Multi-objective Combinatorial Optimization Research Articles

Hierarchical clustering-based framework for a posteriori exploration of Pareto fronts: application on the bi-objective next release problem

IntroductionWhen solving multi-objective combinatorial optimization problems using a search algorithm without a priori information, the result is a Pareto front. Selecting a solution from it is a laborious task if the number of solutions to be analyzed is large. This task would benefit from a systematic approach that facilitates the analysis, comparison and selection of a solution or a group of solutions based on the preferences of the decision makers. In the last decade, the research and development of algorithms for solving multi-objective combinatorial optimization problems has been growing steadily. In contrast, efforts in the a posteriori exploration of non-dominated solutions are still scarce.MethodsThis paper proposes an abstract framework based on hierarchical clustering in order to facilitate decision makers to explore such a Pareto front in search of a solution or a group of solutions according to their preferences. An extension of that abstract framework aimed at addressing the bi-objective Next Release Problem is presented, together with a Dashboard that implements that extension. Based on this implementation, two studies are conducted. The first is a usability study performed with a small group of experts. The second is a performance analysis based on computation time consumed by the clustering algorithm.ResultsThe results of the initial empirical usability study are promising and indicate directions for future improvements. The experts were able to correctly use the dashboard and properly interpret the visualizations in a very short time. In the same direction, the results of the performance comparison highlight the advantage of the hierarchical clustering-based approach in terms of response time.DiscussionBased on these excellent results, the extension of the framework to new problems is planned, as well as the implementation of new validity tests with expert decision makers using real-world data.

A crowd cooperative defense model for mitigating DDoS attacks in Mobile Crowdsensing networks

Mobile Crowdsensing (MCS) is rapidly growing up while encountering severe security threats simultaneously. DDoS attacks tend to disrupt large-scale sensing tasks to the MCS and reduce the availability of MCS. However, the existing centralized defense technology has the problem of high cost and the existing research lacks the application of distributed cooperative characteristics of MCS. A crowd cooperative defense model for mitigating DDoS attacks in MCS is proposed based on these. Firstly, the crowdsensing networks are formally described. The cooperative mechanism of sensing nodes participating in overlapping sensing coalition is generalized, which breaks the independence between the distributed sensing nodes and enables the sensing nodes to cooperate against DDoS attacks. Then, the crowd cooperative defense problem is transformed into a multi-objective combinatorial optimization problem. A multi-objective discrete Harris Hawk optimization (MODHHO) algorithm is designed. The algorithm applies non-dominated sorting and crowding strategy to evaluate the advantages and disadvantages of each cooperative defense solution on the cooperative defense objectives. In addition, the global exploration, local exploitation, and besiege phases are used to continuously update the cooperative defense solutions, and finally obtains the global optimal cooperative defense solution after a certain number of iterations. The simulation results show that the proposed model can minimize the defense cost compared to non-cooperative and non-overlapping sensing coalition methods. Compared with centralized defense, the loss cost of the proposed model is reduced by 61.8%. In addition, the average throughput of the sensing network is increased by 35.5%, which enhances the availability of the sensing network.

Task Containerization and Container Placement Optimization for MEC: A Joint Communication and Computing Perspective

Containers are used by an increasing number of Internet service providers to deploy their applications in multi-access edge computing (MEC) systems. Although container-based virtualization technologies significantly increase application availability, they may suffer expensive communication overhead and resource use imbalances. However, so far there has been a scarcity of studies to conquer these difficulties. In this paper, we design a workflow-based mathematical model for applications built upon interdependent multitasking composition, formulate a multi-objective combinatorial optimization problem composed of two subproblems—graph partitioning and multi-choice vector bin packing, and propose several joint task-containerization-and -container-placement methods to reduce communication overhead and balance multi-type computing resource utilization. The performance superiority of the proposed algorithms is demonstrated by comparison with the state-of-the-art task and container scheduling schemes.

Multi-Objective Combinatorial Optimization Using the Cell Mapping Algorithm for Mobile Robots Trajectory Planning

The use of optimal control theory for motion planning is a challenging task. Cell mapping offers a way to formulate combinatorial optimization problems, allowing the inclusion of complex cost functions as well as multi-objective optimization problems. This paper presents a suboptimal solution for a trajectory planning problem in a workspace with obstacles, for a differential drive mobile robot. This method relies on the use of any linearization technique that allows the regularization of the combinatorial optimization problem. We explore some classical problems in optimal control, i.e., distance, control effort, and navigation time), as well as the multi-objective optimization problem (MOP). We also performed a comparison with two classical path planning algorithms, namely A∗ and RRT∗, to validate the proposed method when the multi-objective optimization problem includes distance in the cost function, achieving a compromise of less than 2% for the worst-case scenario for our case study.

Heuristics for Multi-Vehicle Routing Problem Considering Human-Robot Interactions

Autonomous mobile robots (AMRs) are being used extensively in civilian and military applications for applications such as underground mining, nuclear plant operations, planetary exploration, intelligence, surveillance and reconnaissance (ISR) missions and manned-unmanned teaming. We consider a multi-objective, multiple-vehicle routing problem in which teams of manned ground vehicles (MGVs) and AMRs are deployed respectively in a leader-follower framework to execute missions with differing requirements for MGVs and AMRs while considering human-robot interactions (HRI). HRI studies highlight the costs of managing a team of follower AMRs by a leader MGV. This paper aims to compute feasible visit sequences, replenishments, team compositions and number of MGV-AMR teams deployed such that the requirements for MGVs and AMRs for the missions are met and the routing, replenishment, HRI and team deployment costs are at minimum. The problem is first modeled as a a mixed-integer linear program (MILP) that can be solved to optimality by off-the-shelf commercial solvers for small-sized instances. For larger instances, a variable neighborhood search algorithm is offered to compute near optimal solutions and address the challenges that arise when solving the combinatorial multi-objective routing optimization problem. Finally, computational experiments that corroborate the effectiveness of the proposed algorithms are presented.

Effects of the Random Forests Hyper-Parameters in Surrogate Models for Multi-Objective Combinatorial Optimization: A Case Study using MOEA/D-RFTS

Surrogate models are techniques to approximate the objective functions of expensive optimization problems. Recently, Random Forests have been studied as a surrogate model technique for combinatorial optimization problems. Nonetheless, Random Forests contain several hyper-parameters that are used to control the prediction process. Despite their importance, research on the effects of these hyper-parameters is scarce. Therefore, this paper performs a systematic investigation of the effects of different combinations of values for the Random Forest hyper-parameters on the approximation of well-known multi-objective combinatorial benchmark problems. The results show that the number of samples to consider when building each tree and the minimum number of samples to be at the leaf node are the two most important hyper-parameters in this context.

Multi-objective combinatorial optimization analysis of the recycling of retired new energy electric vehicle power batteries in a sustainable dynamic reverse logistics network.

The recycling of retired new energy vehicle power batteries produces economic benefits and promotes the sustainable development of environment and society. However, few attentions have been paid to the design and optimization of sustainable reverse logistics network for the recycling of retired power batteries. To this end, we develop a six-level sustainable dynamic reverse logistics network model from the perspectives of economy, environment, and society. We solve the multi-objective combinatorial optimization model to explore the layout of the sustainable reverse logistics network for retired new energy vehicle power batteries recycling. A case study is implemented to verify the effectiveness of the proposed model. The results show that (a) the facility nodes near the front of the network fluctuate more by opening and closing; (b) the dynamic reverse logistics network is superior to its static counterpart; and (c) cooperation cost changes affect the transaction volume between third-party and cooperative enterprises and total network cost.

Walsh-based surrogate-assisted multi-objective combinatorial optimization: A fine-grained analysis for pseudo-boolean functions

The aim of this paper is to study surrogate-assisted algorithms for expensive multiobjective combinatorial optimization problems. Targeting pseudo-boolean domains, we provide a fine-grained analysis of an optimization framework using the Walsh basis as a core surrogate model. The considered framework uses decomposition in the objective space, and integrates three different components, namely, (i) an inner optimizer for searching promising solutions with respect to the so-constructed surrogate, (ii) a selection strategy to decide which solution is to be evaluated by the expensive objectives, and (iii) the strategy used to setup the Walsh order hyper-parameter. Based on extensive experiments using two benchmark problems, namely bi-objective NK-landscapes and unconstrained binary quadratic programming problems (UBQP), we conduct a comprehensive in-depth analysis of the combined effects of the considered components on search performance, and provide evidence on the effectiveness of the proposed search strategies. As a by-product, our work shed more light on the key challenges for designing a successful surrogate-assisted multi-objective combinatorial search process.

Determination of Weights for Multiobjective Combinatorial Optimization in Incident Management With an Evolutionary Algorithm

Determination of Weights for Multiobjective Combinatorial Optimization in Incident Management With an Evolutionary Algorithm

Combinatorial Multi-Objective Optimization of SFCL and SMES for the Low-Voltage Ride-Through Fulfillment of Solid-State Transformer

To figure out the low-voltage ride-through (LVRT) problem of a solid-state transformer (SST), this paper proposes a methodology that combinatorically optimizes a resistive superconducting fault current limiter (SFCL) and a superconducting magnetic energy storage (SMES) unit. The goal of minimizing the capacities of the resistive SFCL and the SMES while achieving the LVRT of the SST is designed, and a multi-objective Pareto optimization is carried out. Firstly, the modeling of a three-stage SST with a resistive SFCL and a SMES is presented through theoretical analysis, and the SST's fault transient characteristics are analyzed. Then, the optimization scheme based on the improved non-dominated sorting genetic algorithm-II (NSGA-II) is elaborated. The proposed approach is verified in a typical SST connecting a 10 kV power distribution network and a 380 V electricity grid. Using MATLAB/Simulink and RT-lab real-time simulation platform, different tests are done to check the rationality of the optimal solutions. The results reveal that a satisfying LVRT for the SST is guaranteed while minimizing the ratings of the SFCL and the SMES, and getting a proper reactive current injection. Consequently, the validity and suitableness of the proposed approach are well confirmed.

UAV path planning in presence of occlusions as noisy combinatorial multi-objective optimisation

UAV path planning in presence of occlusions as noisy combinatorial multi-objective optimisation

Multi-Controller Placement Optimization Using Naked Mole-Rat Algorithm over Software-Defined Networking Environment

Software Defined Networking (SDN) is the novel networking paradigm where decoupling of the control plane from the data plane has its inherent advantages. Controller Placement Problem (CPP) involves placing the optimal number of controllers at the appropriate locations while meeting prerequisites such as latency, load balancing, energy and computational time. To achieve scalability, deployment of multiple controllers on large-scale SDN is one of the key challenges. CPP can be addressed as a multi-objective combinatorial optimization problem whose solution is a trade-off between multiple optimization parameters. In this paper, a novel population-based meta-heuristic algorithm viz. Naked Mole-Rat (NMR) Algorithm has been proposed to optimize the location for controller placement based on Switch-Controller (SC), Controller-Controller (CC) latency while maintaining load balancing among the controllers. The ideas and mechanisms are illustrated using two publicly available standard topologies viz. Ernet and Savvis. The controller localization approach implemented with NMR algorithm has slightly a better result as compared with the Bat algorithm.

Fuel loading pattern optimization of ALLEGRO fast reactor using genetic algorithms

In this work the genetic algorithmic (GA) optimization technique is used to find the optimal fuel loading pattern in the experimental fast reactor ALLEGRO. The penalty function method is used to solve this multi-objective combinatorial optimization problem. To evaluate each loading pattern, an interface between the genetic algorithm code and the ERANOS 2.3 deterministic neutronic simulation code was developed. For the simulation of the fuel cycle in ERANOS, the diffusion approach and a 7-group energy structure are used to reduce the computational cost. An integer variable encoding scheme was defined to represent the fuel loading patterns. Two crossover operators, the partially mapped crossover (PMX) and the order crossover (OX), combined with the random mutation operator were implemented as an alternative to the classical operators used in GA. To evaluate the performance of the code the results are compared using two objective functions and two crossover operators. In the first case the operating cycle length is maximized by maximizing the k-eff value at the EOC by satisfying the constraints on the power peaking factor over the cycle, the excess reactivity at the BOC, and the linear heat generation rate constraints. In addition, a condition was imposed that there should be no more than two contiguous positions in the pattern to preserve the power distribution uniformity and to avoid high power peaking factors. The code works very well, and a good solution was found in a reasonable computation time. The best solution corresponds to the PMX operator, and the running time is twice as short compared to the OX operator. In the second case study, a power distribution flatness term is included in the objective function. In this case, a more uniform radial power distribution is obtained but associated with a decrease in cycle length due to the penalty of the flatness term.

Hierarchical Multiobjective Heuristic for PCB Assembly Optimization in a Beam-Head Surface Mounter.

This article proposes a hierarchical multiobjective heuristic (HMOH) to optimize printed-circuit board assembly (PCBA) in a single beam-head surface mounter. The beam-head surface mounter is the core facility in a high-mix and low-volume PCBA line. However, as a large-scale, complex, and multiobjective combinatorial optimization problem, the PCBA optimization of the beam-head surface mounter is still a challenge. This article provides a framework for optimizing all the interrelated objectives, which has not been achieved in the existing studies. A novel decomposition strategy is applied. This helps to closely model the real-world problem as the head task assignment problem (HTAP) and the pickup-and-place sequencing problem (PAPSP). These two models consider all the factors affecting the assembly time, including the number of pickup-and-place (PAP) cycles, nozzle changes, simultaneous pickups, and the PAP distances. Specifically, HTAP consists of the nozzle assignment and component allocation, while PAPSP comprises place allocation, feeder set assignment, and place sequencing problems. Adhering strictly to the lexicographic method, the HMOH solves these subproblems in a descending order of importance of their involved objectives. Exploiting the expert knowledge, each subproblem is solved by an elaborately designed heuristic. Finally, the proposed HMOH realizes the complete and optimal PCBA decision making in real time. Using industrial PCB datasets, the superiority of HMOH is elucidated through comparison with the built-in optimizer of the widely used Samsung SM482.

Generation of optimal (de)centralized layouts for urban drainage systems: A graph-theory-based combinatorial multi-objective optimization framework

• A novel graph-theory-based framework for sewer layout creation is developed. • A generic scheme for decentralized layouts in flat and steep terrains is suggested. • Three layout objective functions are put forward for discarding the feasible layouts. • Layout decentralization could largely reduce the construction costs of the final network. • Layout decentralization could largely improve the resilience response of the network. The suitability and effectiveness of decentralized paradigms in the field of underground conveyance drainage infrastructures for coping with the current and upcoming sustainability and resilience demands has been documented in recent research. However, a generic and holistic framework that can be quickly put in practice is lacking. To this end, this study proposes a scheme for creating and optimizing decentralization scenarios in terms of sewer layout configurations for both flat and steep terrains with the aid of a combinatorial graph-theory-based optimization. Additionally, a novel and generalized formula is derived to determine the degree of centralization coupled with three layout objective functions, thereby eliminating several feasible layout solutions. The results indicate that cherry picking an appropriate sewer structure (topological layout) at the planning stage can largely influence the design construction costs (reduction up to 49% for steep terrain and 25% for flat terrain), as well as the resilience response of the final network. Therefore, as a general rule of thumb, breaking down the centralized network into a decentralized one can reduce construction cost and improve resilience.

What if we increase the number of objectives? Theoretical and empirical implications for many-objective combinatorial optimization

The difficulty of solving a multi-objective optimization problem is impacted by the number of objectives to be optimized. The presence of many objectives typically introduces a number of challenges that affect the choice/design of optimization algorithms. This paper investigates the drivers of these challenges from two angles: (i) the influence of the number of objectives on problem characteristics and (ii) the practical behavior of commonly used procedures and algorithms for coping with many objectives. In addition to reviewing various drivers, the paper makes theoretical contributions by quantifying some drivers and/or verifying these drivers empirically by carrying out experiments on multi-objective combinatorial optimization problems (multi-objective NK-landscapes). We then make use of our theoretical and empirical findings to derive practical recommendations to support algorithm design. Finally, we discuss remaining theoretical gaps and opportunities for future research in the area of multi- and many-objective optimization.

A diversity preservation method for expensive multi-objective combinatorial optimization problems using Novel-First Tabu Search and MOEA/D

Expensive multi-objective combinatorial optimization problems have constraints in the number of objective function evaluations due to time, financial, or resource restrictions. As most combinatorial problems, they are subject to a high number of duplicated solutions. Given the fact that expensive environments limit the number of objective function evaluations, the existence of duplicated solutions heavily impacts the optimization process due to poor diversity and low convergence speed. This paper proposes the Novel-First Tabu Search, a greedy-strategy mechanism that uses Knowledge-Assisted Local Search methods to preserve the population diversity and increase the exploration and exploitation ability of MOEA/D. Experiments are conducted on constrained, unconstrained, multimodal, deceptive, linear, convex, and non-convex Pareto Front multi-objective combinatorial optimization benchmark problems. This paper also conducts an experiment on the real-world, expensive problem of Well Placement Optimization using a benchmark case based on the Namorado oil field, located in the Campos Basin, Brazil. The experimental results and performance comparison with state-of-the-art algorithms demonstrate that the proposed design significantly preserves diversity and increases convergence without violating the constraint in the number of objective function evaluations.

Offline optimization of sensor configuration and integration architecture for efficient cooperative navigation

Multi-agent cooperative navigation can improve navigation performance by taking advantage of inter-agent communication and relative-sensing capabilities. For Multi-Agent Systems (MAS), the achievable navigation performance, communication cost, computation complexity, and sensor cost are directly influenced by the sensor configuration and the integration architecture. To reduce hardware cost and computation/communication load, this paper proposes a feasible method to realize the offline design of sensor configuration and integration architecture for cooperative navigation. Specifically, this goal is achieved by solving a multi-objective combinatorial optimization problem, where the sensor configuration and integration architecture are considered as the optimization variables; the navigation performance requirement is the constraint; and the communication cost, computation complexity, and sensor cost are considered as the optimization objectives. This optimization problem is solved by a Multi-Objective Simulated Annealing (MOSA) algorithm. Using a MAS with three unmanned aerial vehicles as an example, simulations are carried out to validate the proposed method, and the results show its feasibility and effectiveness. The Pareto solutions reveal the characteristics and applicability of different integration architectures in different scenarios, which is meaningful for practical applications.

Biobjective optimization problems on matroids with binary costs

Like most multiobjective combinatorial optimization problems, biobjective optimization problems on matroids are in general intractable and their corresponding decision problems are in general NP-hard. In this paper, we consider biobjective optimization problems on matroids where one of the objective functions is restricted to binary cost coefficients. We show that in this case the problem has a connected efficient set with respect to a natural definition of a neighbourhood structure and hence can be solved efficiently using a neighbourhood search approach. This is, to the best of our knowledge, the first non-trivial problem on matroids where connectedness of the efficient set can be established. The theoretical results are validated by numerical experiments with biobjective minimum spanning tree problems (graphic matroids) and with biobjective knapsack problems with a cardinality constraint (uniform matroids). In the context of the minimum spanning tree problem, colouring all edges with cost 0 green and all edges with cost 1 red leads to an equivalent problem where we want to simultaneously minimize one general objective and the number of red edges (which defines the second objective) in a Pareto sense.

Hybrid Metaheuristics for QoS-Aware Service Composition: A Systematic Mapping Study

With the advent of Service-Oriented Architecture (SOA), services can be registered, invoked, and combined by their identical Quality of Services (QoS) attributes to create a new value-added application that fulfils user requirements. Efficient QoS-aware service composition has been a challenging task in cloud computing. This challenge becomes more formidable in emerging resource-constrained computing paradigms, such as the Internet of Things and Fog. Service composition has regarded as a multi-objective combinatorial optimization problem that falls in the category of NP-hard. Historically, the proliferation of services added to problem complexity and navigated solutions from exact (none-heuristics) approaches to near-optimal heuristics and metaheuristics. Although metaheuristics have fulfilled some expectations, the quest for finding a high-quality, near-optimal solution has led researchers to devise hybrid methods. As a result, research on service composition shifts towards the hybridization of metaheuristics. Hybrid metaheuristics have been promising efforts to transcend the boundaries of metaheuristics by leveraging the strength of complementary methods to overcome base algorithm shortcomings. Despite the significance and frontier position of hybrid metaheuristics, to the best of our knowledge, there is no systematic research and survey in this field with a particular focus on strategies to hybridize traditional metaheuristics. This study’s core contribution is to infer a framework for hybridization strategies by conducting a mapping study that analyses 71 papers between 2008 and 2020. Moreover, it provides a panoramic view of hybrid methods and their experiment setting in respect to the problem domain as the main outcome of this mapping study. Finally, research trends, directions and challenges are discussed to benefit future endeavours.