Distance Minimization Problem Research Articles

Multi-objective sand cat swarm optimization based on adaptive clustering for solving multimodal multi-objective optimization problems

Multimodal multi-objective optimization problems (MMOPs) represent a highly challenging class of complex problems, characterized by the presence of several Pareto solution sets in the decision space which map to the identical Pareto-optimal front. The goal of solving MMOPs is to find multiple distinct Pareto sets to sustain a balance between good convergence and diversification of populations. In this paper, a multi-objective sand cat swarm optimization algorithm (MOSCSO) is developed to address MMOPs. In the MOSCSO algorithm, an adaptive clustering-based specific congestion distance technique is introduced to compute the level of crowdedness. This ensures an even distribution of individuals, avoiding excessive crowding in the local area. Subsequently, enhanced search-and-attack prey updating mechanisms are designed to effectively increase not only the exploration and exploitation capabilities of the algorithm but also to enhance the diversity of the swarm in both the decision space and the objective space. To verify the effectiveness of the proposed algorithm, the MOSCSO is applied to solve the CEC2019 complex multimodal benchmark function. The experimental outcomes illustrate that the proposed approach possesses excellent performance in searching for Pareto solutions compared with other algorithms. Meanwhile, the method is also employed to address the map-based distance minimization problem, which further validates the usefulness of the MOSCSO.

Multiparty distance minimization: Problems and an evolutionary approach

Multiparty multiobjective optimization problems (MPMOPs) have been proposed to represent situations in which involves multiple decision makers, each decision maker concerns on a multiobjective optimization problem (MOP) and their MOPs are different. To study multiparty multiobjective evolutionary algorithms in depth, this paper constructs a series of MPMOPs based on distance minimization problems (DMPs). These MPMOPs, called MPDMPs, can easily represent the solutions in the decision space. Thus, the behaviors of evolutionary algorithms performing on MPDMPs can be conveniently studied including the movement of the solutions and the distribution of the final solutions. To address MPDMPs, the new proposed algorithm OptMPNDS3 uses a multiparty initialization method to initialize the population and the JADE2 operator to generate the offspring. OptMPNDS3 is compared with OptAll, OptMPNDS and OptMPNDS2 on the problem suite. The results show that the performance of OptMPNDS3 is strong and comparable to that of other algorithms.

Graph clustering with Boltzmann machines

Graph clustering is the process of labeling nodes so that nodes sharing common labels form densely connected subgraphs with sparser connections to the remaining vertices. Because of its difficult formulation, we translate the intra-cluster density maximization problem to a distance minimization problem. To achieve this reformulation, we use a novel vertex–vertex distance that accurately reflects density. Specifically, we extend the recent binary quadratic K-medoids formulation to graph clustering. We also generalize a quadratic formulation originally designed for partitioning complete graphs. Because binary quadratic optimization is an NP-hard problem, we obtain numerical solutions for these formulations through the use of two novel Boltzmann machine (meta-)heuristics. For benchmarking purposes, we compare solution quality and computational performances to those obtained using a commercial solver, Gurobi. We also compare clustering quality to the clusters obtained using the popular Louvain modularity maximization method. Our initial results clearly demonstrate the superiority of our problem formulations combined with our Boltzmann machines. In the case of smaller less complex graphs, our formulations solved using Boltzmann machines provide the same solutions as Gurobi, but with solution times that are orders of magnitude lower. In the case of larger and more complex graphs, Gurobi either fails to return meaningful results within a reasonable time frame or returns inferior results. Finally, we also note that both our clustering formulations, the distance minimization and K-medoids, when solved using our Boltzmann machines, yield clusters of superior quality to those obtained with the Louvain algorithm.

A Novel Mutation-based Differential Evolution Algorithm for Solving Real-World Optimization Problems

In today's environment, evolutionary algorithms play a key role in solving optimization problems in mathematical models and applications. This article introduces a multi-objective differential evolution algorithm that extends the single-objective differential evolution (DE) algorithm to solve optimization problems in mathematical models and applications. Many existing algorithms face issues with diversity loss and convergence rate. To address these problems, this article proposes a novel mutation operator called ubiquitination mutation for DE, which has been added to the DE method. The proposed approach was tested on three real-world optimization problems: the next release problem, the multiline distance minimization problem, and data clustering. Results indicate that the proposed mutation operator outperformed state-of-the-art algorithms. In addition, the proposed approach provided better solutions in both single- and multi-objective platforms for various real-world problems.

Heuristic task scheduling on heterogeneous UAVs: A combinatorial optimization approach

A fleet of unmanned aerial vehicles (UAVs) provide a new and unique type of distributed computing paradigm and platform. This is a distributed computing environment with mobile servers, where a server (i.e., a UAV) moves around to process tasks. Task scheduling for UAVs has several unique characteristics, such as heterogeneity, mobility, and locality. UAVs are heterogeneous in the sense that they have different initial positions, flight speeds, and execution times. While task assignment and flight planning have been studied extensively, there has been little research of task scheduling on heterogeneous UAVs within the framework of combinatorial optimization, i.e., heuristic algorithms for NP-hard problems and their performance evaluation when compared with optimal solutions. In this paper, we take a combinatorial optimization approach to addressing the issues in task scheduling for heterogeneous UAVs. The main contributions are summarized as follows. We define eight combinatorial optimization problems, i.e., four time-centric problems including the completion time minimization problem, the total time minimization problem, the finished tasks maximization with time constraint problem, the reward maximization with time constraint problem; and four distance-centric problems including the longest distance minimization problem, the total distance minimization problem, the finished tasks maximization with distance constraint problem, the reward maximization with distance constraint problem. We prove that all these problems are NP-hard. We develop two efficient and effective heuristic algorithmic frameworks to solve our problems, one for minimization problems and one for maximization problems. We derive lower/upper bounds for the optimal solutions. We evaluate the performance of our heuristic algorithms by comparing their solutions with optimal solutions and show that they are able to produce near-optimal solutions. To the best of the author’s knowledge, this is the first paper which studies task scheduling on heterogeneous UAVs using a combinatorial optimization approach.

Adaptive goal-oriented data sampling in Data-Driven Computational Mechanics

Data-Driven (DD) computing is an emerging field of Computational Mechanics, motivated by recent technological advances in experimental measurements, the development of highly predictive computational models, advances in data storage and data processing, which enable the transition from a material data-scarce to a material data-rich era. The predictive capability of DD simulations is contingent on the quality of the material data set, i.e. its ability to closely sample all the strain–stress states in the phase space of a given mechanical problem. In this study, we develop a methodology for increasing the quality of an existing material data set through iterative expansions. Leveraging the formulation of the problems treated with the DD paradigm as distance minimization problems, we identify regions in phase space with poor data coverage, and target them with additional experiments or lower-scale simulations. The DD solution informs the additional experiments so that they can provide better coverage of the phase space of a given application.We first illustrate the convergence properties of the approach through a DD finite element simulation of a linear elastic cylinder under triaxial compression. The same numerical experiment is then performed on a specimen of Hostun sand, a material with complex history-dependent behavior. Data sampling is performed with Level-Set Discrete Element Method (LS-DEM) calculations of unit cells representative of this granular material, subjected to loading paths determined by the proposed method. It is shown that this adaptive expansion of the data set, tailored for a particular application, leads to convergent and accurate DD predictions, without the computational cost of using large databases with potentially redundant or low-quality data.

Distance minimizing based data‐driven computational method for the finite deformation of hyperelastic materials

AbstractThe distance minimizing based data‐driven solvers are developed for the finite deformation analysis of three‐dimensional (3D) compressible and nearly incompressible hyperelastic materials in this work. The data‐driven solvers bypass the construction of a constitutive equation for the hyperelastic materials by considering a dataset of Green‐Lagrange strain‐second Piola–Kirchhoff stress pairs. They recast the boundary‐value problems into the distance minimization problems with basic kinematical and mechanical constraints. Moreover, the deviatoric/volumetric split of stress and the additional incompressible constraint are further introduced into the solver for the nearly incompressible hyperelastic materials. Several representative three‐dimensional examples are presented and the results demonstrate the good capability and robustness of the proposed data‐driven solvers.

OADC: An Obstacle-Avoidance Data Collection Scheme Using Multiple Unmanned Aerial Vehicles

Unmanned aerial vehicles (UAVs) are used widely for data collection in wireless sensor networks (WSNs). UAVs visit the sensors to collect the data. UAV-aided data collection is a challenging problem because different paths of a UAV, i.e., visiting orders of sensors, affect energy consumption and data delivery times. The problem becomes more difficult when there are obstacles in the path of the UAV. Thus, the UAV needs to take a detour to avoid them, resulting in different travel distances and times. Therefore, this study formulated the obstacle-aware path planning problem of UAVs, i.e., the obstacle-constrained distance minimization (OCDM) problem, as an integer linear programming problem (ILP) to minimize the total traveling distances of all UAVs while considering the UAVs’ flight time constraints. First, a possible detour-points-selection algorithm called vector rotation-angle-based obstacle avoidance (VRAOA) is proposed to find the detour points around each obstacle in the environment. Then, a genetic algorithm with VRAOA (GA w/VRAOA)is developed to find the trajectories of the UAVs, using the VRAOA and Dijkstra algorithm to find a detour path if there is an obstacle between any two sensors. Finally, simulations were performed for algorithm variants, where GA w/VRAOA outperformed others.

Energy minimizing order picker forklift routing problem

The material handling systems used in warehouses involve important operations such as the usage of order picker forklifts. These order picker forklifts provide efficient utilization of the storage space by their ability in moving in narrow aisles and picking items from high level racks. Routing the order picker forklifts to pick ordered items belongs to the operational decision level and is done in high frequency. Therefore, finding an energy-efficient route for an order picker forklift can yield significant savings in the energy consumption in warehouses and the resulting CO2 emission. In this paper, we introduce and study the energy minimizing order picker forklift routing problem (EMFRP) which aims to find an energy-efficient route for an order picker forklift to pick a given list of items. To our knowledge, this is the first study that considers the order picker forklifts in the context of the order picking problem. We calculate the forklift’s energy consumption in both horizontal and vertical moves considering the effects of friction forces, the acceleration and deceleration of the forklift, and its load. A mixed integer programming formulation and a dynamic programming approach are developed to solve small size instances of the EMFRP exactly. To solve larger instances, we provide tour construction and tour improvement heuristics and integrate them into a single solution approach. Computational results show that the proposed heuristic approach finds high quality solutions. Moreover, it is observed that significant energy savings can be achieved by solving the EMFRP instead of the classical distance minimization problem.

A Novel Multiobjective Fireworks Algorithm and Its Applications to Imbalanced Distance Minimization Problems

Recently, multimodal multiobjective optimization problems (MMOPs) have received increasing attention. Their goal is to find a Pareto front and as many equivalent Pareto optimal solutions as possible. Although some evolutionary algorithms for them have been proposed, they mainly focus on the convergence rate in the decision space while ignoring solutions diversity. In this paper, we propose a new multiobjective fireworks algorithm for them, which is able to balance exploitation and exploration in the decision space. We first extend a latest single-objective fireworks algorithm to handle MMOPs. Then we make improvements by incorporating an adaptive strategy and special archive guidance into it, where special archives are established for each firework, and two strategies (i.e., explosion and random strategies) are adaptively selected to update the positions of sparks generated by fireworks with the guidance of special archives. Finally, we compare the proposed algorithm with eight state-of-the-art multimodal multiobjective algorithms on all 22 MMOPs from CEC2019 and several imbalanced distance minimization problems. Experimental results show that the proposed algorithm is superior to compared algorithms in solving them. Also, its runtime is less than its peers'.

Dynamic Virtual Topology Aided Networking and Routing for Aeronautical Ad-Hoc Networks

Aeronautical Ad-hoc Networks (AANETs) have been proposed as the promising complement to terrestrial networks for promoting the global interconnection to provide in-flight network service, emergency communication, vessel traffic service, etc. However, the large network scale of AANETs may induce severe synchronization overhead when the traditional topology-based networking algorithms are adopted. Moreover, the high-dynamic topology and changeable flight routes make the existing position-based routing algorithms suffer loop routing and forwarding failure. Motivated by these problems, this paper aims at developing efficient and low-cost networking and routing algorithms relying on the concept of dynamic virtual topology which organizes the disordered topology of AANETs into a structural and simplified one. The basic idea is that each connected aircraft is assigned with a unique and sequentially increased Virtual Identifier (VID) and thus all the connected aircrafts are organized into a virtual cluster consisting of one trunk and several branches. An event-driven synchronization mechanism is leveraged for maintaining the virtual topology as well as relieving the communication burden imposed by periodical broadcasting. By jointly considering the geographic locations and the virtual locations of aircrafts, we formulate the routing problem in AANETs as a weighted distance minimization problem, and further propose a novel routing algorithm, namely Trunk-Branch Cooperation aided Routing (TBCR) algorithm. Specifically, TBCR employs the geographic greedy forwarding strategy for enhancing its flexibility and boosts the routing efficiency by adopting the loop-free virtual topology based local forwarding. For extending the networking and routing algorithms to the global range, a multi-domain routing solution is also provided. Extensive experimental results show that the proposed Virtual Topology based Networking (VTN) cooperated with TBCR can reduce at least 30% average end-to-end transmission delay in large-scale AANETs and provide more than 90% lower synchronization overhead than the existing solutions.

Robust distance metric optimization driven GEPSVM classifier for pattern classification

Proximal support vector machine via generalized eigenvalues (GEPSVM) is one of the most successful methods for classification problems. However, GEPSVM is vulnerable to outliers since it learns classifiers based on the squared L2-norm distance without a specific strategy to deal with the outliers. Motivated by existing studies that improve the robustness of GEPSVM via the L1-norm distance or not-squared L2-norm distance formulation, a novel GEPSVM formulation that minimizes the p-order of L2-norm distance is proposed, namely, L2,p-GEPSVM. This formulation weakens the negative effects of both light and heavy outliers in the data. An iterative algorithm is designed to solve the general L2,p-norm distance minimization problems and rigorously prove its convergence. In addition, we adjust the parameters of L2,p-GEPSVM to balance the accuracy and training time. This is especially useful for larger datasets. Extensive results indicate that the L2,p-GEPSVM improves the classification performance and robustness in various experimental settings.

Many-Objective Evolutionary Algorithm based on Dominance Degree

For many-objective optimization problems, the comparability of non-dominated solutions is always an essential and fundamental issue. Due to the inefficiency of Pareto dominance for many-objective optimization problems, various improved dominance relations have been proposed to enhance the evolutionary pressure. However, these variants have one thing in common that they treat each solution in a static manner, and the relations between any two solutions are just defined as a kind of static spatial adjacencies, resulting in the unquantifiable comparability. Different from them, this paper proposes a dominance degree metric, which treats solutions as different stages of a dynamic motion process. The dynamic motion process represents the continuous changes of the degree of one solution from Pareto dominating others to being Pareto dominated by others. Based on the dominance degree, this paper proposes a Many-Objective Evolutionary Algorithm based on Dominance Degree, in which the mating selection and environmental update strategies are redesigned accordingly. The proposed method is comprehensively tested with several state-of-the-art optimizers on two popular test suites and practical multi-point distance minimization problems. Experimental results demonstrate its effectiveness and superiority over other optimizers in terms of the convergence, diversity and spread.

Information-Utilization-Method-Assisted Multimodal Multiobjective Optimization and Application to Credit Card Fraud Detection

Different from multiobjective optimization problems (MOPs), multimodal MOPs (MMOPs) focus on both decision and objective spaces rather than only objective one. Thus, finding a good Pareto front approximation and finding the maximal number of equivalent Pareto optimal solutions for each objective vector in the Pareto front are two core tasks for them. Although some multimodal multiobjective evolutionary algorithms have been proposed to handle them, they can quickly converge to the easy-to-find equivalent Pareto optimal solutions, thereby losing their ability to improve solution diversity in decision space and performance in objective space. To address the above issues, this work proposes a new information utilization method. Its core idea is to randomly extract a certain amount of decision variable information from the current optimal solutions to construct an information vector, which is, in turn, used to assist the generation of elite solutions. The proposed method can assist any available intelligent optimizers to improve their performance in solving MMOPs. This is confirmed by experimental results obtained from solving 22 such problems from CEC2019 and 12 scalable imbalanced distance minimization problems through a number of optimizers. Finally, we apply the proposed method to credit card fraud detection problems to show its practical significance.

Robust Hybrid Beamforming in Millimeter Wave Systems With Closed-Form Least-Square Solutions

Robust hybrid beamforming is developed for millimeter wave multiple-input multiple-output (MIMO) systems. The channel state information (CSI) with correlated estimation errors is used for averaging the mutual information formulation. It is proved that the robust hybrid beamforming scheme can be solved via an Euclidean distance minimization problem as the design with the perfect CSI assumption. An alternating method is proposed to solve the hybrid processors with closed-form least-square solutions in each iteration. Simulation results show that the proposed beamforming scheme prevails existing hybrid beamforming designs.

CARIN

Recent studies have proposed to use the Channel State Information (CSI) of WiFi wireless channel for human gesture recognition. As an important application, CSI-based driver activity recognition in passenger vehicles has received increasing research attention. However, a serious limitation of almost all the existing WiFi-based recognition solutions is that they can only recognize the activity of a single person at a time, because the activities of other people (if performed at the same time) can interfere with the WiFi signals. In a sharp contrast, there can often be one or more passengers in any vehicles. In this paper, we propose CARIN, CSI-based driver Activity Recognition under the INterference of passengers. CARIN features a combination-based solution that profiles all the possible activity combinations of driver and (one or more) passengers in offline training and then performs recognition online. To attack possible combination explosion, we first leverage in-car pressure sensors to significantly reduce combinations, because there are only limited seating options in a passenger vehicle. We then formulate a distance minimization problem for fast runtime recognition. In addition, a period analysis methodology is designed based on the kNN classifier to recognize activities that have a sequence of body movements, like continuous head nodding due to driver fatigue. Our results in a real car with 3,000 real-world traces show that CARIN can achieve an overall F1 score of 90.9%, and outperforms the three state-of-the-art solutions by 32.2%.

Collaboration Improves the Capacity of Mobile Edge Computing

This article studies the capacity of edge caching systems. Capacity is analyzed from the perspective of node mobility, caching, content popularity, etc., neglecting the influence of edge node cooperation on system performance. However, cooperation among edge nodes has been shown to substantially improve the system performance at the expense of a cooperation cost. Therefore, we attempt to maximize the capacity of mobile edge computing (MEC) subject to a budget constraint on the cooperation cost. We first transform the capacity maximization problem into a transmission distance minimization problem; then, we explore the average transmission distance of each source-to-destination pair under the assumption that the locations of the edge nodes follow a Poisson point process (PPP). We find that both the average transmission distance and the cooperation cost are associated with a key parameter, i.e., the number of content copies. We use the Lagrangian multiplier method to calculate the optimal copy number and propose a file allocation algorithm to store these copies. Finally, we analyze the influence of various parameters on the system capacity. The numerical results verify the efficiency of our solution compared with classic works.

Multi-objective distance minimization problems – applications in technical systems

Abstract This article describes the Distance Minimisation Problem (DMP) from a metaheuristic optimisation point of view. The problem is motivated by real applications and can be used to test the performance of optimisation methods like Evolutionary Algorithms. After formally describing the problem and its extensions using different metrics or dynamics, we perform experiments with well-known metaheuristic methods to demonstrate the performance on various DMP instances. The results show that modern algorithms like NSGA-II and SMPSO can struggle with this kind of problem under certain conditions, especially when Manhattan distances are used. On the other hand, specialised methods like GRA lack diversity of solutions in some cases. This indicates that even modern and powerful metaheuristic algorithms need to be chosen with care and with the respective optimisation task in mind.

Iterative Signal Detection for Large-Scale GSM-MIMO Systems

Generalized spatial modulations (GSM) represent a novel multiple input multiple output (MIMO) scheme, which can be regarded as a compromise between spatial multiplexing MIMO and conventional spatial modulations, achieving both spectral efficiency and energy efficiency. Due to the high computational complexity of the maximum likelihood detector in large antenna settings and symbol constellations, in this correspondence paper we propose a lower complexity iterative suboptimal detector. The derived algorithm comprises a sequence of simple processing steps, namely, an unconstrained Euclidean distance minimization problem, an element-wise projection over the signal constellation, and a projection over the set of valid active antenna combinations. To deal with scenarios where the number of possible active antenna combinations is large, an alternative version of the algorithm, which adopts a simpler cardinality projection, is also presented. Simulation results show that, compared with other existing approaches, both versions of the proposed algorithm are effective in challenging underdetermined scenarios where the number of receiver antennas is lower than the number of transmitter antennas.

Multiline Distance Minimization: A Visualized Many-Objective Test Problem Suite

Studying the search behavior of evolutionary many-objective optimization is an important, but challenging issue. Existing studies rely mainly on the use of performance indicators which, however, not only encounter increasing difficulties with the number of objectives, but also fail to provide the visual information of the evolutionary search. In this paper, we propose a class of scalable test problems, called multiline distance minimization problem (ML-DMP), which are used to visually examine the behavior of many-objective search. Two key characteristics of the ML-DMP problem are: 1) its Pareto optimal solutions lie in a regular polygon in the 2-D decision space and 2) these solutions are similar (in the sense of Euclidean geometry) to their images in the high-dimensional objective space. This allows a straightforward understanding of the distribution of the objective vector set (e.g., its uniformity and coverage over the Pareto front) via observing the solution set in the 2-D decision space. Fifteen well-established algorithms have been investigated on three types of ten ML-DMP problem instances. Weakness has been revealed across classic multiobjective algorithms (such as Pareto-based, decomposition-based, and indicator-based algorithms) and even state-of-the-art algorithms designed especially for many-objective optimization. This, together with some interesting observations from the experimental studies, suggests that the proposed ML-DMP may also be used as a benchmark function to challenge the search ability of optimization algorithms.