Multi-objective Combinatorial Optimization Problems Research Articles

Balanced task allocation and motion planning of a multi-robot system under fuzzy time windows

PurposeA fleet of mobile robots has been effectively used in various application domains such as industrial plant inspection. This paper proposes a solution to the combined problem of task allocation and motion planning problem for a fleet of mobile robots which are requested to operate in an intelligent industry. More specifically, the robots are requested to serve a set of inspection points within given service time windows. In comparison with the conventional time windows, our problem considers fuzzy time windows to express the decision maker’s satisfaction for visiting an inspection point.Design/methodology/approachThe paper develops a unified approach to the combined problem of task allocation and motion planning for a fleet of mobile robots with three objectives: (a) minimizing the total travel cost considering all robots and tasks, (b) balancing fairly the workloads among robots and (c) maximizing the satisfaction grade of the decision maker for receiving the services. The optimization problem is solved by using a novel combination of a Genetic Algorithm with pareto solutions and fuzzy set theory.FindingsThe computational results illustrate the efficiency and effectiveness of the proposed approach. The experimental analysis leverages the potential for using fuzzy time windows to reflect real situations and respond to demanding situations.Originality/valueThis paper provides trade-off solutions to a realistic combinatorial multi-objective optimization problem considering concurrently the motion and path planning problem for a fleet of mobile robots with fuzzy time windows.

New techniques to improve neighborhood exploration in pareto local search

Pareto Local Search (PLS) is an extension of local search to multiobjective combinatorial optimization problems (MCOPs). It is widely used as a building block in many multiobjective metaheuristics. However, it suffers from poor anytime behavior and long convergence time. In this paper, we focus on improving the neighborhood exploration mechanism to accelerate PLS. In total, we propose three new search strategies, namely, Promising List, Don’t Look Bits and Continuing Search and implement them on the multiobjective Traveling Salesman Problem (mTSP) and the multiobjective Unconstrained Binary Quadratic Programming (mUBQP) problem. In Promising List, features of problem structure are utilized to guide the local search. In Don’t Look Bits, neighborhood moves that are less promising to produce improving solutions are skipped. In Continuing Search, the agent will start from where previous neighborhood exploration stops to avoid repetitive neighborhood moves. The experimental results verify the effectiveness of the three techniques both individually and collaboratively on most of the test instances. Besides, one proposed PLS variant outperforms two state-of-the-art PLS-based algorithms.

A deep reinforcement learning algorithm framework for solving multi-objective traveling salesman problem based on feature transformation

As a special type of multi-objective combinatorial optimization problems (MOCOPs), the multi-objective traveling salesman problem (MOTSP) plays an important role in practical fields such as transportation and robot control. However, due to the complexity of its solution space and the conflicts between different objectives, it is difficult to obtain satisfactory solutions in a short time. This paper proposes an end-to-end algorithm framework for solving MOTSP based on deep reinforcement learning (DRL). By decomposing strategies, solving MOTSP is transformed into solving multiple single-objective optimization subproblems. Through linear transformation, the features of the MOTSP are combined with the weights of the objective function. Subsequently, a modified graph pointer network (GPN) model is used to solve the decomposed subproblems. Compared with the previous DRL model, the proposed algorithm can solve all the subproblems using only one model without adding weight information as input features. Furthermore, our algorithm can output a corresponding solution for each weight, which increases the diversity of solutions. In order to verify the performance of our proposed algorithm, it is compared with four classical evolutionary algorithms and two DRL algorithms on several MOTSP instances. The comparison shows that our proposed algorithm outperforms the compared algorithms both in terms of training time and the quality of the resulting solutions.

Improving Pareto Local Search Using Cooperative Parallelism Strategies for Multiobjective Combinatorial Optimization.

Pareto local search (PLS) is a natural extension of local search for multiobjective combinatorial optimization problems (MCOPs). In our previous work, we improved the anytime performance of PLS using parallel computing techniques and proposed a parallel PLS based on decomposition (PPLS/D). In PPLS/D, the solution space is searched by multiple independent parallel processes simultaneously. This article further improves PPLS/D by introducing two new cooperative process techniques, namely, a cooperative search mechanism and a cooperative subregion-adjusting strategy. In the cooperative search mechanism, the parallel processes share high-quality solutions with each other during the search according to a distributed topology. In the proposed subregion-adjusting strategy, a master process collects useful information from all processes during the search to approximate the Pareto front (PF) and redivide the subregions evenly. In the experimental studies, three well-known NP-hard MCOPs with up to six objectives were selected as test problems. The experimental results on the Tianhe-2 supercomputer verified the effectiveness of the proposed techniques.

Generating Diagnostic and Actionable Explanations for Fair Graph Neural Networks

A plethora of fair graph neural networks (GNNs) have been proposed to promote algorithmic fairness for high-stake real-life contexts. Meanwhile, explainability is generally proposed to help machine learning practitioners debug models by providing human-understandable explanations. However, seldom work on explainability is made to generate explanations for fairness diagnosis in GNNs. From the explainability perspective, this paper explores the problem of what subgraph patterns cause the biased behavior of GNNs, and what actions could practitioners take to rectify the bias? By answering the two questions, this paper aims to produce compact, diagnostic, and actionable explanations that are responsible for discriminatory behavior. Specifically, we formulate the problem of generating diagnostic and actionable explanations as a multi-objective combinatorial optimization problem. To solve the problem, a dedicated multi-objective evolutionary algorithm is presented to ensure GNNs' explainability and fairness in one go. In particular, an influenced nodes-based gradient approximation is developed to boost the computation efficiency of the evolutionary algorithm. We provide a theoretical analysis to illustrate the effectiveness of the proposed framework. Extensive experiments have been conducted to demonstrate the superiority of the proposed method in terms of classification performance, fairness, and interpretability.

Multiobjective Combinatorial Optimization Using a Single Deep Reinforcement Learning Model.

This article proposes utilizing a single deep reinforcement learning model to solve combinatorial multiobjective optimization problems. We use the well-known multiobjective traveling salesman problem (MOTSP) as an example. Our proposed method employs an encoder-decoder framework to learn the mapping from the MOTSP instance to its Pareto-optimal set. Specifically, it leverages a novel routing encoder to extract information for both the entire multiobjective aspect and every individual objective from the MOTSP instance. The global embeddings and each objective's embeddings are adaptively aggregated via a routing network to form the subproblems' embedding that can well represent the MOTSP features. Using a modified context embedding, the subproblems' embeddings are fed into a decoder to produce a set of approximate Pareto-optimal solutions in parallel. Additionally, we develop a Top-k baseline to enable more efficient data utilization and lightweight training for our proposed method. We compare our method with heuristic-based and learning-based ones on various types of MOTSP instances, and the experimental results show that our method can solve MOTSP instances in real-time and outperform the other algorithms, especially on large-scale problem instances.

Decomposition with adaptive composite norm for evolutionary multi-objective combinatorial optimization

The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multi-objective problem into a series of single-objective subproblems for collaborative optimization. The weighted sum (WS) method and the Tchebycheff (TCH) method are the two most popular scalarization methods. They have pros and cons in solving multi-objective combinatorial optimization problems (MOCOPs) the WS method allows MOEA/D to converge faster than the TCH method; the WS-based MOEA/D cannot obtain unsupported non-dominated vectors, while the TCH-based one can overcome this shortcoming. This inspired us to use the WS method to drive the population towards the Pareto front and then switch to the TCH method to maintain a more diverse population. To better balance convergence and diversity, we propose a new scalarization strategy called adaptive composite norm (ACN). The ACN strategy can combine the WS and the TCH with dynamic weighting. The experiments consider 16 instances including 4 MOCOPs and run on the PlatEMO. Results reveal that MOEA/D-ACN can rank first and significantly outperform the other evolutionary multi-objective combinatorial optimization algorithms on almost all instances.

Role of combinatorial optimization problems for the efficient decision making of a company- Case study-

All company seeks to improve their performance through achieving several objectives to stay in the labor market and increase competitiveness. The problem lies in the fact that it often relies on traditional methods for efficient decision-making, causing a waste of time and effort. The paper aims to find the best car service stations among several proposed stations by the Naftal Company, which seeks to achieve the two most important objectives; maximizing lubricants and tires revenues, and maximizing fuel and LPG revenues for the year 2019. The new applied case study was done with the help of the binary multi-objective knapsack problem, which is considered one of the most important problems in multi-objective combinatorial optimization problems. The problem was solved by the epsilon constraint method using MATLAB and CPLEX software. The study results confirmed that the proposed efficient solution set (Pareto optimal solutions) provides the decision maker with a comprehensive view of how to make their decision in a scientific, thoughtful, logical, and convincing manner that suits his situation and puts him at ease, away from trial and error or relying on self-experience.

Flexible Offloading and Task Scheduling for IoT Applications in Dynamic Multi-Access Edge Computing Environments

Nowadays, multi-access edge computing (MEC) has been widely recognized as a promising technology that can support a wide range of new applications for the Internet of Things (IoT). In dynamic MEC networks, the heterogeneous computation capacities of the edge servers and the diversified requirements of the IoT applications are both asymmetric, where and when to offload and schedule the time-dependent tasks of IoT applications remains a challenge. In this paper, we propose a flexible offloading and task scheduling scheme (FLOATS) to adaptively optimize the computation of offloading decisions and scheduling priority sequences for time-dependent tasks in dynamic networks. We model the dynamic optimization problem as a multi-objective combinatorial optimization problem in an infinite time horizon, which is intractable to solve. To address this, a rolling-horizon-based optimization mechanism is designed to decompose the dynamic optimization problem into a series of static sub-problems. A genetic algorithm (GA)-based computation offloading and task scheduling algorithm is proposed for each static sub-problem. This algorithm encodes feasible solutions into two-layer chromosomes, and the optimal solution can be obtained through chromosome selection, crossover and mutation operations. The simulation results demonstrate that the proposed scheme can effectively reduce network costs in comparison to other reference schemes.

Third-party software library migration at the method-level using multi-objective evolutionary search

Software developers commonly use third-party software libraries to reduce implementation efforts and mitigate errors in their source code while building high-quality and reliable software. To support software evolution, newer libraries are released periodically with added features, improvements in performance as well as critical updates such as bug fixes. Hence, older, existing (source) libraries need to be replaced with their newer, updated (target) counterparts, in a process known as library migration. Typically, library migration is a time-consuming, manual, and error-prone process that requires developers to analyze the source and target library code and its documentation. Specifically, developers examine Application Programming Interface (API) implementations and documentation to replace each source API with a target API without modifying the underlying software functionality. While recent works have used various techniques to recommend suitable target library replacements, these approaches do not generalize well, e.g., when a source library method needs to be replaced by one or more target library APIs or methods. To address this limitation, we propose the use of multi-objective evolutionary algorithms to identify suitable method replacements during library migration. In particular, we formulate library migration at the method-level as a multi-objective combinatorial optimization problem and examine the performance of 7 multi-objective evolutionary algorithms: UNSGAIII, RNSGAII, AGEMOEA, SMSEMOA, NSGAII, IBEA and MOEAD. We use method signature and documentation similarity, and co-occurrence probability to accurately recommend one or more target library methods. We evaluate our approach by conducting an empirical study on 9 popular Java library migrations mined from 57,447 open-source projects on GitHub. Our results demonstrate that UNSGAIII, RNSGAII, AGEMOEA, SMSEMOA, NSGAII, IBEA and MOEAD achieve 90%, 89%, 94%, 90%, 91%, 94%, and 71% precision on average, and 83%, 23%, 58%, 63%, 58%, 60% and 17% average recall respectively. In the interest of reproducibility, we make all code and results publicly available at: http://bit.ly/MOO-api-migration.

Deep reinforcement learning for multi-objective combinatorial optimization: A case study on multi-objective traveling salesman problem

Multi-objective combinatorial optimization problems (MOCOPs) widely exist in real applications, and most of them are computationally difficult or NP-hard. How to solve MOCOPs efficiently has been a challenging issue. The heuristic algorithms have achieved good results on MOCOPs, while they require careful hand-crafted heuristics and iterative computing for the solutions. Recently, deep reinforcement learning (DRL) has been employed to solve combinatorial optimization problems, and many DRL-based algorithms have been proposed with promising results. However, it is difficult for these existing algorithms to obtain diverse solutions efficiently for MOCOPs. In this paper, we propose an algorithm named MOMDAM to solve MOCOPs. In MOMDAM, the attention model (AM) is used and can simply modify the encoder to facilitate the construction of solutions with any weight vector, as well as the multiple decoders (MD) are employed to obtain diverse policies to further improve the diversity and convergence of the solutions. Experimental results on the bi-objective traveling salesman problem show that, MOMDAM significantly outperforms some state-of-the-art algorithms in terms of solution quality and running time.

A hybrid multi-start metaheuristic scheduler for astronomical observations

In this paper, we investigate Astronomical Observations Scheduling which is a type of Multi-Objective Combinatorial Optimization Problem, and detail its specific challenges and requirements and propose the Hybrid Accumulative Planner (HAP), a hybrid multi-start metaheuristic scheduler able to adapt to the different variations and demands of the problem. To illustrate the capabilities of the proposal in a real-world scenario, HAP is tested on the Atmospheric Remote-sensing Infrared Exoplanet Large-survey (Ariel) mission of the European Space Agency (ESA), and compared with other studies on this subject including an Evolutionary Algorithm (EA) approach. The results show that the proposal outperforms the other methods in the evaluation and achieves better scientific goals than its peers. The consistency of HAP in obtaining better results on the available datasets for Ariel, with various sizes and constraints, demonstrates its competence in scalability and adaptability to different conditions of the problem.

Fuel loading pattern optimization of ALLEGRO fast reactor using the tabu search metaheuristic technique

In this work an improved tabu search (TS) 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. The objective function and constrains are computed via an interface between the developed optimizer and the ERANOS 2.3 deterministic code. To reduce the running time, the operating cycle simulation is carried out using the diffusion approximation and a 7-group neutron energy structure. The proposed objective function maximizes the k-eff value at the end of cycle, satisfying the maximum power factor, the excess hot reactivity, and the linear heat generation rate constraints. A novel procedure developed in ERANOS to perform fuel assembly swaps for neighbor search is presented. The algorithm performed as expected throughout the iterative process and, unlike other metaheuristics based on local search, did not get stuck in local optima, which is a well-known advantage of tabu search technique.

Harris Hawks Optimization-Based Clustering Algorithm for Vehicular Ad-Hoc Networks

Vehicular ad-hoc network (VANET) is highly dynamic due to the high speed and sparse distribution of vehicles on the road. This creates major challenges (e.g., network fragmentation, packet routing) for the researchers to enable robust, reliable, and scalable communication, especially in a highly dense network. Clustering in VANET is one of the remedies to address the scalability issue. However, it is observed in the literature, that existing clustering techniques produce a high number of clusters for the vehicular environment. Consequently, it increases the consumption of scarce resources in a wireless network. Furthermore, it also increases the communication overhead as well as the number of hops for data routing. As a result communication latency also increases and the reliability of communication protocol decreases. So it is highly desirable to find out the optimal clusters for a given vehicular environment. As finding optimal clusters is a multi-objective combinatorial optimization problem, therefore by employing nature-inspired meta-heuristic algorithms we can optimize the multi-objective problem. To this end, we proposed a novel clustering algorithm based on the Harris Hawks Optimization (HHO) algorithm for VANET (HHOCNET). HHO algorithm is a nature-inspired meta-heuristic algorithm inspired by the foraging maneuver of hawks called surprise pounce. The proposed framework imitates the cooperative foraging maneuver of hawks (i.e., surprise pounce for creating optimized vehicular clusters). The stochastic operators of the HHO algorithm and proper maintenance of the equilibrium state between the operations of exploration and exploitation enable the proposed algorithm to escape from the local optima and provide a globally optimal solution (i.e., the optimal number of vehicular clusters). Simulations are performed in MATLAB and the results are compared with the state-of-art schemes (i.e., Gray Wolf optimization-based clustering algorithm (GWOCNET), Multi-objective Particle Swarm Optimization (MO, PSO), and Comprehensive Learning Particle Swarm Optimization (CLPSO)) using different performance metrics. The results demonstrate that the proposed approach is an effective approach for clustering in VANET and outer performs the other benchmark algorithms in terms of optimizing the multi-objective clustering problem. HHOCNET algorithm selects 36.04% of nodes as cluster heads while the existing state-of-the-art schemes are providing 50.42%, 56.7%, and 60.89% for GWOCNET, CLPSO, and Multi-objective Particle Swarm Optimization (MOPSO). The proposed HHOCNET algorithm enhances the performance of the vehicular network by up to 15%. Consequently, it increases network efficiency by reducing the consumption of the required wireless resources. It also reduces the number of hops for packet routing. Hence it achieves a minimum end-to-end communication latency.

Fairness in maximal covering location problems

This paper provides a mathematical optimization framework to incorporate fairness measures from the facilities’ perspective to discrete and continuous maximal covering location problems. The main ingredients to construct a function measuring fairness in this problem are the use of (1) ordered weighted averaging operators, a popular family of aggregation criteria for solving multiobjective combinatorial optimization problems; and (2) α-fairness operators which allow generalizing most of the equity measures. A general mathematical optimization model is derived which captures the notion of fairness in maximal covering location problems. The models are first formulated as mixed integer non-linear optimization problems for both the discrete and the continuous location spaces. Suitable mixed integer second order cone optimization reformulations are derived using geometric properties of the problem. Finally, the paper concludes with the results obtained from an extensive battery of computational experiments on real datasets. The obtained results support the convenience of the proposed approach.

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.

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.

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.

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.

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.