-objective differential evolution algorithm (ISADE). Optimization results indicate that application of ISADE can greatly improve the yield of TPA with low combustion loss without degenerating TA quality.

Comparison of the Searching Behavior of NSGA-II, SAMODE, and Borg MOEAs Applied to Water Distribution System Design Problems

AbstractA number of multiobjective evolutionary algorithms (MOEAs) have been developed and applied to water resource optimization problems over the past decade. The comparative performance of these MOEAs has been investigated often according to their overall end-of-run results (quality of optimal fronts) within prespecified computational budgets. Despite the importance of such comparative analyses, these studies have provided little knowledge of how different MOEAs navigate through the decision space toward the Pareto front. To address this issue, this paper uses a range of metrics to quantitively characterize MOEAs’ run-time searching behavior, with a focus on the statistics of search quality and convergence progress. The metrics are applied to three state-of-the-art MOEAs, including the nondominated sorting genetic algorithm-II (NSGA-II), self-adaptive multiobjective differential evolution (SAMODE), and Borg, for six water distribution system (WDS) design problems with the objectives of minimizing netwo...

Multi-Objective Aerodynamic Optimization Design and Data Mining of a High Pressure Ratio Centrifugal Impeller

An automated three-dimensional multi-objective optimization and data mining method is presented by integrating a self-adaptive multi-objective differential evolution algorithm (SMODE), 3D parameterization method for blade profile and meridional channel, Reynolds-averaged Navier–Stokes (RANS) solver technique and data mining technique of self-organizing map (SOM). Using this method, redesign of a high pressure ratio centrifugal impeller is conducted. After optimization, 16 optimal Pareto solutions are obtained. Detailed aerodynamic analysis indicates that the aerodynamic performance of the optimal Pareto solutions is greatly improved. By SOM-based data mining on optimized solutions, the interactions among objective functions and significant design variables are analyzed. The mechanism behind parameter interactions is also analyzed by comparing the data mining results with the performance of typical designs.

Coupled Self-Adaptive Multiobjective Differential Evolution and Network Flow Algorithm Approach for Optimal Reservoir Operation

AbstractThis paper presents a coupled self-adaptive multiobjective differential evolution and network flow algorithm for the optimal operation of complex multipurpose reservoir systems. The developed algorithm (i.e., self-adaptive multiobjective differential evolution) is compared to nondominated sorting genetic algorithm II using a set of common test problems and a real-world case study. An out-of-kilter method for minimal-cost flow problems is used to optimize the water resource system from self-adaptive multiobjective differential evolution inputs driven by the evolutionary process. Self-adaptive multiobjective differential evolution is then used to evaluate objective functions based on the outputs from out-of-kilter algorithm and the process continues until the stop criterion is met. The advantages of the proposed approach include (1) flexible evolutionary algorithms for solving highly complex objective function, and (2) efficient network flow method for dealing with large and highly constrained probl...

An efficient hybrid approach for multiobjective optimization of water distribution systems

An efficient hybrid approach for the design of water distribution systems (WDSs) with multiple objectives is described in this paper. The objectives are the minimization of the network cost and maximization of the network resilience. A self-adaptive multiobjective differential evolution (SAMODE) algorithm has been developed, in which control parameters are automatically adapted by means of evolution instead of the presetting of fine-tuned parameter values. In the proposed method, a graph algorithm is first used to decompose a looped WDS into a shortest-distance tree (T) or forest, and chords (Ω). The original two-objective optimization problem is then approximated by a series of single-objective optimization problems of the T to be solved by nonlinear programming (NLP), thereby providing an approximate Pareto optimal front for the original whole network. Finally, the solutions at the approximate front are used to seed the SAMODE algorithm to find an improved front for the original entire network. The proposed approach is compared with two other conventional full-search optimization methods (the SAMODE algorithm and the NSGA-II) that seed the initial population with purely random solutions based on three case studies: a benchmark network and two real-world networks with multiple demand loading cases. Results show that (i) the proposed NLP-SAMODE method consistently generates better-quality Pareto fronts than the full-search methods with significantly improved efficiency; and (ii) the proposed SAMODE algorithm (no parameter tuning) exhibits better performance than the NSGA-II with calibrated parameter values in efficiently offering optimal fronts.

Design of mixed H-two/H-infinity optimal control systems using multiobjective differential evolution algorithm

In this paper, the mixed H-two/H-infinity control synthesis problem is stated as a multiobjective optimization problem, with objectives of minimizing the H-two and H-infinity norms simultaneously. Instead of building a LMIs-based synthesis algorithm, a self-adaptive control parameter multiobjective differential evolution algorithm is developed directly in the controller parameters space. In the case of systems with polytopic uncertainties, the worst case norm computation is formulated as an implicit optimization problem, and the proposed self-adaptive differential evolution is employed to calculate the worst case H-two and H-infinity norms. The numerical examples illustrate the power and validity of the proposed approach for the mixed H-two/H-infinity control multiobjective optimal design.

Design of a Parallel Manipulator Based on Multi-Objective Self-Adaptive Differential Evolution Algorithm

In order to improve highly non-isotropic input-output relations in the optimal design of a parallel robot, this paper presents a method based on a multi-objective self-adaptive differential evolution (MOSaDE) algorithm.The approach considers a solution-diversity mechanism coupled with a memory of those sub-optimal solutions found during the process. In theMOSaDE algorithm, both trial vector generation strategies and their associated control parameter values were gradually self-adapted by learning from their previous experiences in generating promising solutions. Consequently, a more suitable generation strategy along with its parameter settings could be determined adaptively to match different phases of the search processevolution.Furthermore, a constraint-handling mechanism is added to bias the search to the feasible region of the search space. The obtained solution will be a set of optimal geometric parameters and optimal PID control gains. The empirical analysis of thenumerical results shows the efficiency of the proposed algorithm.