Tchebycheff Approach Research Articles

Energy, cost and job-tardiness-minimized scheduling of energy-intensive and high-cost industrial production systems

Energy consumption, production cost, and efficiency are highly concerned by decision makers of energy-intensive and high-cost industrial production systems. Intelligent production scheduling is a necessary means to achieve their optimization. This work delves into a novel multi-objective production scheduling problem arising from a steel hot-rolling process, which is a representative energy-intensive and high-cost industrial process. The challenge of the problem involves scheduling customized production jobs subject to intricate process constraints with the goal to minimize three objective functions, i.e., energy consumption, setup cost, and the number of tardy jobs. A mixed integer linear programming model is formulated for the problem. In order to solve it, an improved multi-objective evolutionary algorithm based on decomposition is presented. The algorithm incorporates problem-specific encoding and model-based decoding mechanisms, rendering it well-suited for addressing the concerned multi-constrained multi-objective optimization problem. The introduced modified Tchebycheff approach mitigates the impact of objective functions with varying value ranges on the algorithm’s convergence. Additionally, a Metropolis acceptance criterion is integrated to facilitate the escape from local optimal solutions, enhancing the algorithm’s global optimization capability. Numerous experiments are conducted to verify the effectiveness of the improvements and to compare the performance of the presented algorithm against its competitive peers. The results demonstrate its high performance, suggesting its significant potential for its application to steel hot-rolling systems.

Multiobjective ranking binary artificial bee colony for gene selection problems using microarray datasets

Microarray cancer gene expression datasets are high dimensional and complex for efficient computational analysis. Thus, selecting high discriminative genes from microarray data has become increasingly interesting in the field of bioinformatics. This article addresses the problem of designing a gene selection algorithm which is modeled as a multiobjective optimization problem with the sensitivity, specificity and the number of selected genes. Then, a multi-objective ranking binary artificial bee colony algorithm based on decomposition is proposed to select the optimal subset of dimensions from the original high dimensional data while retaining a subset that satisfies the defined objective. First, the Fisher-Markov selector is used to choose a fixed number of microarray data. Second, to make artificial bee colony algorithm suitable for the binary problem, a novel binary update strategy is proposed to balance the exploration and exploitation ability. Third, multi-objective ranking binary artificial bee colony algorithm is proposed by integrating tchebycheff approach into the ranking binary artificial bee colony algorithm. Finally, the multi-objective ranking binary artificial bee colony algorithm based on decomposition (MORBABC/D) method is used for feature selection, and extreme learning machine is used as the classifier with 10 fold cross-validation method. In order to show the effectiveness and efficiency of the algorithm, the proposed algorithm is tested on eight microarray dataset. Experimental studies have been carried out to investigate the ability of the proposed algorithm.

Multi-Objective Robust Beamforming for Integrated Satellite and Aerial Networks Supporting Heterogeneous Services

An integrated satellite and aerial network (ISAN) is considered a promising candidate to provide seamless connectivity for future wireless communication systems. In this paper, we propose a multi-objective based robust beamforming (BF) scheme for an ISAN to support heterogeneous services with high flexibility, where the satellite network serves various heterogeneous satellite terminals through multicast non-orthogonal multiple access (MC-NOMA), while the aerial network offers services to many internet of things devices using layered division multiplexing (LDM). Specifically, we first formulate a multi-objective optimization problem (MOOP) to achieve a good trade-off between sum rate maximization and total transmit power minimization. To tackle this mathematically intractable problem, we exploit the weighted Tchebycheff approach to transform the MOOP into a single-objective problem. Since only the angular information based channel state information is available, we exploit the angular discretization method and sequential convex approximation to design a robust BF algorithm to obtain the Pareto optimal solutions. Finally, simulation results demonstrated that our proposed scheme can achieve a optimal trade-off between multiple performance metrics with high spectrum and energy efficiency, so as to support heterogeneous services in the ISAN and fill the gap of only single type of serivce in the existing ISAN works.

Surrogate-assisted MOEA/D for expensive constrained multi-objective optimization

In this paper, an adaptive surrogate-assisted MOEA/D framework (ASA-MOEA/D) is proposed for solving computationally expensive constrained multi-objective optimization problems, in which three specific search strategies are adaptively implemented based on the optimization states of subproblems to achieve targeted searches for different subproblems. To maintain feasibility, the RBF-based local search models are constructed by comprehensively considering the orthogonal distance difference and constraint satisfaction information for guiding infeasible solutions of the infeasible subproblems into feasible regions. To maintain convergence, the RBF surrogates of the aggregated objective and constraints are employed to construct local search models for locating better feasible solutions. To maintain diversity, the subregions of unexplored subproblems are effectively explored by utilizing the valuable information of their neighboring elite solutions. Moreover, the solution with the maximum overall uncertainty of RBF surrogates is selected for progressively increasing the prediction accuracies of surrogates. Therefore, ASA-MOEA/D strikes an adaptive balance among diversity, feasibility and convergence with the assistance of RBF surrogates as the optimization progresses. Empirical studies on three classical test suites demonstrate that ASA-MOEA/D with tchebycheff approach achieves highly competitive performance over other four state-of-the-art algorithms.

Multi-Objective Optimization for Bandwidth-Limited Federated Learning in Wireless Edge Systems

This paper studies a bandwidth-limited federated learning (FL) system where the access point is a central server for aggregation and the energy-constrained user equipemnts (UEs) with limited computation capabilities (e.g., Internet of Things devices) perform local training. Limited by the bandwidth in wireless edge systems, only a part of UEs can participate in each FL training round. Selecting different UEs could affect the FL performance, and selected UEs need to allocate their computing resource effectively. In wireless edge FL systems, simultaneously accelerating FL training and reducing computing-communication energy consumption are of importance. To this end, we formulate a multi-objective optimization problem (MOP). In MOP, the model training convergence is difficult to calculate accurately. Meanwhile, MOP is a combinatorial optimization problem, with the high-dimension mix-integer variables, which is proved to be NP-hard. To address these challenges, a multi-objective evolutionary algorithm for the bandwidth-limited FL system (MOEA-FL) is proposed to obtain a Pareto optimal solution set. In MOEA-FL, an age-of-update-loss method is first proposed to transform the original global loss function into a convergence reference function. Then, MOEA-FL divides MOP into N single objective subproblems by the Tchebycheff approach and optimizes the subproblems simultaneously by evolving a population. Extensive experiments have been carried out on MNIST dataset and a medical case called TissueMNIST dataset for both the i.i.d and non-i.i.d data setting. Experimental results demonstrate that MOEA-FL performs better than other algorithms and verify the robustness and scalability of MOEA-FL.

A new multi-objective profit-driven micro-CHP planning model under participation in thermal and electrical markets

Recently, residential micro-combined heat and power (µCHP) systems have been increasingly used worldwide and simultaneously participated in thermal and electrical markets. To enhance practicality of µCHP system planning (MSP), this research proposes a new multi-objective optimization model for MSP considering investment costs and participation profits in thermal and electrical markets. A multi-objective optimization problem includes more than one objective and usually these objectives are competing which means that there is no single optimal solution that simultaneously optimizes all of them. Maximizing the participation profits along with minimizing investment costs can more effectively persuade investors to invest on MSP. Additionally, exergy efficiency and thermal discomfort level are considered in the proposed multi-objective model. Moreover, an improved lexicographic weighted Tchebycheff (ILWT) approach is developed for solving the proposed multi-objective MSP problem, which generates effective Pareto optimal solutions with a low computation burden. The proposed MSP model and ILWT solution approach are tested on a real-world µCHP system. It is shown that the proposed MSP model achieves a significant total cost reduction by the amount of 24.5% compared with conventional MSP model. Also, the proposed ILWT, compared with its nearest competitor, obtains about 3% higher preference with more than 39% lower computation time.

A decomposition-based multi-objective particle swarm optimization algorithm with a local search strategy for key quality characteristic identification in production processes

Identifying the key quality characteristics (KQCs) (including part and process parameters) in production processes is essential for quality control. In this paper, we propose a data-driven KQC identification method based on production process data. We model KQC identification as a multi-objective feature selection problem of maximizing the geometric mean (GM) and minimizing the number of selected QCs (features). GM can evaluate the importance of a QC subset by measuring its predictive ability for product quality. To solve this optimization model, we propose a multi-objective optimization algorithm called MOPSO-LS that combines particle swarm optimization (PSO) with a local search strategy. MOPSO-LS adopts a decomposition approach, i.e., Tchebycheff approach (TA), to update personal best positions (pbests) during the iterations. Thus, diversified and high quality solutions can be maintained by the pbests of particles. Moreover, the local search strategy aims to update the non-dominated set found by MOPSO-LS during the iterations with two basic local search steps, i.e., a) adding and b) removing a feature, which can improve the convergence performance of MOPSO-LS. We have verified the proposed method on four production datasets. The experimental results indicate that MOPSO-LS can select a few KQCs with a good capability for predicting product quality, which shows the effectiveness of MOPSO-LS for KQC identification. Further comparisons show that MOPSO-LS obtains better search performance than four typical multi-objective optimization algorithms.

Performance Tradeoff of MVNOs in OFDMA-Based Virtualized Wireless Networks

In this paper, we analyze the tradeoff between the profits gained by mobile virtual network operators (MVNOs) in an orthogonal frequency division multiple access (OFDMA)-based virtualized wireless networks (VWNs). In this respect, MVNOs rent the network resources from a mobile network operator (MNO) to create virtual resources based on allocated rates and the cost due to allocated transmit powers in two different strategies: resource-based isolation strategy and rate-based isolation strategy. In resource-based isolation strategy, it is assumed that the whole bandwidth in each base station is divided equally between MVNOs whereas in rate-based isolation strategy, the whole bandwidth in each base station is allocated dynamically between MVNOs. We then formulate a multi-objective optimization problem (MOOP) to show the tradeoff between the maximum profit of each MVNO. To solve the formulated MOOP, we adopt the weighted Tchebycheff approach, which can provide the complete Pareto optimal region for nonconvex problems. Thus, by developing such formulation, we will be able to find the best profit gained by MVNOs. We also employ monotonic optimization to obtain the global optimal solutions of the non-convex problems by applying polyblock outer approximation algorithm. Our numerical results show the importance of the aforementioned tradeoffs and confirm that the proposed geometric programming (GP) based algorithm achieves excellent performance as compared to the monotonic method.

Multi-objective robust secure beamforming for cognitive satellite and UAV networks

A multi-objective optimization based robust beam-forming (BF) scheme is proposed to realize secure transmission in a cognitive satellite and unmanned aerial vehicle (UAV) network. Since the satellite network coexists with the UAV network, we first consider both achievable secrecy rate maximization and total transmit power minimization, and formulate a multi-objective optimization problem (MOOP) using the weighted Tchebycheff approach. Then, by supposing that only imperfect channel state information based on the angular information is available, we propose a method combining angular discretization with Taylor approximation to transform the non-convex objective function and constraints to the convex ones. Next, we adopt semi-definite programming together with randomization technology to solve the original MOOP and obtain the BF weight vector. Finally, simulation results illustrate that the Pareto optimal trade-off can be achieved, and the superiority of our proposed scheme is confirmed by comparing with the existing BF schemes.

A bi-objective robust optimization approach for the management of infectious wastes with demand uncertainty during a pandemic

The current global COVID-19 pandemic attracts public attention to the management of waste generated by health-care activities. Due to the hazardous nature, infectious waste requires the design of a multi-tiered system to provide cost-efficient and eco-friendly services of waste collection, transportation, treatment, and final disposal. However, the impact of uncertainties has not been well studied in the existing literature. Considering the presence of random waste generation during a pandemic, we aim to answer the following questions: 1) where to locate temporary transfer stations and temporary treatment centers; 2) how to plan collection tours among the small generation nodes and temporary transfer stations; 3) how to plan the direct transportation from large generation nodes to treatment centers; 4) how to transport waste from temporary transfer stations to treatment centers, and 5) how to transport wastes from treatment centers to disposal facilities. The relevant cost and associated risk are respectively formulated and assessed using a scenario-based bi-objective robust approach. The complexity of the resulting mathematical model motivated the adaption and comparison of three multi-objective optimization approaches, including the goal programming method, a lexicographic weighted Tchebycheff approach, and an augmented ϵ-constraint solution technique. A case study based on the real situation in Wuhan, China, during the COVID-19 outbreak is conducted to demonstrate the workability of the proposed model and provide managerial insights for infectious waste management. The computational results show that our proposed model can more than double the demand fulfillment rate at an approximately 40% lower cost when facing a distinctively high increment in the amount of infectious waste.

Using Multi-Objective Bat Algorithm for Solving Multi-Objective Non-linear Programming Problem

Human beings are greatly inspired by nature. Nature has the ability to solve very complex problems in its own distinctive way. The problems around us are becoming more and more complex in the real time and at the same instance our mother nature is guiding us to solve these natural problems. Nature gives some of the logical and effective ways to find solutions to these problems. Nature acts as an optimized source for solving the complex problems. Decomposition is a basic strategy in traditional multi-objective optimization. However, it has not yet been widely used in multi-objective evolutionary optimization. 
 Although computational strategies for taking care of Multi-objective Optimization Problems (MOPs) have been accessible for a long time, the ongoing utilization of Evolutionary Algorithm (EAs) to such issues gives a vehicle to tackle extremely enormous scope MOPs.
 MOBATD is a multi-objective bat algorithm that incorporates the dominance concept with the decomposition approach. Whilst decomposition simplifies the MOP by rewriting it as a set of Tchebycheff Approach, solving these problems simultaneously, within the BAT framework, might lead to premature convergence because of the leader selection process which uses the Tchebycheff Approach as a criterion. Dominance plays a major role in building the leaders archive, allowing the selected leaders to cover less dense regions while avoiding local optima and resulting in a more diverse approximated Pareto front. The results from 5 standard MOPs show that the MOBATD outperforms some developmental methods based on decomposition. All the results were achieved by MATLAB (R2017b).

On Multi-Objective Multi-Item Solid Transportation Problem in Fuzzy Environment

This paper discusses the reliability of multi-objective multi-item solid transport (F-MOMIST) problem with the transportation of penalties represented by the trapezoidal fuzzy numbers. We extended the existing F-MOMIST by introducing the fuzzy efficient concept and fuzzy crisp. We propose a weighting Tchebycheff approach to efficiently solve F-MOMIST. In the proposed approach, we first describe the first type of stability set corresponding to the optimal $$\alpha $$ -Pareto solution and then use the proposed approach to evaluate the first type of stability set corresponding to the $$\alpha $$ -optimal compromise solutions. A numerical case study to check the validity of the proposed approach is presented. The results of comparative experiments show that the proposed method is sufficiently effective in solving F-MOMIST and has better performance than the existing methods.

A new Algorithm to Solve Multi-Objective Optimization Problem Based on Decomposition Property

MOBATD is a multi-target bat calculation that fuses the strength idea with the decay approach is proposed as another calculation. While decay improves the multi-target issue (MOP) by changing it as a lot of Tchebycheff Approach, taking care of these issues all the while, inside the BAT structure, may prompt untimely assembly in light of the pioneer determination process which utilizes the Tchebycheff Approach as a model. Predominance assumes a significant job in building the pioneers document permitting the chose pioneers to cover less thick areas staying away from neighborhood optima and bringing about a progressively differing approximated Pareto front. Results from 12 standard MOPs show MOBATD outflanks two cutting edge decay based transformative techniques.

Power Efficient Secure Full-Duplex SWIPT Using NOMA and D2D with Imperfect CSI.

The secure full-duplex (FD) simultaneous wireless information and power transfer (SWIPT) system and non-orthogonal multiple access (NOMA) have been deemed two promising technologies for the next generation of wireless communication. In this paper, the network is combined with device-to-device (D2D) and a practical bounded channel state information (CSI) estimation scheme. A system total transmit power minimization problem is studied and formulated as a multi-objective optimization (MOO) problem via the weighted Tchebycheff approach. A set of linear matrix inequalities (LMI) is used to transform the non-convex form of constraints into the convex form. Considering the imperfect CSI of the potential eavesdropper for robust power allocation, a bounded transmission beamforming vector design along with artificial noise (AN) is used, while satisfying the requirements from the secrecy rates as well as the energy harvesting (EH) task. Numerical simulation results validate the convergence performance and the trade-off between the uplink (UL) and downlink (DL) data transmit power. It is also shown that by FD and NOMA, the performance of the proposed algorithm is higher than that of half-duplex (HD) and orthogonal multiple access (OMA).

A many-objective evolutionary algorithm based on decomposition with dynamic resource allocation for irregular optimization

The multi-objective optimization problem has been encountered in numerous fields such as high-speed train head shape design, overlapping community detection, power dispatch, and unmanned aerial vehicle formation. To address such issues, current approaches focus mainly on problems with regular Pareto front rather than solving the irregular Pareto front. Considering this situation, we propose a many-objective evolutionary algorithm based on decomposition with dynamic resource allocation (MaOEA/D-DRA) for irregular optimization. The proposed algorithm can dynamically allocate computing resources to different search areas according to different shapes of the problem’s Pareto front. An evolutionary population and an external archive are used in the search process, and information extracted from the external archive is used to guide the evolutionary population to different search regions. The evolutionary population evolves with the Tchebycheff approach to decompose a problem into several subproblems, and all the subproblems are optimized in a collaborative manner. The external archive is updated with the method of shift-based density estimation. The proposed algorithm is compared with five state-of-the-art many-objective evolutionary algorithms using a variety of test problems with irregular Pareto front. Experimental results show that the proposed algorithm out-performs these five algorithms with respect to convergence speed and diversity of population members. By comparison with the weighted-sum approach and penalty-based boundary intersection approach, there is an improvement in performance after integration of the Tchebycheff approach into the proposed algorithm.

Delay-Aware Resource Management for Multi-Service Coexisting LTE-D2D Networks With Wireless Network Virtualization

To satisfy the rapid growth of data service demands on the limited spectrum resources, wireless network virtualization (WNV) has been proposed as a promising technology in the future wireless networks. Meanwhile, Device-to-Device (D2D) communication, as an underlay to cellular networks, is also a proposed solution to promote the spectrum efficiency. However, it is a challenge to design an appropriate virtual resource slicing strategy among different wireless service providers in the two-tier LTE-D2D networks. In this paper, considering dynamic traffic arrivals and time-varying channel conditions, the virtualized resource management in the multi-service coexisting LTE-D2D networks is formulated into a multi-objective stochastic optimization problem. Leveraging on weighted Tchebycheff approach and Lyapunov optimization technique, the multi-objective stochastic optimization problem can be transformed into a delay-aware optimization problem, which is a mixed-integer nonlinear programming (MINLP) problem and can be transformed into a convex one by a series of reformulation. A distributed algorithm based on the alternating direction method of multipliers (ADMM) is proposed to obtain a close-to-optimal solution with a lower computational complexity. Finally, the simulation results show that the proposed scheme can achieve a performance-delay tradeoff related to the control factor V with at most 0.2% performance loss compared with the optimal solution.

A Two-Stage Evolutionary Fuzzy Clustering Framework for Noisy Image Segmentation

This article presents a two-stage evolutionary fuzzy clustering framework for noisy image segmentation. It is a bi-stage system comprising a multi-objective optimization stage and a fuzzy clustering segmentation stage. In the multi-objective optimization stage, the fuzzy clustering on pixels in inhomogeneous regions is converted into a multi-objective problem, which can preserve image details while restraining noise. The multi-objective problem is decomposed into several sub-problems by the Tchebycheff approach. A trade-off can be obtained by optimizing these sub-problems simultaneously. In the fuzzy clustering segmentation stage, fuzzy clustering with the trade-off between preserving image details and restraining noise is performed on the whole observed image. To deal with this fuzzy clustering problem, an adaptive evolutionary fuzzy clustering algorithm with spatial information is proposed. Experiment results on synthetic and real images illustrate the effectiveness of the proposed framework for noisy image segmentation.

Multi-Objective Optimization for Full-Duplex SWIPT Systems

This paper studies a multi-objective optimization (MOO) problem in full-duplex (FD) networks with simultaneous wireless information and power transfer (SWIPT). In the considered networks, an FD base station (BS) communicates with multiple half-duplex (HD) uplink (UL) and downlink (DL) users simultaneously. The energy receivers (ERs) harvest energy from the ambient radio frequency (RF) signals and may act as potential eavesdroppers. Specifically, there exists two conflicting yet important system design objectives, i.e., secrecy energy efficiency (SEE) maximization and energy harvesting efficiency (EHE) maximization. An MOO design based on the weighted Tchebycheff approach is proposed to investigate the tradeoff between these two design objectives. The proposed design takes into account the quality-of-service (QoS) guarantees of secrecy rate and energy harvesting (EH) under the imperfect channel state information (CSI) of ERs. The formulated MOO problem is solved with a two-layer optimization algorithm, where the modified Dinkelbach method is applied to deal with the generalized fractional programming (FP) in the outer layer problem and semidefinite relaxation (SDR), successive convex approximation (SCA) as well as S-procedure methods are applied to transfer the inner layer problem into a convex iterative program. Moreover, we propose a suboptimal solution to the formulated problem and analyze the computational complexities. Finally, numerical results are provided to demonstrate the effectiveness of the proposed algorithms and reveal a tradeoff region between SEE and EHE.

Multi-objective optimization design for multi-source multicasting MIMO AF relay systems

In this paper, we consider a multi-source multicasting two-hop multi-input multi-output amplify-forward (AF) relay system, where multiple source nodes multicast their own messages to a group of receivers with the cooperation of an AF relay node. In particular, we aim at minimizing the transmission power consumption and the mean-squared error (MSE) of the receiver estimated signal simultaneously. However, the two objectives are coupled and even conflicting. In view of this, a multi-objective optimization (MOO) framework is adopted to achieve the trade-off between the two objectives. The formulated MOO problem (MOOP) takes into account the constraints of the MSE upper bound and the maximum transmission power budget. Since the MOOP is non-convex and hard to tackle, we propose a resource allocation algorithm by exploiting the weighted Tchebycheff approach and the optimal structure of the relay precoding matrix. Simulation results not only demonstrate the effectiveness of the proposed algorithm, but also unveil an important trade-off between the total power consumption and the MSE at receivers.

A multi-objective tabu search algorithm based on decomposition for multi-objective unconstrained binary quadratic programming problem

Unconstrained binary quadratic programming problem (UBQP) is a well-known NP-hard problem. In this problem, a quadratic 0–1 function is maximized. Numerous single-objective combinatorial optimization problems can be expressed as UBQP. To enhance the expressive ability of UBQP, a multi-objective extension of UBQP and a set of benchmark instances have been introduced recently. A decomposition-based multi-objective tabu search algorithm for multi-objective UBQP is proposed in this paper. In order to obtain a good Pareto set approximation, a novel weight vector generation method is first introduced. Then, the problem is decomposed into a number of subproblems by means of scalarizing approaches. The choice of different types of scalarizing approaches can greatly affect the performance of an algorithm. Therefore, to take advantages of different scalarizing approaches, both the weighted sum approach and the Tchebycheff approach are utilized adaptively in the proposed algorithm. Finally, in order to better utilize the problem-specific knowledge, a tabu search procedure is designed to further optimize these subproblems simultaneously. Experimental results on 50 benchmark instances indicate that the proposed algorithm performs better than current state-of-the-art algorithms.