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High-level synthesis (HLS) has democratized field programmable gate arrays (FPGAs) by enabling high-level device programmability and rapid microarchitecture customization through the use of directives. Nevertheless, the manual selection of the appropriate directives, i.e., the annotations included in the high-level source code to instruct the synthesis process, is a difficult task for programmers without a hardware background. In this letter, we present CollectiveHLS, an ultrafast knowledge-based HLS design optimization method that automatically extracts the most promising directive configurations and applies them to the original source code. The proposed optimization scheme is a fully data-driven approach for generalized HLS tuning, as it is not based on quality of result models or meta-heuristics. We design, implement, and evaluate our method with more than 100 applications of Machsuite, Rodinia, and GitHub on a ZCU104 FPGA. We achieve an average geometric mean speedup of x14.1 and x10.5 compared to the unoptimized, i.e., without HLS directives and optimized designs, a high design feasibility score, and an average inference latency of 38 ms. [ABSTRACT FROM AUTHOR]

Rural areas, with their vast land and abundant resources, are ripe for the development of distributed energy systems. A two-stage dispatch optimization model has been proposed for a virtual power plant (VPP) in this paper, with the aim of maximizing operational revenue, minimizing costs for villagers, and reducing carbon emissions. This model leverages a benefit allocation strategy based on Pareto optimization, ensuring a balanced approach to conflicting objectives such as financial gain, risk management, and environmental impact. The effectiveness of various allocation strategies is evaluated using the Ideal Point method, which assesses options based on their proximity to an ideal outcome across three critical dimensions: risk, benefit, and carbon emission reduction. This method provides an assessment of each strategy’s impact, ensuring that the chosen strategy is holistic. Case study results have shown that the proposed two-stage model, when combined with the Ideal Point-Pareto optimization method, can effectively utilize dispersed resources in rural areas to enhance operational efficiency and reduce carbon emissions from energy consumption processes. Additionally, with a 47% reduction in computational volume compared to traditional scalar and particle swarm optimization algorithms.

A key enabling technology for DC collection systems in offshore wind farms is a suitable wind turbine DC/DC converter. However, there is no consensus regarding the topology, design, or operating frequency of this converter. This paper presents an optimization and comparison of four DC/DC converter topologies, including 1-phase, 3-phase, unidirectional, and bidirectional converters. The converters are compared in terms of their reliability, volume, weight and losses at switching frequencies ranging from 500 Hz to 5 kHz. The medium frequency transformer for each converter is designed using multi-objective optimization, and the overall converter volume calculation takes into account the insulation requirements and physical configuration of the components. The results show that if only unidirectional operation is required, the 1-phase single active bridge is the preferred option due to its high reliability, small size and low losses with an optimal operating frequency of up to 2.5 kHz. For bidirectional systems, the 1-phase and 3-phase dual active bridge topologies have a similar efficiency and optimal operating frequency of 1 kHz. Despite its higher volume, the 3-phase version is the preferred option due to its higher reliability and lower device stresses, provided there is enough available space.

This paper presents an approach for reducing the memory requirements of periodically executed dataflow applications, while minimizing the period when deployed on a many-core target. Often, implementations of dataflow applications suffer from data duplication if identical data has to be processed by multiple actors. In fact, multi-cast (also called fork) actors can produce huge memory overheads when storing and communicating copies of the same data. As a remedy, so-called Multi-Reader Buffers (MRBs) can be utilized to forward identical data to multiple actors in a First In First Out (FIFO) manner while storing each data item only once by sharing. However, using MRBs may increase the achievable period due to contention when accessing the shared data. This paper proposes a novel multi-objective design space exploration approach that selectively replaces multi-cast actors with MRBs and explores actor and FIFO channel mappings to find trade-offs between the objectives of period, memory footprint, and core cost. In distinction to the state-of-the-art, our approach considers (i) memory-size constraints for on-chip memories, (ii) hierarchical memories to implement the buffers, e.g., tile-local memories, (iii) supports heterogeneous many-core platforms, i.e., core-type dependent actor execution times, and (iv) optimizes the buffer placement and overall scheduling to minimize the execution period by proposing a novel combined actor and communication scheduling heuristic for period minimization called Communication-Aware Periodic Scheduling on Heterogeneous Many-core Systems (CAPS-HMS). Our results show that the explored Pareto fronts improve a hypervolume indicator over a reference approach by up to 66 % for small to mid-size applications and 90 % for large applications. Moreover, selectively replacing multi-cast actors with corresponding MRBs proves to be always superior to never or always replacing them. Finally, it is shown that the quality of the explored Pareto fronts does not degrade when replacing the efficient scheduling heuristic CAPS-HMS by an Integer Linear Program (ILP) solver that requires orders of magnitude higher solver times and thus cannot be applied to large scale dataflow network problems.

The prior domain knowledge, i.e., the regularity property of continuous multiobjective optimization problems (MOPs), could be learned to guide the search for evolutionary multiobjective optimization. This paper proposes a learning-to-guide strategy (LGS) for assisting the search for multiobjective optimization algorithms in dealing with MOPs. The main idea behind LGS is to capture the regularity via learning techniques to guide the evolutionary search to generate promising offspring solutions. To achieve this, a generative model called the generative topographic mapping (GTM) is adopted to capture the manifold distribution of a population. A set of regular grid points in the latent space are mapped into the decision space within some manifold structures to guide the search for mating with some parents for offspring generation. Following this idea, three alternative LGS-based generation operators are developed and investigated, which combine the local and global information in the offspring generation. To learn the regularity more efficiently in an algorithm, the proposed LGS is embedded in an efficient evolutionary algorithm (called LGSEA). The LGSEA includes an incremental training procedure aimed at reducing the computational cost of GTM training by reusing the built GTM model. The developed algorithm is compared with some newly developed or classical learning-based algorithms on several benchmark problems. The results demonstrate the advantages of LGSEA over other approaches, showcasing its potential for solving complex MOPs. [ABSTRACT FROM AUTHOR]

Evolutionary multiobjective algorithms have become a popular choice to tackle the clustering problem. On the one hand, the simultaneous optimization of complementary clustering criteria offers an increased robustness to changes in data characteristics. On the other hand, the evolutionary search is able to approximate the Pareto optimal front and deliver a set of trade-offs between these criteria in a single algorithm execution. Decision making is the concluding stage of the pipeline, having as its goal the selection of a single, final solution from the set of candidate trade-offs produced. This is a complex task for which a definitive answer does not seem to be available, as the underlying assumptions of existing techniques may not hold for all applications. In this paper, we investigate an alternative approach to address this challenge: posing it as a learning problem. The key idea is to build a model that, given a proper characterization of solutions and their context (defined by the full approximation solution set and the specific clustering task at hand), is able to estimate quality and facilitate the identification of the best choice. To evaluate the suitability of this approach, we conduct a series of experiments over diverse synthetic and real-world datasets, including comparisons against a range of representative decision-making strategies from the literature. Our proposal exhibits greater flexibility in dealing with problems of varying characteristics, consistently outperforming the reference methods considered. This study demonstrates that it is possible to learn from the decision-making process in example settings and generalize the acquired knowledge to new scenarios.

Precision livestock farming promises substantial advantages in terms of animal welfare, product quality and reducing methane emissions, but requires continuous and reliable data on the animal's behavior. While systems suitable for use within the barn exist, grazing over long distances poses challenges. Here, we address this issue by proposing an ultra low-power Edge AI device, minimizing data transmission requirements and potentially improving accuracy as compared to classification-based solutions. Namely, we propose cow behavior distribution regression with Recurrent Neural Networks (RNNs), dubbed TinyCowNet, to estimate mixed-label sample spaces. Without quantization, the random search to minimize resources and maximize accuracy shows networks requiring a memory of 76kB on average and offering an accuracy up to 95.7%. These are implementable on a wide range of low-power Micro Controller Units (MCU) and Field Programmable Gate Arrays (FPGA). Furthermore, our proposed post-training full-integer quantization for RNNs combined with power estimation on 45nm CMOS using experimental literature shows a TinyCowNet occupying a memory around $\approx 2$ kB, having a hypothetical power consumption on the order of 200nW, delivering an accuracy of 95.2% and a Matthews correlation coefficient of 0.86. This work paves the way for the future creation of low-cost, highly accurate cow behavior estimation devices with long battery life that reduce the entry barriers currently hindering precision livestock farming outside the barn.

There have been numerous attempts at solving the optimal camera placement problem across multiple applications. Exact linear programming-based, as well as, heuristic combinatorial optimization methods were shown to be successful in providing optimal or near-optimal solutions to this problem. Working over a discrete space model is the general practice when solving the camera placement problem. However, discretized environments often limit the methods’ usage only to small-scale datasets due to resource and time constraints that grow exponentially with the number of 3D points collected from the discrete space. We propose a multi-resolution approach that enables the usage of existing optimization algorithms on large real-world problems modelled using high resolution 3D grids. Our method works by grouping together the given discrete set of possible camera locations into clusters of points, multiple times, resulting in multiple resolution levels. Camera placement optimization is repeated for all resolution levels while propagating the optimized solution from low to high resolutions. Our experiments on both simulated and real data with grids of varying sizes show that using our multi-resolution approach, existing camera placement optimization methods can be used even on high resolution grids consisting of hundreds of thousands of points. Our results also show that the strategy of grouping points together by exploiting underlying 3D geometry to optimize camera poses is not only significantly faster than optimizing on the entire set of samples but, it also provides better camera coverage.

Recently, large-scale multiobjective optimization has received increasing attention from the evolutionary multiobjective optimization (EMO) community. This has led to the emergence of a specialized research area called evolutionary large-scale multiobjective optimization (ELMO). In general, it is believed that multiobjective optimization problems become more difficult as the number of decision variables increases. However, the following two counterintuitive observations are obtained from careful examinations of recent ELMO studies. One is that experimental results on some large-scale multiobjective test problems were improved by increasing the number of decision variables. The other is that better results were obtained for some other large-scale multiobjective test problems by conventional EMO algorithms (EMOAs) than state-of-the-art ELMO algorithms (ELMOAs). These observations suggest that ELMOAs have not always been evaluated on appropriate test problems. Moreover, their performance is not always better than the performance of conventional EMOAs. In this letter, we first re-examine the performance of ELMOAs and conventional EMOAs on a wide variety of scalable multiobjective test problems. Then, counterintuitive experimental results are analyzed using the anytime performance evaluation scheme and distributions of randomly generated initial solutions. Based on the analysis, suggestions on how to handle large-scale multiobjective test problems with counterintuitive results are proposed. [ABSTRACT FROM AUTHOR]

Conventional multiobjective optimization algorithms (MOEAs) with or without preferences are successful in solving multi- and many-objective optimization problems. However, a strong hypothesis underlying their performance is that MOEAs are able to find a representative solution set to cover the entire Pareto-optimal front (PF) and decision makers are able to conveniently and precisely articulate their preference, which is not always easy to fulfill in practice. Accordingly, it is suggested that representative solutions in the naturally interesting regions of the PF rather than the whole PF should be targeted. A large body of research has been proposed to search or identify the knees or knee regions over the past decades. Therefore, this article aims to provide a comprehensive survey of the research on knee-oriented optimization. We start with a discussion of the importance and basic concepts of the knees, followed by a summary of knee-oriented benchmarks and indicators. After that, knee-oriented frameworks and techniques, and real-world applications are presented. Finally, potential challenges are pointed out and a few promising future lines of research are suggested. The survey offers a new perspective to develop MOEAs for solving multi- and many-objective optimization problems. [ABSTRACT FROM AUTHOR]

We present a novel algorithm that allows us to gain detailed insight into the effects of sparsity in linear and nonlinear optimization. Sparsity is of great importance in many scientific areas such as image and signal processing, medical imaging, compressed sensing, and machine learning, as it ensures robustness against noisy data and yields models that are easier to interpret due to the small number of relevant terms. It is common practice to enforce sparsity by adding the $\ell _1$ ℓ 1 -norm as a penalty term. In order to gain a better understanding and to allow for an informed model selection, we directly solve the corresponding multiobjective optimization problem (MOP) that arises when minimizing the main objective and the $\ell _1$ ℓ 1 -norm simultaneously. As this MOP is in general non-convex for nonlinear objectives, the penalty method will fail to provide all optimal compromises. To avoid this issue, we present a continuation method specifically tailored to MOPs with two objective functions one of which is the $\ell _1$ ℓ 1 -norm. Our method can be seen as a generalization of homotopy methods for linear regression problems to the nonlinear case. Several numerical examples – including neural network training – demonstrate our theoretical findings and the additional insight gained by this multiobjective approach. [ABSTRACT FROM AUTHOR]

This study deals with the problem of road side unit (RSU) location optimization for origin-destination (OD) demand estimation. With the point-to-point measurement provided by RSUs in connected vehicle environment, the errors of OD demand estimation come from two sources: 1) the lack of enough path flow information; and 2) the vehicle-to-RSU (V2R) communication delay. However, increasing the amount of path flow information collected by RSUs results in the increase of V2R communication delay encountered by each collected data packet. Moreover, it is difficult to find a global optimal solution by formulating the problem as a single objective program. To address the investigated problem, this study proposes a novel framework consisting of solving a bi-objective RSU location optimization problem and an OD demand estimation problem. This RSU location optimization problem is formulated as a bi-objective nonlinear binary integer program to balance the maximization of the amount of path flow information and the minimization of V2R communication delay. The OD demand estimation problem is formulated as a least square estimator to identify the RSU location scheme with the smallest OD demand estimation error, among the Pareto optimal solutions to the bi-objective program. An efficient $\varepsilon $ -constraint method is developed to generate the Pareto optimal solutions. The numerical example demonstrates that the proposed framework achieves 6.95 lower root-mean-square error of OD demand estimation, compared with the baseline framework. [ABSTRACT FROM AUTHOR]

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 $\mu $ -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 $\mu $ subproblems of the cone decomposition approach is infinitely close to that of the optimal $\mu $ -distribution for large enough $\mu $ 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 $\mu $ -distribution convergence in the terms of hypervolume error compared with six other popular multiobjective algorithms. [ABSTRACT FROM AUTHOR]

Expensive multiobjective optimization problems pose great challenges to evolutionary algorithms due to their costly evaluation. Building cheap surrogate models to replace the expensive real models has been proved to be a practical way to reduce the number of costly evaluations. Supervised learning techniques from the community of machine learning have been widely applied to build either regressors, which approximate the fitness values of candidate solutions, or classifiers, which estimate the categories of candidate solutions. Considering the characteristics of the data produced in optimization, this article proposes a new surrogate model, called a relation model, for evolutionary multiobjective optimization. Instead of estimating the qualities of candidate solutions directly, the relation model tries to estimate the relationship between a pair of solutions $\langle \mathbf {x}, \mathbf {y}\rangle $ , i.e., $\mathbf {x}$ dominates $\mathbf {y}$ , $\mathbf {x}$ is dominated by $\mathbf {y}$ , or $\mathbf {x}$ is nondominated with $\mathbf {y}$ in the case of multiobjective optimization. To implement this idea, first a balanced training set is prepared, then a classifier is built based on the training data set to learn the relationship, and finally, the classifier with a voting-scoring strategy is applied to estimate the relationship between the candidate solutions and parent solutions. By this way, the promising candidate solutions are recognized and evaluated by the real models. The new approach is applied to three well-known benchmark suites and two real-world applications, and the experimental results suggest that the proposed method outperforms some state-of-the-art methods based on regression and classification models on the given instances. [ABSTRACT FROM AUTHOR]

Due to the high variability and uncertainty of the wind speed, an interval forecast can provide more information for decision makers to achieve a better energy management compared to the traditional point forecast. In this article, a knee-based lower upper bound estimation method (K-LUBE) is proposed to construct wind speed prediction intervals (PIs). First, we analyze the underlying limitations of traditional direct interval forecast methods, i.e., their obtained PIs often fail to achieve a good balance between the interval width and the coverage probability. K-LUBE resolves the difficulty based on a multiobjective optimization framework in conjunction with a knee selection criterion. Specifically, a PI-NSGA-II multiobjective optimization algorithm is designed to obtain a set of Pareto-optimal solutions. A parameter transfer and a sample training strategies are developed to significantly improve the convergence speed of the optimization procedure. Then, the knee selection criterion is introduced to select the best tradeoff solution among the obtained solutions. In comparison with traditional methods, this method can always provide a reliable PI for decision makers. The procedure is automatic and requires no parameter to be specified in advance, making it more practical for use. The effectiveness of the proposed K-LUBE method is demonstrated through extensive comparisons with four traditional direct interval forecast methods and four classical benchmark models. [ABSTRACT FROM AUTHOR]

Sparse multiobjective optimization problems (MOPs) have become increasingly important in many applications in recent years, e.g., the search for lightweight deep neural networks and high-dimensional feature selection. However, little attention has been paid to sparse large-scale MOPs, whose Pareto-optimal sets are sparse, i.e., with many decision variables equal to zero. To address this issue, this article proposes an enhanced competitive swarm optimization algorithm assisted by a strongly convex sparse operator (SCSparse). A tricompetition mechanism is introduced into competitive swarm optimization, aiming to strike a better balance between exploration and exploitation. In addition, the SCSparse is embedded in the position updating of the particles to generate sparse solutions. Our simulation results show that the proposed algorithm outperforms the state-of-the-art methods on both sparse test problems and application examples. [ABSTRACT FROM AUTHOR]

In the framework of induction hardening, the coil design task is particularly suitable to be formulated as a multi-objective optimization problem. In fact, the Pareto front estimation raises the issue of guaranteeing a satisfactory diversity and number of non-dominated solutions to be provided to the decision maker (DM). In this article, a generative adversarial network (GAN) and a forward neural network (FNN), which is cascade connected to the GAN generator, produce additional Pareto optimal solutions starting from the results of a genetic algorithm [non-dominated sorting genetic algorithm (NSGA II)] used as a training set. The FNN ensures an accurate prediction of the objectives of the added solutions, removing the need for further field analyses. This method is first tested against two analytical problems and subsequently validated on a three-objective coil design task to illustrate its utility for a real-world case. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing including endmember extraction and abundance estimation has been investigated successively in recent years due to increasingly hyperspectral processing requirements. As one type of decision after solution paradigm, the multiobjective endmember estimation (MoEE) method is able to obtain a set of Pareto optimal solutions, thus providing a wealth of information to determine the most representative endmembers. In addition, multiobjective optimization methods also have the characteristics of flexible modeling, excellent global convergence, commendable adaptability, and so on. However, the evolutionary algorithms designed for this kind of method generally use little spatial–spectral information of the hyperspectral image. In this article, we delve into the memetic strategy by exploiting the topological structure of hyperspectral data in the high-dimensional space to establish a vertex-directed MoEE method, termed VD-MoEE. According to the frequently used linear mixture model, endmembers of hyperspectral images are generally distributed at the vertices of the hyperspectral data manifold. Therefore, we design a vertex-directed local search operator to guide the search direction of the individuals in evolutionary algorithms. Experimental results on synthetic and real datasets demonstrated that the proposed VD-MOEE is able to achieve appealing performance in terms of solution selection and accuracy in comparison with several classic and state-of-the-art endmember estimation methods. [ABSTRACT FROM AUTHOR]

Many real-world multi-objective optimization problems (MOPs) are characterized by a large number of decision variables, where the decision variables are mostly set to zero in the Pareto optimal solutions. Although some multi-objective evolutionary algorithms (MOEAs) have been tailored for large-scale MOPs in recent years, most of them do not consider the sparse nature of Pareto optimal solutions, and their effectiveness to sparse MOPs has not been investigated. Therefore, this work aims to compare the performance of MOEAs on sparse MOPs by suggesting a comprehensive performance indicator. In comparison to existing indicators assessing the convergence and diversity of a solution set according to predefined reference points, the proposed indicator can assess the convergence, diversity, and sparsity without using any reference point. Based on the proposed indicator, an experiment is conducted to compare the performance of 11 state-of-the-art MOEAs on 60 test instances taken from benchmark suites and real-world applications. The statistical results show that some MOEAs are significantly better than the others for solving sparse MOPs, and the proposed indicator is effective for the performance assessment on sparse MOPs. [ABSTRACT FROM AUTHOR]

How to evaluate Pareto front approximations generated by multi/many-objective optimizers is a critical issue in the field of multiobjective optimization. Currently, there exist two types of comprehensive quality indicators (i.e., volume-based and distance-based indicators). Distance-based indicators, such as inverted generational distance (IGD), are usually computed by summing up the distance of each reference point to its nearest solution. Their high computational efficiency leads to their prevalence in many-objective optimization. However, in the existing distance-based indicators, the distributions of the solution sets are usually neglected, leading to their lack of ability to well distinguish between different solution sets. This phenomenon may become even more severe in high-dimensional space. To address such an issue, a kernel-based indicator (KBI) is proposed as a comprehensive indicator. Different from other distance-based indicators, a kernel-based maximum mean discrepancy is adopted in KBI for directly measuring the difference that can characterize the convergence, spread, and uniformity of two sets, i.e., the solution set and reference set, by embedding them in reproducing kernel Hilbert space (RKHS). As a result, KBI not only reflects the distance between the solution set and the reference set but also can reflect the distribution of the solution set itself. In addition, to maintain the desirable weak Pareto compliance property of KBI, a nondominated set reconstruction approach is also proposed to shift the original solution set. The detailed theoretical and experimental analysis of KBI is provided in this article. The properties of KBI have also been analyzed by the optimal $\mu $ -distribution. [ABSTRACT FROM AUTHOR]

The use of ensemble approaches in the single-objective evolutionary algorithms is ubiquitous, but ensembles of multiobjective evolutionary algorithms (MOEAs) have achieved relatively little attention. On the other hand, manually selecting a suitable MOEA to solve an actual multiobjective optimization problem (MOP) is time-consuming and challenging. Therefore, developing a multiobjective hyperheuristic to allocate computational resources for multiple MOEAs in an intelligent approach is beneficial. In this work, an autoselection strategy of MOEAs based on the performance indicator (MOEAS-PI) is introduced to alleviate the abovementioned problem. In the MOEAS-PI, the performance of each constituent MOEA in the pool is assessed according to a real-time and comprehensive performance indicator, which contains both the current and future performances. The MOEAS-PI is able to easily choose the best performing MOEA during the evolutionary process. Also, it can enhance the robustness of MOEAs and reduce the application risk. The effectiveness of the MOEAS-PI is carefully evaluated on 23 MOPs. Simulation results demonstrate that the MOEAS-PI is an effective and efficient method to integrate the advantages of each individual algorithm. Finally, the MOEAS-PI is utilized to solve a translation control problem of an immersed tunnel element under current flow. Experimental results reveal that the MOEAS-PI is a reliable and effective optimization approach to solve actual MOPs. Note to Practitioners—Multiobjective optimization problems (MOPs) have been commonly found in various fields. However, a single MOEA cannot guarantee its sufficient robustness and adaptability in solving MOPs. Therefore, this study aims to propose a multiobjective hyperheuristic algorithm to improve the robustness of MOEAs. The performance of the proposed algorithm is tested on benchmark test functions and an actual MOP. The results show that the proposed approach can select a suitable MOEA to solve a particular type of MOPs during the evolutionary process and provide a solution set for decision-makers to control the translation of an immersed tunnel element under different objectives/operator environments. [ABSTRACT FROM AUTHOR]

This article proposes an adaptive localized decision variable analysis approach under the decomposition-based framework to solve the large-scale multiobjective and many-objective optimization problems (MaOPs). Its main idea is to incorporate the guidance of reference vectors into the control variable analysis and optimize the decision variables using an adaptive strategy. Especially, in the control variable analysis, for each search direction, the convergence relevance degree of each decision variable is measured by a projection-based detection method. In the decision variable optimization, the grouped decision variables are optimized with an adaptive scalarization strategy, which is able to adaptively balance the convergence and diversity of the solutions in the objective space. The proposed algorithm is evaluated with a suite of test problems with 2–10 objectives and 200–1000 variables. Experimental results validate the effectiveness and efficiency of the proposed algorithm on the large-scale multiobjective and MaOPs. [ABSTRACT FROM AUTHOR]

Non-orthogonal multiple access (NOMA) assisted mobile edge computing (MEC) has recently attracted significant attention due to its superior capability to reduce the energy consumption and the latency of MEC offloading. In this paper, a general hybrid NOMA-MEC offloading strategy is proposed, which includes conventional orthogonal multiple access (OMA) and pure NOMA based offloading as special cases. A multi-objective optimization problem is formulated to minimize the energy consumption for MEC offloading, and a low-complexity resource allocation solution is derived and shown to be Pareto-optimal. Furthermore, by analyzing the properties of the obtained resource allocation solution, important insights regarding NOMA-MEC offloading are obtained. For example, it is proved that pure NOMA-MEC offloading cannot outperform hybrid NOMA-MEC. In addition, a precise condition under which NOMA-MEC outperforms OMA-MEC is established, and shown to match the one previously developed for the two-user special case. Furthermore, the developed analytical results also establish an interesting analogy between the proposed hybrid NOMA-MEC power allocation scheme and the well-known water-filling strategy. [ABSTRACT FROM AUTHOR]

Given the fast growth of on-demand transportation services and ride-sharing platforms, the concept of private vehicle ownership is rapidly declining. Although there are multiple fully-grown ride-sharing systems, they are proprietary and centrally controlled. Facilitating ride-sharing using a localized distributed coordination between the riders and the drivers is in need. However, fully distributed systems deal with a large number of variables and objectives and are often sub-optimal. In this paper, we propose a distributed ride-sharing system with multiple objectives which are often conflicting to each other. Therefore, we model it as a multi-objective optimization problem and solve it using the Ant Colony optimization technique which sports a multi-agent behavior. We critically analyze the spatio-temporal challenges posed by the ride sharing problem and define novel performance metrics to capture the underlying subtlety of the distributed system performance. An in-depth experimentation with recent large-scale single-ride taxi trip data from Chicago shows that our solution can ensure up to 79.65% success rate of ride sharing. We have shown that ride sharing is more successful during non-peak traffic hours due to less contention and a healthy balance in passenger and taxi numbers. Further, it has been observed that ride-sharing always reduces the total distance travelled by all the taxis and the total number of taxis on-road; both of which positively impact road congestion and environment. The results obtained from the experiments are very much comparable to real time behaviour of taxi networks. Finally, a revenue framework is proposed to analyse nuances of the operating environment. [ABSTRACT FROM AUTHOR]

The decomposition-based evolutionary algorithm (MOEA/D) has attained excellent performance in solving optimization problems involving multiple conflicting objectives. However, the Pareto-optimal front (POF) of many multiobjective optimization problems (MOPs) has irregular properties, which weakens the performance of MOEA/D. To address this issue, we devise a dynamic transfer reference point-oriented MOEA/D with local objective-space knowledge (DTR-MOEA/D). The design principle is based on three original and rigorous mechanisms. First, the individuals are projected onto a line segment (two-objective case) or a 3-D plane (three-objective case) after being normalized in the objective space. The line segment or the plane is divided into three different regions: 1) the central region; 2) the middle region; and 3) the edge region. Second, a dynamic transfer criterion of the reference point is developed based on the population density relationships in different regions. Third, a strategy of population diversity enhancement guided by local objective-space knowledge is adopted to improve the diversity of the population. Finally, the experimental results conducted on 16 benchmark MOPs and eight modified MOPs with irregular POF shapes verify that the proposed DTR-MOEA/D has attained a strong competitiveness compared with other representative algorithms. [ABSTRACT FROM AUTHOR]

While designing control for a class of underactuated mechanical systems (UMSs), the uncertainty and the prescribed nonholonomic tracking trajectories should be taken into consideration. Uncertainty considered in this article is time varying and bounded, and the bound of uncertainty is described using the fuzzy set theory, namely, fuzzy UMSs. An analytical dynamics-based view is taken in which the prescribed tracking trajectories are viewed as servo constraints which can be linear, nonlinear, holonomic, and nonholonomic. Using this view, a novel closed form solution of adaptive robust control is found with leakage type adaptive law to guarantee deterministic system performance, including uniform boundedness and uniform ultimate boundedness. In order to find the optimal dual gain parameters of the designed control, a two-player cooperative game is proposed for which the Pareto optimality can always be guaranteed. The effectiveness of the proposed control is shown through numerical simulation of a two-wheeled inverted pendulum vehicle. [ABSTRACT FROM AUTHOR]

A mixed-integer programming (MIP) problem contains not only constraints but also integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts with different sizes. Several popular methods (e.g., rounding and truncation) have been proposed to deal with integer restrictions. Although it is easy for these methods to generate an integer, they tend to converge to an integer which is located in a feasible part with a big size. If the optimal solution is not in this feasible part, they are very likely to converge to a local optimal solution due to the loss of diversity of the population. To overcome this shortcoming, a biobjective optimization-based two-phase method is proposed in this article. In the first phase, a measure function is designed to compute the degree that a solution violates integer restrictions. By employing this measure function as the second objective function and removing integer restrictions, a MIP problem is transformed into a constrained biobjective optimization problem (CBOP). It can be proven that the Pareto optimal solution of the transformed CBOP which satisfies integer restrictions is the optimal solution of the original MIP problem. To solve the transformed CBOP, a new comparison rule is designed. After the first phase, the population can approach the Pareto optimal solution which satisfies integer restrictions. Then, the second phase is implemented to enhance the convergence precision and obtain the optimal solution. In addition, we design 12 test problems to verify the effectiveness of the proposed method. The results demonstrate that the proposed method shows better performance against five state-of-the-art evolutionary algorithms for MIP. [ABSTRACT FROM AUTHOR]

In this study, a multi-objective mayfly optimization algorithm based on dimensional swap variation (DSV-MOMA) is proposed to solve Multi-objective RFID network planning problem (MORNP). The contributions of this work are as following: firstly, improving multi-objective mayfly optimization algorithm (MOMA)’s ability to solve high-dimensional nonlinear optimization problems; secondly, DSV-MOMA is used to solve the MORNP problem, and optimize two and three of the four objective functions simultaneously; lastly, the fuzzy decision mechanism is used to select an optimal solution objectively from pareto optimal solutions. The proposed DSV-MOMA algorithm contributes to having better diversity and convergence when solving high dimensional nonlinear and discontinuous test functions in comparison to other popular metaheuristic algorithms. DSV-MOMA also performs well when dealing with MORNP problems. In most experiments, DSV-MOMA can reduce interference effectively, and obtain satisfactory load balance and power while ensuring a higher coverage. [ABSTRACT FROM AUTHOR]

Hypervolume is widely used in the evolutionary multiobjective optimization (EMO) field to evaluate the quality of a solution set. For a solution set with $\mu $ solutions on a Pareto front, a larger hypervolume means a better solution set. Investigating the distribution of the solution set with the largest hypervolume is an important topic in EMO, which is the so-called hypervolume-optimal $\mu $ -distribution. Theoretical results have shown that the $\mu $ solutions are uniformly distributed on a linear Pareto front in two dimensions. However, the $\mu $ solutions are not always uniformly distributed on a single-line Pareto front in three dimensions. They are only uniform when the single-line Pareto front has one constant objective. In this article, we further investigate the hypervolume-optimal $\mu $ -distribution in three dimensions. We consider the line-based and plane-based Pareto fronts. For the line-based Pareto fronts, we extend the single-line Pareto front to two-line and three-line Pareto fronts, where each line has one constant objective. For the plane-based Pareto fronts, the linear triangular and inverted triangular Pareto fronts are considered. First, we show that the $\mu $ solutions are not always uniformly distributed on the line-based Pareto fronts. The uniformity depends on how the lines are combined. Then, we show that a uniform solution set on the plane-based Pareto front is not always optimal for hypervolume maximization. It is locally optimal with respect to a $(\mu +1)$ selection scheme. Our results can help researchers in the community to better understand and utilize the hypervolume indicator. [ABSTRACT FROM AUTHOR]

Apart from improving motion accuracy, increasing productivity while reducing computer numerical control machine tools' carbon footprint is vital in the manufacturing industry. Several studies have proposed corner smoothing methods that improve cycle time for piecewise linear paths by exploiting axial limits to achieve time-optimal trajectories. Energy-saving is not considered an objective in these methods. This paper presents a method of generating Pareto optimal corner smoothing trajectories that trade-off the contradicting objectives of minimizing cycle time and energy consumption. The trajectories along linear paths and smoothed corners are respectively described using jerk limited acceleration profiles and kinematic corner smoothing methods. An energy consumption model of an industrial two-axis feed drive system is identified and used in solving the bi-objective optimization problem. From the resulting Pareto frontier, the best trade-off trajectory is selected as the one that minimizes both objectives. The proposed method's effectiveness is vindicated experimentally, where the best trade-off trajectory achieves respectively 65.87 % and 60.44 % of the time and energy-saving potentials.

In the immediate aftermath of large-scale disasters, emergency logistics services play important roles in saving lives and reducing losses. Efficient relief logistics scheduling depends on the accurate transport time information for available routes. However, this information cannot be obtained precisely until a vehicle uses the road. Considering the correlation between information acquisition and logistics operations, this paper focuses on a multiperiod online decision-making problem to simulate the information acquiring process. This problem can be referenced for emergency resource scheduling scenarios in which previous decisions impact knowledge for future logistics plans. A multi-trip cumulative capacitated vehicle routing problem with uncertain transportation time is investigated as the basic model. The tradeoff between transportation efficiency and the unknown transport time discovery rate is considered in a multiobjective evolutionary algorithm (MOEA). A memetic algorithm (MA) and a robust optimization (RO) -MA for single-period post-disaster emergency logistics are also proposed to solve the problem for comparison. In these algorithms, evolutionary operators that benefit solution fixing and variation are proposed. In the experiments, a real-world instance is employed. A simulative experimental environment is established. Dynamic information gained within the process of logistics scheduling is highlighted via multi-period online optimization. Different scenarios corresponding to estimates in emergency situations are provided to validate the performance of the algorithms. The experimental results show that the hybrid strategy, MOEA+MA, can obtain the best result in more than half of the considered cases which demonstrates the necessary balance between obtaining information and transportation efficiency.

Demand response (DR) has received much attention for its ability to balance the changing power supply and demand with flexibility. DR aggregators play an important role in aggregating flexible loads that are too small to participate in electricity markets. In this work, a DR operation framework is presented to enable local management of customers to participate in electricity market. A novel optimization model is proposed for the DR aggregator with multiple objectives. On one hand, it attempts to obtain the optimal design of different DR contracts as well as the portfolio management so that the DR aggregator can maximize its profit. On the other hand, the customers' welfare should be maximized to incentivize users to enroll in DR programs which ensure the effective and flexible load control. The consumer psychology is introduced to model the consumers' behavior during contract signing. Several simulation studies are performed to demonstrate the feasibility of the proposed model. The results illustrate that the proposed model can ensure the profit of the DR aggregator whereas the customers' welfare is considered.

Manufacturing industries aim to improve product quantity and quality. These trade-off objectives are typically manifested as cycle time reduction and motion accuracy improvement. Corner smoothing approaches that reduce the cycle time of piecewise linear trajectories are proposed in the literature. This study tackles the two objectives by Pareto-optimal corner smoothing with constraints imposed as kinematic limits, continuity conditions and user-specified cornering tolerance. Linear and cornering motions along a contour are respectively described by jerk-limited acceleration profiles and a modified kinematic corner smoothing with interrupted acceleration (KCSIA) approach. A Pareto frontier is generated by the divide and conquer algorithm, where the solution nearest to the utopia point is selected as the best trade-off solution. The effectiveness of the proposed method is validated through experiments, where the best trade-off solution reduces the maximum and average contouring errors by 47.53% and 25.40% while it increases cycle time by 2.53% compared to KCSIA.

Multi-criteria optimization problems represent a crucial task for any designer of a public service system due to conflicting criteria, which have to be faced. Possible solution of this almost unsolvable situation can be seen in obtaining a series of solutions, where it is impossible to improve one of the criteria without worsening some of the others. Full set of such non-dominated solutions is called Pareto front. The multi-criteria optimization problem can be solved by submitting the Pareto front or its approximation on contracting authority’s board for possible negotiation with representative of public. This paper deals with methods, which are able to produce a series of non-dominated solutions of bi-criteria public service system design problem. The first criterion considered is average response time and the second one corresponds to the number of users located behind a given limit of response time. We suggest two approaches to the problem. The first of them is an exact approach, which produces Pareto front of the bi-criteria problem. The second approach makes use of an evolutionary hybridized algorithm, which uses so called elite set, to save temporary non-dominated solutions. In the computational study, we try to verify the hypothesis that it is possible to approximate the Pareto front by utilizing the evolutionary algorithm. We also suggest a way of hybridization and tuning the algorithm to obtain a good approximation in acceptable computational time.

Model-based reinforcement learning is expected to be a method that can safely acquire the optimal policy under real-world conditions by using a stochastic dynamics model for planning. Since the stochastic dynamics model of the real world is generally unknown, a method for learning from state transition data is necessary. However, model learning suffers from the problem of bias-variance trade-off. Conventional model learning can be formulated as a minimization problem of expected loss. Failure to consider higher-order statistics for loss would lead to fatal errors in long-term model prediction. Although various methods have been proposed to explicitly handle bias and variance, this paper first formulates a new loss function, especially for sequential training of the deep neural networks. To explicitly consider the bias-variance trade-off, a new multi-objective optimization problem with the augmented weighted Tchebycheff scalarization, is proposed. In this problem, the bias-variance trade-off can be balanced by adjusting a weight hyperparameter, although its optimal value is task-dependent and unknown. We additionally propose a general-purpose and efficient meta-optimization method for hyperparameter(s). According to the validation result on each epoch, the proposed meta-optimization can adjust the hyperparameter(s) towards the preferred solution simultaneously with model learning. In our case, the proposed meta-optimization enables the bias-variance trade-off to be balanced for maximizing the long-term prediction ability. Actually, the proposed method was applied to two simulation environments with uncertainty, and the numerical results showed that the well-balanced bias and variance of the stochastic model suitable for the long-term prediction can be achieved.

In order to improve the energy efficiency of urban rail transit system, it is necessary to figure out the key factor(s) that restrain(s) train rapidity and energy conservation and understand the inner complex relationships among them. We first define energy-saving and rapid train control/operation, then simulate and analyze the microscopic train behavior between two successive stations. The result reflects that due to the constraint of the short inter-station distance, the train has no space and time to take advantage of its excellent performance in speed and has to stop frequently at every station, which leads to the increase of energy consumption and the prolongation of running time. Based on the above energy consumption analysis of the microscopic train behavior, a hierarchical Pareto 0–1 integer programming with consideration of passenger flow distribution and public transport characteristics is presented to organically integrate microscopic train control with macroscopic train organization. The case study shows that the presented method can greatly promote the energy-efficient and rapid train operation of urban rail transit system. This study is also helpful to the planning and construction of future cities and urban rail transit systems.

Radio Access Network (RAN) slicing is a promising architectural technology to address extremely diversified service demands and provide profitable business models for future mobile networks. In RAN slicing architecture, self-healing is an important functional module to minimize the impact of network failings on the performance of RAN slices. However, self-healing of burgeoning sliced RAN is vastly different from that of traditional RAN and has been rarely investigated. In this paper, we address the Self-healing of RAN Slice (SRANS) problem by modeling it as a Pareto optimization problem with the aim of maximizing the self-healing utilities of individual RAN slices. To deal with the weakness of diversity maintenance in traditional Pareto optimization methods, we propose a Generative Adversarial Network (GAN) based Pareto Optimization (GPO) framework. Specifically, we employ self-conditioned GANs to replace the offspring reproduction module in the traditional Evolutionary Algorithm (EA), where the insufficiency of diversity maintenance in EAs is effectively overcome. Furthermore, we theoretically prove that GPO framework is guaranteed to converge to the optimal Pareto solution set. Numerical results demonstrate that the convergence of proposed GPO framework can be expedited by enhancing the diversity of solution sets in solving the SRANS problem. Compared with traditional schemes, GPO can achieve significant performance gain in terms of the utilities and isolation level of repaired RAN slices. [ABSTRACT FROM AUTHOR]

Offspring generation plays an important role in evolutionary multiobjective optimization. However, generating promising candidate solutions effectively in high-dimensional spaces is particularly challenging. To address this issue, we propose an adaptive offspring generation method for large-scale multiobjective optimization. First, a preselection strategy is proposed to select a balanced parent population, and then these parent solutions are used to construct direction vectors in the decision spaces for reproducing promising offspring solutions. Specifically, two kinds of direction vectors are adaptively used to generate offspring solutions. The first kind takes advantage of the dominated solutions to generate offspring solutions toward the Pareto optimal set (PS) for convergence enhancement, while the other kind uses those nondominated solutions to spread the solutions over the PS for diversity maintenance. The proposed offspring generation method can be embedded in many existing multiobjective evolutionary algorithms (EAs) for large-scale multiobjective optimization. Experiments are conducted to reveal the mechanism of our proposed adaptive reproduction strategy and validate its effectiveness. Experimental results on some large-scale multiobjective optimization problems have demonstrated the competitive performance of our proposed algorithm in comparison with five state-of-the-art large-scale EAs. [ABSTRACT FROM AUTHOR]

In this letter, we consider a multi-input multi-output (MIMO) dual-functional radar and communication (DFRC) system, where a co-designed waveform is optimized for dual purposes of detecting multiple targets and serving several single-antenna users. In particular, two novel waveform design optimization problems based on constructive interference (CI) are proposed, where a constraint of waveform similarity error (WSE) and a joint radar-communication objective function are imposed under a Pareto optimization framework, by taking into account different transmit power constraints. To tackle the proposed optimization problems, we propose specifically tailored convex optimization techniques by using manifold algorithms. Numerical results show that the CI-based methods outperform the existing least-squares (LS) based methods, in terms of the symbol error rate (SER), without the need of knowing the exact constellation power. [ABSTRACT FROM AUTHOR]

Various intelligent algorithms are applied in optimization design, and the differential evolution (DE) algorithm is widely applied with its excellent convergence speed and convergence precision. This study analyzed the advantages and disadvantages of the existing multi-objective differential evolution (MODE) algorithm, and developed a MODE algorithm based on the adaptive weight and the multi-population strategy (MODE/AWMS). The proposed algorithm was verified using test functions. MODE/AWMS exhibited certain advantages compared with several other multi-objective optimization algorithms. Taking a polarized magnetic relay as an example, MODE/AWMS was used to optimize its key parameters by establishing a rapid calculation model of its electromagnetic mechanism. The electromagnetic force (EMF) of the release position was improved, which verified the validity of MODE/AWMS.

Optimization on the basis of sustainability brings important benefits to manufacturing process as sustainable productions constitute a crucial aspect in modern manufacturing. This paper presents a new formalized framework for optimizing the sustainability of manufacturing processes. Unlike previous approaches, the proposed technique combines a methodology for selecting the sustainability indicators and a multi-objective optimization for improving the three sustainability pillars (economy, environment and society). While selecting the significant sustainability indicators in the considered manufacturing process relies on the ABC judgment method, the Saaty's method enables weighting the chosen indicators in order to combine them into suitable economic, environmental and social sustainability indexes. Other technological aspects, usually taken as objectives in previous works, are considered constraints in the proposed approach. The optimization is performed by using nature inspired heuristics, which return the set of non-dominated solutions (also known as Pareto front), from which the most convenient alternative is chosen by the decision maker, depending on the specific conditions of the process. For illustrating the usage of the proposed framework, it is applied to the optimization of a submerged arc welding process. Compared with currently used welding parameters, the computed optimal solution outperforms the economic and environmental sustainability while keeps equal the social impact. The results show not only the effectiveness of the proposed approach, but also its flexibility by giving a set of possible solutions which can be chosen depending on how are ranked the sustainability pillars.

Active brake control systems are able to use more accurate control designs on the real-time knowledge of wheel slip such as tire braking forces and external momentums. A multi-objective Pareto type optimization approach is used to evaluate the inconsistent points of the optimization design namely those of minimizing the directional deviation while achieving maximum braking forces on wheels. Moreover, the optimal target slip values defined by the braking purposes like as shorter stopping distance and stability increment by keeping the vehicle in the straight line. This gets by the control of the longitudinal and lateral slip dynamics of each wheel concerning to the road conditions. A controller is optimally brought up by manipulating optimal control law with weights of two control inputs with mathematical and probabilistic characterization. The first-passage probability of critical response levels is used to directly control the vehicle directional stability. An impressive simulation technique based on Monte Carlo method named asymptotic sampling is applied to define the required first-passage probabilities and the Latin Hypercube sampling is used to design of experiments and to cover the design space. Afterwards, a Pareto-type optimization approach is applied to a trade-off between the inconsistent points of the optimization design. The simulation is conducted by the validated vehicle model and the results are indicated that the probability-based control design is represented as a preferable braking performance in comparison with the other systems for braking in sever conditions.

Obstructive sleep apnea (OSA) is a common sleep disorder characterized by interrupted breathing during sleep. Because of the cost, complexity, and accessibility issue related to polysomnography, the gold standard test for apnea detection, automation of the diagnostic test based on a simpler method is desired. Several signals can be used for apnea detection, such as airflow and electrocardiogram. However, the reduction of airflow normally leads to a decrease in the blood oxygen saturation level (SpO2). This signal is usually measured by a pulse oximeter, a sensor that is cheap, portable, and easy to assemble. Therefore, the SpO2 was chosen as the reference signal. Feature based classifiers with shallow neural networks have been developed to provide apnea detection using SpO2. However, two main issues arise, the need for feature creation and the selection of the more relevant features. Deep neural networks can solve these issues by employing featureless methods. Among multiple deep classifiers that have been developed, convolution neural networks (CNN) are gaining popularity. However, the selection of the CNN structure and hyperparameters are typically done by experts, where prior knowledge is essential. With these problems in mind, an algorithm for automatic structure selection and hyper parameterization of a one dimension CNN was developed to detect OSA events using only the SpO2 signal. Three different input sizes and databases were tested, and the best model achieved an average accuracy, sensitivity, and specificity of 94%, 92%, and 96%, respectively.

Sparse level-set formulations allow practitioners to find the minimum 1-norm solution subject to likelihood constraints. Prior art requires this constraint to be convex. Extending these approaches to nonconvex likelihood constraints enables outlier robust methods. In this letter, we develop an efficient approach for nonconvex likelihoods, using Regula Falsi root-finding techniques to solve the level-set formulation. Regula Falsi methods are simple, derivative-free and efficient. The approach provably extends level-set methods to the broader class of nonconvex inverse problems. Practical performance is illustrated using $\ell _1$ -regularized Student's t inversion, which is a nonconvex problem used to develop outlier-robust approaches. [ABSTRACT FROM AUTHOR]

Multimodal multiobjective problems (MMOPs) arise frequently in the real world, in which multiple Pareto-optimal solution (PS) sets correspond to the same point on the Pareto front. Traditional multiobjective evolutionary algorithms (MOEAs) show poor performance in solving MMOPs due to a lack of diversity maintenance in the decision space. Thus, recently, many multimodal MOEAs (MMEAs) have been proposed. However, for most existing MMEAs, the convergence performance in the objective space does not meet expectations. In addition, many of them cannot always obtain all equivalent Pareto solution sets. To address these issues, this study proposes an MMEA based on a weighted indicator, termed MMEA-WI. The algorithm integrates the diversity information of solutions in the decision space into an objective space performance indicator to maintain the diversity in the decision space and introduces a convergence archive to ensure a more effective approximation of the Pareto-optimal front (PF). These strategies can readily be applied to other indicator-based MOEAs. The experimental results show that MMEA-WI outperforms some state-of-the-art MMEAs on the chosen benchmark problems in terms of the inverted generational distance (IGD) and IGD in the decision space (IGDX) metrics. [ABSTRACT FROM AUTHOR]

A real-world multiobjective optimization problem (MOP) usually has differently scaled objectives. Objective space normalization has been widely used in multiobjective optimization evolutionary algorithms (MOEAs). Without objective space normalization, most of the MOEAs may fail to obtain uniformly distributed and well-converged solutions on MOPs with differently scaled objectives. Objective space normalization requires information on the Pareto front (PF) range, which can be acquired from the ideal and nadir points. Since the ideal and nadir points of a real-world MOP are usually not known a priori, many recently proposed MOEAs tend to estimate and update the two points adaptively during the evolutionary process. Different methods to estimate ideal and nadir points have been proposed in the literature. Due to inaccurate estimation of the two points (i.e., inaccurate estimation of the PF range), objective space normalization may deteriorate the performance of an MOEA. Different methods have also been proposed to alleviate the negative effects of inaccurate estimation. This article presents a comprehensive survey of objective space normalization methods, including ideal point estimation methods, nadir point estimation methods, and different methods based on the utilization of the estimated PF range. [ABSTRACT FROM AUTHOR]

Cognitive radio (CR) is a promising technology for addressing resource scarcity in wireless networks. However, in the current CR-based framework, when resource availability changes, existing resource allocation algorithms restart the optimization process without using historical information. In addition, most previous studies have focused on one or two objectives and some have only addressed pure power control or spectrum allocation, limiting the potential of CR. Thus, this article proposes a dynamic multiobjective approach for power and spectrum allocation in a CR-based environment in which the available spectrum channels vary over time and multiple objectives are involved. This article presents a dynamic multiobjective optimization problem (MOP) with the objectives of energy efficiency, fairness, and spectrum utilization and an approach of Pareto optimality. A dynamic resource allocation algorithm comprising a hybrid initialization method and feasible point generation mechanisms is proposed to solve the dynamic MOP. To dynamically adjust resource allocation, historical approximate Pareto optimal solutions, represented by a center and a manifold, are used to predict the new optima. The proposed approach can yield a better convergence level and convergence rate than those attained by comparable multiobjective resource allocation algorithms. Compared with conventional single-objective approaches, it achieves an excellent balance between the objectives. [ABSTRACT FROM AUTHOR]

This article derives necessary and sufficient conditions for Pareto optimal solutions in infinite horizon cooperative difference games of autonomous systems with exponentially discounted performances. First, the $\mathcal {N}$ constrained optimal control problems are converted into an unconstrained characterization with mixed endpoint constraints by introducing appropriate auxiliary states. Second, the infinite horizon cooperative difference games are transformed equivalently into an augmented and truncated finite horizon optimization problem by defining two real-valued functions and the necessary conditions are derived based on the maximum principle (MP) of discrete-time type. Moreover, we present sufficient conditions for general nonautonomous systems. Finally, the results developed are employed to address the linear quadratic (LQ) cooperative difference games for fixed as well as arbitrary initial states. [ABSTRACT FROM AUTHOR]