Bi-objective Optimization Algorithm Research Articles

Bi-objective ship speed optimization based on machine learning method and discrete optimization idea

With the introduction of increasingly stringent carbon dioxide (CO2) emission regulations in the shipping industry, shipping companies face significant pressure to reduce emissions while ensuring profitable ship operations. A practical bi-objective speed optimization (BSO) algorithm for container ships is developed based on the variable weight idea, the discrete optimization idea, and the ideal point method to meet the urgent needs of shipping companies to improve operating profits and reduce emissions. By constructing two BSO models of ship main engine fuel consumption-ship sailing time and ship operating costs (SOC)-ship CO2 emissions (SCE), the effectiveness of the BSO algorithm is confirmed through extensive optimization experiments. The results show that compared to the historical sailing results, the BSO reduces the SOC by 4.43 % without causing a significant increase in the SCE, and reduces the SCE by 0.25 %. Moreover, the results demonstrate the effectiveness and feasibility of the BSO in reducing the cost of ship operations while reducing the impact on the environment. The results provide valuable references for shipping companies in the trade-off analysis between economic and environmental benefits and optimization decision-making.

Integrated System Design for Post-Disaster Management: Multi-Facility, Multi-Period, and Bi-Objective Optimization Approach

Disaster management requires efficient allocation of essential facilities with consideration of various objectives. During the response and recovery phase of disaster management (RRDM), various types of missions occur in multiple periods, and each of them needs different support from facilities. In this study, a bi-objective mathematical model was derived to support multi-period RRDM by optimal allocation of required facilities such as drone stations, shelters, emergency medical facilities, and warehouses according to the mission life cycle. Connectivity between facilities was considered to ensure inter-facility complementarity. For efficient derivation of Pareto solutions, a modified epsilon-constraint algorithm for bi-objective optimization was developed. The algorithm was tested with a realistic disaster simulation scenario using HAZUS 4.0 as a demonstration of the benefits of the proposed approach. With the simulation experiments, the proposed approach was expected to provide efficient operational plans and guidelines to decision makers for the bi-objective optimization problem in RRDM systems. In addition, the consideration of inter-facility connectivity can play an important role in the RRDM, especially for robustness and readiness.

Electromagnetic cloak design with mono-objective and bi-objective optimizers: seeking the best tradeoff between protection and invisibility

We revisit the design of cloaks, without resorting to any geometric transform. Cancellation techniques and anomalous resonances have been applied for this purpose. Instead of a deductive reasoning, we propose a novel mono-objective optimization algorithm, namely a ternary grey wolf algorithm, and we adapt a bi-objective optimization algorithm. Firstly, the proposed chaotic ternary grey wolf algorithm searches three-valued spaces for all permittivity values in the cloak while minimizing the summation of a protection criterion and an invisibility criterion. Secondly, a bi-objective genetic algorithm is adapted to find pairs of optimal values of invisibility and protection.

Solving dynamic satellite image data downlink scheduling problem via an adaptive bi-objective optimization algorithm

The satellite image data downlink scheduling problem (SIDSP) plays a critical role in the mission planning operation of earth observation satellites. However, with recent developments in satellite technology, the traditional SIDSP is poorly effective for modern satellites. To offer additional modeling flexibility and renewed capabilities, a dynamic SIDSP (DSIDSP), which combines two interlinked operations of image data segmentation and image data downlink dynamically, was introduced. We have formulated the DSIDSP as a bi-objective problem of optimizing the image data transmission rate and the service-balance degree. Harnessing the power of an adaptive large neighborhood search (ALNS) algorithm with a nondominated sorting genetic algorithm II (NSGA-II), an adaptive bi-objective memetic algorithm, NSGA2ALNS, is developed to solve DSIDSP. Results of extensive computational experiments carried out using benchmark instances are also presented. Our experimental results reveal that the NSGA2ALNS algorithm is an effective and efficient method of solving DSIDSP based on various performance metrics. In addition, new benchmark instances are also provided for DSIDSP that could be used in future research.

A knowledge-based constructive estimation of distribution algorithm for bi-objective portfolio optimization with cardinality constraints

Portfolio optimization is an essential and practical model for financial decision making. With the consideration of some real-world constraints, especially the cardinality constraints, the problem becomes much more challenging as it converts to a mixed-integer quadratic multi-objective optimization problem. To solve this problem, we propose a knowledge-based constructive estimation of distribution algorithm (KC-EDA) with the following three features. First, a hybrid design of Ant colony optimization (ACO) and Estimation distribution algorithm (EDA) is used to solve this mixed-variable optimization problem based on knowledge information. Second, a knowledge accumulation mechanism is designed to discover the internal relationship among the assets. The mechanism can not only guide the selection of assets effectively but also enable the use of historical information during evolution to direct the allocation of investment proportion. Third, a constructive approach is applied to construct portfolios under the constraints. This hybrid and constructive approach is incorporated into the multi-objective evolutionary framework and the experiment has been performed on the SZ50, SZ180, and SZ380 datasets (from January 2014 to December 2018). The experimental results demonstrate the effectiveness of KC-EDA in solving the portfolio optimization problem with cardinality constraints.

Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization

Convergence Rates of the Stochastic Alternating Algorithm for Bi-Objective Optimization

Urban traffic signal control robust optimization against Risk-averse and Worst-case cyberattacks

Ensuring the cybersecurity of urban traffic signal control systems has become increasingly important in the digital age. This study proposes a passive countermeasure by designing robust signal control plans to mitigate the risks of worst-case and risk-averse cyberattacks. To achieve this objective, the study develops two bi-level simulation-based optimization (SO) models and solves them using an improved biobjective robust simulation-based optimization (IBORSO) algorithm. The attack-defense process is formulated as a Stackelberg game, where the lower level attacker aims to find optimal attack plans to degrade traffic efficiency and safety indices, while the upper level defender adjusts the signal control plan to compensate for the effects of the attack on traffic efficiency and safety indices. The proposed approach is evaluated on an urban road network in Changsha, China. The results show that the developed robust signal control plans can withstand risk-averse and worst-case attacks and perform better than the counterpart ones in terms of biobjective performance. The proposed bi-level modeling framework and solution algorithm can be used to build robust traffic signal control systems that are resilient to cyberattacks.

Biobjective robust Network-wide traffic signal optimization against Cyber-attacks

In the cyber age, modern traffic signal control systems are inevitably exposed to a wide range of cyber-attacks, which would negatively impact traffic system performance. To defend against direct cyber-attacks that alter signal settings directly and maliciously by hacking into the wireless connected traffic control center or signal controllers, this study applies a precautionary and inexpensive measure of designing the robust signal control plan. This is realized by modelling the biobjective traffic signal control simulation-based optimization (SO) problem under cyber-attacks in a bi-level framework, with the aim of minimizing the negative impact of potential cyber-attacks on traffic efficiency and safety performance. Depending on the type of attacker with complete or incomplete knowledge on traffic signal control system, two typical bi-level models exist. Then, we propose an improved biobjective robust simulation-based optimization (IBORSO) algorithm to solve the two models, during which the sequential interaction between the attacker and the defender is seen as the Stackelberg game, and the resulting equilibrium solutions are the desired robust signal control plans to withstand cyber-attacks. An urban road network in Changsha, China, is modelled as the experimental site and numerical results show the effectiveness of IBORSO in solving the two bi-level models. Meanwhile, the solved robust signal control plans can defend against two typical attacks satisfactorily and achieve better or comparable biobjective performance compared with the field-implemented one and optimized ones by biobjective efficient global optimization (BOEGO).

A two-stage evolutionary algorithm for noisy bi-objective optimization

For noisy bi-objective optimization problems, the algorithm is affected by noise differently in different optimization stages. Generally speaking, only when the impact of the noise is non-negligible, the noise may lead to errors in the quality evaluation of the solutions, and then affect the performance of the algorithm. Therefore, we propose an adaptive switch strategy to make the algorithm switch adaptively among different noise treatments depending on the noise impact to solve noisy bi-objective optimization problems. In addition, a data selection strategy and a model performance estimation method are proposed to enhance the modeling-based denoising method. Furthermore, an output solution selection is used to select more reliable non-dominated solutions as the final output at the late stage of optimization. The performance of the proposed algorithm is verified on the DTLZ and WFG problems. From the experimental results, it can be found that the proposed algorithm is very competitive with other existing algorithms designed for noisy bi-objective optimization problems.

Lyapunov control of finite-dimensional quantum systems based on bi-objective quantum-behaved particle swarm optimization algorithm

This paper presents a Lyapunov control scheme to drive finite-dimensional closed and Markovian open quantum systems into any target pure state with as high fidelity and as little time as possible. The control law is established by a Lyapunov function with an unknown Hermitian operator, where the eigenvectors of the operator are constructed based on the condition that the LaSalle invariant set contains the desired target state and a set of optimal eigenvalues of the Hermitian operator is searched by the quantum-behaved particle swarm optimization (QPSO) algorithm. In particular, for open systems, when the denominator in the control law is quite small, we propose an improved QPSO algorithm with constraints to enhance the flexibility in implementation. Finally, numerical simulations are carried out on a five-level and a three-qubit closed quantum systems, and a five-level and a ten-level open quantum systems. Simulation results demonstrate that the proposed control scheme can achieve high-fidelity transfer to desired target states for high-dimensional closed and open quantum systems.

An Angle-Based Bi-Objective Optimization Algorithm for Redundancy Allocation in Presence of Interval Uncertainty

Uncertainty is a practical issue in system design optimization because some characteristics of components, such as reliability and cost, cannot be determined precisely in many situations. Considering the imprecise characteristics of components, few works have focused on the multi-objective optimization for the redundancy allocation due to the challenges of comparing multi intervals. To tackle the issue, a novel angle-based bi- objective redundancy allocation algorithm is proposed in this study, introducing three original contributions: 1) An angle-based interval crowding distance (ICA) is especially designed for effective performance and reduced computational time; 2) Two techniques are applied to tackle the problem: An elite selection for mutation is presented for generating better offsprings; A penalty-guided constraint handling technique is introduced for converting the problem into an unconstrained one. 3) Since a set of optimal solutions is obtained by the proposed method and no preference on uncertainties is provided, this paper proposes a novel knee interval method to help DMs make a decision. To be specific, the proposed ICA can describe the distribution of the whole population intuitively and effectively, considering not only the angle between two compared individuals but also the angle range of the interval values. The computational results from two typical experiments demonstrate that the proposed algorithm is more efficient than other state-of-the-art algorithms, generating Pareto sets with less repeating individuals, stronger convergence, wider distribution, less imprecision, and reduced computational time. Note to Practitioners—This article is motivated by two practical problems in multi-objective redundancy allocation in presence of interval uncertainty: First, this paper tries to solve the multi-objective redundancy allocation problem with the imprecise characteristics of components, which is rarely considered in the field of reliability optimization design. Second, the calculation of the crowding distance needs extra time cost and is less efficient. To tackle this issue, an interval crowding angle is especially designed, considering not only the angle between two compared individuals, but also the angle range of the interval values. The proposed method can be embedded in most multi-objective interval evolutionary algorithms to compute the diversity of the individuals. The goal of this study is to allocate the economy and high-reliable components for practitioners. The computational results verify its effectiveness and efficiency. Besides, in many cases the practitioners know only few or no preferences, this paper proposes a knee point analysis of interval values that allows practitioners to select the optimal solution with large hypervolume and less imprecision among a set of solutions.

A Bi-Objective Learn-and-Deploy Scheduling Method for Bursty and Stochastic Requests on Heterogeneous Cloud Servers

In this article, we consider the dynamic allocation of bursty requests stochastically arriving at heterogeneous servers with uncertain setup times. Lower expected response time and less power consumption are desirable objectives of users and service providers respectively. However, sudden increase and decrease of cloud servers caused by bursty requests are rather challenging to get an appropriate trade-off between the two conflicting objectives which are closely related to the launched servers. The heterogeneity of the cloud servers further makes it more difficult to decide how to switch on and off servers and effectively and efficiently allocate bursty requests with balanced objectives. Based on a Markov decision process, a real-time bilevel decision-making model is constructed for unallocated requests which includes: whether to launch a server and which type of server to launch. A learn-and-deploy algorithm framework is proposed which contains two complementary stages. In the first stage, an effective offline bi-objective optimization algorithm is proposed to learn a set of policies, which provides helpful trade-off information for a decision-maker to choose a preferred policy <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a posteriori</i> . In terms of the system status, a policy decides whether to launch a server according to a state-action table and which server to launch using a server priority sequence. In the second stage, a computationally efficient policy deployment method is proposed to search the corresponding action in the selected policy based on the current system status and apply it to the real-time system. Experimental studies over a large number of random and real instances have been conducted to validate the effectiveness of the proposed bilevel model and algorithm. Compared to the most recent existing method, the performance of the proposed approach can at most achieve an 80% improvement on power consumption and 20% improvement on response time.

Maritime traffic clustering to capture high-risk multi-ship encounters in complex waters

Maritime traffic situational awareness is fundamental to the safety of maritime transportation. The state-of-the-art research primarily attaches importance to collision risk estimation and evaluation between/among ships but encounters the challenges of capturing the high-risk traffic clusters in complex waters. This paper develops a systematic traffic clustering approach to enhance traffic pattern interpretability and proactively discover high-risk multi-ship encounter scenarios, in which both the conflict connectivity and spatial compactness of encounter ships are considered. Specifically, a novel hybrid clustering approach that integrates a composite distance measure, a constrained Shared Nearest Neighbour clustering, and a fine-tuning strategy is developed to segment maritime traffic into multiple conflict-connected and spatially compact clusters. Meanwhile, a hierarchical bi-objective optimization algorithm is introduced to search for optimal clustering solutions. Through maritime traffic data obtained from the Ningbo-Zhoushan Port, a thorough methodology performance evaluation is carried out through application demonstration and validation. Experiment results reveal that the new approach: 1) can effectively capture the high-risk/density traffic clusters; 2) is robust with respect to various traffic scenarios; and 3) can be extended to assist in collision risk management. It therefore offers new insights into enhancing maritime traffic surveillance capabilities and eases the design of risk management strategy.

Theoretical Analysis and Empirical Validation of the Conical Area Evolutionary Algorithm for Bi-Objective Optimization

Multiobjective evolutionary algorithms (EAs) based on decomposition are becoming successful and popular. Particularly, a conical area EA (CAEA) was developed to heighten the convergence and population diversity of decomposition-based algorithms for bi-objective optimization by employing a cone decomposition approach. The global Pareto optimality of cone decomposition was proved. It means that the optimum of every conical subproblem of the cone decomposition approach is Pareto optimal in the entire bi-objective space in the presence of a continuous frontier segment within its associated subregion. In this article, based on the global Pareto optimality, we further reveal that the cone decomposition approach also has a desired ability of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> -distribution convergence for bi-objective optimization. We first prove by the monotonicity and additivity of the Lebesgue measure and the squeeze theorem for limits that the hypervolume of the optimal solutions of all <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> subproblems of the cone decomposition approach is infinitely close to that of the optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> -distribution for large enough <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> in the presence of a continuous frontier. Meanwhile, the original CAEA is further improved to better approximate the optimal solutions of conical subproblems. The experimental results on bi-objective benchmark problems show that the improved CAEA achieves higher qualities of frontiers and better <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> -distribution convergence in the terms of hypervolume error compared with six other popular multiobjective algorithms.

A kriging-assisted bi-objective constrained global optimization algorithm for expensive constrained optimization problems

Computationally expensive constrained optimization problems are challenging owing to their high complexity and computational cost. To solve these problems efficiently, a kriging-assisted bi-objective constrained global optimization (BOCGO) algorithm is developed, where three phases with three bi-objective subproblems are performed. In phase I, the constraints are searched locally and globally to find the feasible region. Once a feasible region has been located, the two terms of the constrained expected improvement function are utilized to exploit and explore the feasible region in phase II. As the kriging models are accurate enough in the concerned region, a local search is processed to improve the optimal solution in phase III. The capability of the BOCGO algorithm is demonstrated by comparison with two classical and two state-of-the-art algorithms on 20 problems and an engineering simulation problem. The results show that the BOCGO algorithm performs better in more than three-fifths of problems, illustrating its effectiveness and robustness.

Bi-objective optimization strategy of energy consumption and shift shock based driving cycle-aware bias coefficients for a novel dual-motor electric vehicle

A novel dual-motor electric vehicle (DMEV) with superior energy efficiency depends on its diverse operation modes. However, the operation mode shift will lead to the ride comfort problem owing to the uncertainty of the actual driving cycles. To address this issue, bi-objective optimization strategy-based driving cycle-aware bias coefficients is proposed to tradeoff between energy consumption and shift shock. Firstly, the system efficiency and the shift shock models are developed for DMEV. The torque distribution coefficient is defined to be a control variable for the bi-objective optimization of system efficiency and ride comfort. Furthermore, this study combines the bi-objective optimization algorithm with driving cycle recognition to introduce the optimized bias coefficient to determine the driving cycle-aware bias coefficient for the mentioned optimized target objectives. Then, the non-dominated sorting genetic algorithm-II is applied for the bi-objective optimization, which produces a group of the Pareto solutions including the energy consumption and shift shock. Moreover, the proposed bi-objective optimization strategy is conducted by controlling the optimized bias lines for the optimal torque distribution of the novel dual-motor powertrain system. Ultimately, numerous validations and comparisons demonstrate that the proposed strategy effectively accomplishes the trade-off optimization between energy consumption and shift shock in real-time.

Solving Dynamic Satellite Image Data Downlink Scheduling Problem Via an Adaptive Bi-Objective Optimization Algorithm

Solving Dynamic Satellite Image Data Downlink Scheduling Problem Via an Adaptive Bi-Objective Optimization Algorithm

A static semi-kitting strategy system of JIT material distribution scheduling for mixed-flow assembly lines

The green scheduling plays an increasingly important role in many manufacturing enterprises and trading off the Just-in-Time (JIT) and energy efficiency is a complex optimization problem. A static semi-kitting strategy is proposed to deal with a bi-objective JIT material distribution scheduling problem considering energy consumption (BJMDSP-EC) for mixed-flow assembly lines. A mathematical model that aims to minimize the total energy consumption and the total line-side inventory is established, which meets the request of energy saving and JIT. Due to the NP-hard nature of the proposed problem, a Memory-based Bi-objective Chaotic Gravitational Search Algorithm (MBCGSA) is developed to solve the BJMDSP-EC, which hybridizes the Gravitational Search Algorithm (GSA) and the non-dominated sorting genetic algorithm-II (NSGA-II). The memory-based search strategy and the chaotic gravity constant are applied to the bi-objective optimization algorithm to balance exploration and exploitation. Moreover, clustering and Cauchy deviates are utilized to initialize the population, and two local search optimization operators are designed to optimize two objectives. Finally, computational experiments are performed to evaluate the performance of the MBCGSA by being compared with two other bi-objective optimization algorithms, the multi-objective particle swarm optimization (MOPSO) and NSGA-II, and the results reveal the effectiveness and efficiency of the MBCGSA when solving BJMDSP-EC.

Application of small-scale compressed air energy storage in the daily operation of an active distribution system

While compressed air energy storage (CAES) has many applications in the field of generation and transmission power systems based on the state-of-the-art, this paper proposes the application of small-scale CAESs (SCAESs) in form of a storage aggregator in the daily operation of an active distribution system (ADS), joining the distribution system operator (DSO) for the participation in the day-ahead (DA) wholesale market. An innovative two-agent modeling approach is formulated. The first agent is responsible for aggregating SCAES units and the profit maximization of the aggregator is based on the distribution local marginal price. The DSO as the second agent receives the DA scheduling from the independent SCAES aggregator and is thus responsible for the secure operation of the ADS, utilizing solar and dispatchable distributed generation (DG) as well as purchasing power from the wholesale market. Linear programming is used for the formulation and optimization of the SCAES aggregator, while a bi-objective optimization algorithm (with the objectives of minimum operating cost as well as minimum power loss and emissions in different scenarios) is employed for DSO scheduling. The results show that the CAES aggregator can offer a considerable impact for power loss reduction, specifically, when diesel generators are not committed in the system operation (i.e., where emission has very low values between 10,000 and 12000 kg). Additionally, the CAES aggregator could reduce the operation costs of the grid in a wide range of operations, even though for the scenario in which the CAES units are not under the control of the DSO anymore and also are scheduled to maximize their own profit. Moreover, results demonstrated that CAES units can be a significant voltage control device for a distribution grid with different objectives. Finally, some conclusions are duly drawn.

Observation scheduling problem for AEOS with a comprehensive task clustering

Considering the flexible attitude maneuver and the narrow field of view of agile Earth observation satellite (AEOS) together, a comprehensive task clustering (CTC) is proposed to improve the observation scheduling problem for AEOS (OSP-FAS). Since the observation scheduling problem for AEOS with comprehensive task clustering (OSWCTC) is a dynamic combination optimization problem, two optimization objectives, the lossrate (LR) of the image quality and the energy consumption (EC), are proposed to format OSWCTC as a bi-objective optimization model. Harnessing the power of an adaptive large neighborhood search (ALNS) algorithm with a nondominated sorting genetic algorithm II (NSGA-II), a bi-objective optimization algorithm, ALNS+NSGA-II, is developed to solve OSWCTC. Based on the existing instances, the efficiency of ALNS+NSGA-II is analyzed from several aspects, meanwhile, results of extensive computational experiments are presented which disclose that OSPFAS considering CTC produces superior outcomes.