Reinforcement Learning With Multiple Relational Attention for Solving Vehicle Routing Problems

In this article, we study the reinforcement learning (RL) for vehicle routing problems (VRPs). Recent works have shown that attention-based RL models outperform recurrent neural network-based methods on these problems in terms of both effectiveness and efficiency. However, existing RL models simply aggregate node embeddings to generate the context embedding without taking into account the dynamic network structures, making them incapable of modeling the state transition and action selection dynamics. In this work, we develop a new attention-based RL model that provides enhanced node embeddings via batch normalization reordering and gate aggregation, as well as dynamic-aware context embedding through an attentive aggregation module on multiple relational structures. We conduct experiments on five types of VRPs: 1) travelling salesman problem (TSP); 2) capacitated VRP (CVRP); 3) split delivery VRP (SDVRP); 4) orienteering problem (OP); and 5) prize collecting TSP (PCTSP). The results show that our model not only outperforms the learning-based baselines but also solves the problems much faster than the traditional baselines. In addition, our model shows improved generalizability when being evaluated in large-scale problems, as well as problems with different data distributions.

GMP: A Genetic Mission Planner for Heterogeneous Multirobot System Applications

The use of multiagent systems (MASs) in real-world applications keeps increasing, and diffuses into new domains, thanks to technological advances, increased acceptance, and demanding productivity requirements. Being able to automate the generation of mission plans for MASs is critical for managing complex missions in realistic settings. In addition, finding the right level of abstraction to represent any generic MAS mission is important for being able to provide general solution to the automated planning problem. In this article, we show how a mission for heterogeneous MASs can be cast as an extension of the traveling salesperson problem (TSP), and we propose a mixed-integer linear programming formulation. In order to solve this problem, a genetic mission planner (GMP), with a local plan refinement algorithm, is proposed. In addition, the comparative evaluation of CPLEX and GMP is presented in terms of timing and optimality of the obtained solutions. The algorithms are benchmarked on a proposed set of different problem instances. The results show that, in the presence of timing constraints, GMP outperforms CPLEX in the majority of test instances.

A Two-Objective ILP Model of OP-MATSP for the Multi-Robot Task Assignment in an Intelligent Warehouse

Multi-robot task assignment is one of the main processes in an intelligent warehouse. This paper models multi-robot task assignment in an intelligent warehouse as an open-path multi-depot asymmetric traveling salesman problem (OP-MATSP). A two-objective integer linear programming (ILP) model for solving OP-MDTSP is proposed. The theoretical bound on the computational time complexity of this model is O(n!). We can solve the small multi-robot task assignment problem by solving the two-objective ILP model using the Gurobi solver. The multi-chromosome coding-based genetic algorithm has a smaller search space, so we use it to solve large-scale problems. The experiment results reveal that the two-objective ILP model is very good at solving small-scale problems. For large-scale problems, both EGA and NSGA3 genetic algorithms can efficiently obtain suboptimal solutions. It demonstrates that this paper’s multi-robot work assignment methods are helpful in an intelligent warehouse.

Solving large break minimization problems in a mirrored double round-robin tournament using quantum annealing

Quantum annealing has gained considerable attention because it can be applied to combinatorial optimization problems, which have numerous applications in logistics, scheduling, and finance. In recent years, with the technical development of quantum annealers, research on solving practical combinatorial optimization problems using them has accelerated. However, researchers struggle to find practical combinatorial optimization problems, for which quantum annealers outperform mathematical optimization solvers. Moreover, there are only a few studies that compare the performance of quantum annealers with the state-of-the-art solvers, such as Gurobi and CPLEX. This study determines that quantum annealing demonstrates better performance than the solvers in that the solvers take longer to reach the objective function value of the solution obtained by the quantum annealers for the break minimization problem in a mirrored double round-robin tournament. We also explain the desirable performance of quantum annealing for the sparse interaction between variables and a problem without constraints. In this process, we demonstrate that this problem can be expressed as a 4-regular graph. Through computational experiments, we solve this problem using our quantum annealing approach and two-integer programming approaches, which were performed using the latest quantum annealer D-Wave Advantage, and Gurobi, respectively. Further, we compare the quality of the solutions and the computational time. Quantum annealing was able to determine the exact solution in 0.05 seconds for problems with 20 teams, which is a practical size. In the case of 36 teams, it took 84.8 s for the integer programming method to reach the objective function value, which was obtained by the quantum annealer in 0.05 s. These results not only present the break minimization problem in a mirrored double round-robin tournament as an example of applying quantum annealing to practical optimization problems, but also contribute to find problems that can be effectively solved by quantum annealing.

Tackling the rich vehicle routing problem with nature-inspired algorithms

In the last decades, the classical Vehicle Routing Problem (VRP), i.e., assigning a set of orders to vehicles and planning their routes has been intensively researched. As only the assignment of order to vehicles and their routes is already an NP-complete problem, the application of these algorithms in practice often fails to take into account the constraints and restrictions that apply in real-world applications, the so called rich VRP (rVRP) and are limited to single aspects. In this work, we incorporate the main relevant real-world constraints and requirements. We propose a two-stage strategy and a Timeline algorithm for time windows and pause times, and apply a Genetic Algorithm (GA) and Ant Colony Optimization (ACO) individually to the problem to find optimal solutions. Our evaluation of eight different problem instances against four state-of-the-art algorithms shows that our approach handles all given constraints in a reasonable time.

A GRASP-Based Approach for Planning UAV-Assisted Search and Rescue Missions

Search and Rescue (SAR) missions aim to search and provide first aid to persons in distress or danger. Due to the urgency of these situations, it is important to possess a system able to take fast action and effectively and efficiently utilise the available resources to conduct the mission. In addition, the potential complexity of the search such as the ruggedness of terrain or large size of the search region should be considered. Such issues can be tackled by using Unmanned Aerial Vehicles (UAVs) equipped with optical sensors. This can ensure the efficiency in terms of speed, coverage and flexibility required to conduct this type of time-sensitive missions. This paper centres on designing a fast solution approach for planning UAV-assisted SAR missions. The challenge is to cover an area where targets (people in distress after a hurricane or earthquake, lost vessels in sea, missing persons in mountainous area, etc.) can be potentially found with a variable likelihood. The search area is modelled using a scoring map to support the choice of the search sub-areas, where the scores represent the likelihood of finding a target. The goal of this paper is to propose a heuristic approach to automate the search process using scarce heterogeneous resources in the most efficient manner.

Hyper-Heuristic Based on ACO and Local Search for Dynamic Optimization Problems

Hyper-heuristics comprise a set of approaches that are motivated (at least in part) by the objective of intelligently combining heuristic methods to solve hard optimization problems. Ant colony optimization (ACO) algorithms have been proven to deal with Dynamic Optimization Problems (DOPs) properly. Despite the good results obtained by the integration of local search operators with ACO, little has been done to tackle DOPs. In this research, one of the most reliable ACO schemes, the MAX-MIN Ant System (MMAS), has been integrated with advanced and effective local search operators, resulting in an innovative hyper-heuristic. The local search operators are the Lin–Kernighan (LK) and the Unstringing and Stringing (US) heuristics, and they were intelligently chosen to improve the solution obtained by ACO. The proposed method aims to combine the adaptation capabilities of ACO for DOPs and the good performance of the local search operators chosen in an adaptive way and based on their performance, creating in this way a hyper-heuristic. The travelling salesman problem (TSP) was the base problem to generate both symmetric and asymmetric dynamic test cases. Experiments have shown that the MMAS provides good initial solutions to the local search operators and the hyper-heuristic creates a robust and effective method for the vast majority of test cases.

The Buy-Online-Pick-Up-in-Store Retailing Model: Optimization Strategies for In-Store Picking and Packing

Online shopping is growing fast due to the increasingly widespread use of digital services. During the COVID-19 pandemic, the desire for contactless shopping has further changed consumer behavior and accelerated the acceptance of online grocery purchases. Consequently, traditional brick-and-mortar retailers are developing omnichannel solutions such as click-and-collect services to fulfill the increasing demand. In this work, we consider the Buy-Online-Pick-up-in-Store concept, in which online orders are collected by employees of the conventional stores. As labor is a major cost driver, we apply and discuss different optimizing strategies in the picking and packing process based on real-world data from a German retailer. With comparison of different methods, we estimate the improvements in efficiency in terms of time spent during the picking process. Additionally, the time spent on the packing process can be further decreased by applying a mathematical model that guides the employees on how to organize the articles in different shopping bags during the picking process. In general, we put forward effective strategies for the Buy-Online-Pick-up-in-Store paradigm that can be easily implemented by stores with different topologies.

A New Constructive Heuristic Driven by Machine Learning for the Traveling Salesman Problem

Recent systems applying Machine Learning (ML) to solve the Traveling Salesman Problem (TSP) exhibit issues when they try to scale up to real case scenarios with several hundred vertices. The use of Candidate Lists (CLs) has been brought up to cope with the issues. A CL is defined as a subset of all the edges linked to a given vertex such that it contains mainly edges that are believed to be found in the optimal tour. The initialization procedure that identifies a CL for each vertex in the TSP aids the solver by restricting the search space during solution creation. It results in a reduction of the computational burden as well, which is highly recommended when solving large TSPs. So far, ML was engaged to create CLs and values on the elements of these CLs by expressing ML preferences at solution insertion. Although promising, these systems do not restrict what the ML learns and does to create solutions, bringing with them some generalization issues. Therefore, motivated by exploratory and statistical studies of the CL behavior in multiple TSP solutions, in this work, we rethink the usage of ML by purposely employing this system just on a task that avoids well-known ML weaknesses, such as training in presence of frequent outliers and the detection of under-represented events. The task is to confirm inclusion in a solution just for edges that are most likely optimal. The CLs of the edge considered for inclusion are employed as an input of the neural network, and the ML is in charge of distinguishing when such edge is in the optimal solution from when it is not. The proposed approach enables a reasonable generalization and unveils an efficient balance between ML and optimization techniques. Our ML-Constructive heuristic is trained on small instances. Then, it is able to produce solutions—without losing quality—for large problems as well. We compare our method against classic constructive heuristics, showing that the new approach performs well for TSPLIB instances up to 1748 cities. Although ML-Constructive exhibits an expensive constant computation time due to training, we proved that the computational complexity in the worst-case scenario—for the solution construction after training—is O(n2logn2), n being the number of vertices in the TSP instance.

A Multi-Start Algorithm for Solving the Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints

This work presents a multistart algorithm for solving the capacitated vehicle routing problem with 2D loading constraints (2L-CVRP) allowing for the rotation of goods. Research dedicated to graph theory and symmetry considered the vehicle routing problem as a classical application. This problem has complex aspects that stimulate the use of advanced algorithms and symmetry in graphs. The use of graph modeling of the 2L-CVRP problem by undirected graph allowed the high performance of the algorithm. The developed algorithm is based on metaheuristics, such as the Constructive Genetic Algorithm (CGA) to construct promising initial solutions; a Tabu Search (TS) to improve the initial solutions on the routing problem, and a Large Neighborhood Search (LNS) for the loading subproblem. Although each one of these algorithms allowed to solve parts of the 2L-CVRP, the combination of these three algorithms to solve this problem was unprecedented in the scientific literature. In our approach, a parallel mechanism for checking the loading feasibility of routes was implemented using multithreading programming to improve the performance. Additionally, memory structures such as hash-tables were implemented to save time by storing and querying previously evaluated results for the loading feasibility of routes. For benchmarks, tests were done on well-known instances available in the literature. The results proved that the framework matched or outperformed most of the previous approaches. As the main contribution, this work brings higher quality solutions for large-size instances of the pure CVRP. This paper involves themes related to the symmetry journal, mainly complex algorithms, graphs, search strategies, complexity, graph modeling, and genetic algorithms. In addition, the paper especially focuses on topic-related aspects of special interest to the community involved in symmetry studies, such as graph algorithms and graph theory.

Comparison of the Sub-Tour Elimination Methods for the Asymmetric Traveling Salesman Problem Applying the SECA Method

There are many sub-tour elimination constraint (SEC) formulations for the traveling salesman problem (TSP). Among the different methods found in articles, usually three apply more than others. This study examines the Danzig–Fulkerson–Johnson (DFJ), Miller–Tucker–Zemlin (MTZ), and Gavish–Graves (GG) formulations to select the best asymmetric traveling salesman problem (ATSP) formulation. The study introduces five criteria as the number of constraints, number of variables, type of variables, time of solving, and differences between the optimum and the relaxed value for comparing these constraints. The reason for selecting these criteria is that they have the most significant impact on the mathematical problem-solving complexity. A new and well-known multiple-criteria decision making (MCDM) method, the simultaneous evaluation of the criteria and alternatives (SECA) method was applied to analyze these criteria. To use the SECA method for ranking the alternatives and extracting information about the criteria from constraints needs computational computing. In this research, we use CPLEX 12.8 software to compute the criteria value and LINGO 11 software to solve the SECA method. Finally, we conclude that the Gavish–Graves (GG) formulation is the best. The new web-based software was used for testing the results.

Dynamic Shortest Paths Methods for the Time-Dependent TSP

The time-dependent traveling salesman problem (TDTSP) asks for a shortest Hamiltonian tour in a directed graph where (asymmetric) arc-costs depend on the time the arc is entered. With traffic data abundantly available, methods to optimize routes with respect to time-dependent travel times are widely desired. This holds in particular for the traveling salesman problem, which is a corner stone of logistic planning. In this paper, we devise column-generation-based IP methods to solve the TDTSP in full generality, both for arc- and path-based formulations. The algorithmic key is a time-dependent shortest path problem, which arises from the pricing problem of the column generation and is of independent interest—namely, to find paths in a time-expanded graph that are acyclic in the underlying (non-expanded) graph. As this problem is computationally too costly, we price over the set of paths that contain no cycles of length k. In addition, we devise—tailored for the TDTSP—several families of valid inequalities, primal heuristics, a propagation method, and a branching rule. Combining these with the time-dependent shortest path pricing we provide—to our knowledge—the first elaborate method to solve the TDTSP in general and with fully general time-dependence. We also provide for results on complexity and approximability of the TDTSP. In computational experiments on randomly generated instances, we are able to solve the large majority of small instances (20 nodes) to optimality, while closing about two thirds of the remaining gap of the large instances (40 nodes) after one hour of computation.

Integer Programming for Learning Directed Acyclic Graphs from Continuous Data

Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the form of a mathematical programming model that can naturally incorporate a superstructure to reduce the set of possible candidate DAGs. We use a negative log-likelihood score function with both [Formula: see text] and [Formula: see text] penalties and propose a new mixed-integer quadratic program, referred to as a layered network (LN) formulation. The LN formulation is a compact model that enjoys as tight an optimal continuous relaxation value as the stronger but larger formulations under a mild condition. Computational results indicate that the proposed formulation outperforms existing mathematical formulations and scales better than available algorithms that can solve the same problem with only [Formula: see text] regularization. In particular, the LN formulation clearly outperforms existing methods in terms of computational time needed to find an optimal DAG in the presence of a sparse superstructure.

The Proposition of a Mathematical Model for the Location of Electrical and Electronic Waste Collection Points

Given the environmental impacts produced by the growing increase in waste electrical and electronic equipment (WEEE) and their current inadequate management, this article proposes a mathematical model to define the best location for installing WEEE collection points. The objective is to minimize the cost of the reverse logistics system concerning transportation, installation, opportunity cost, and distance between points and demand. We used a heuristic created from the greedy randomized adaptive search procedure and genetic algorithm meta-heuristics to solve the model, with part of the model variables being defined by another heuristic or by the JuMP v.0.21.2 and CLP Solver v.0.7.1 packages, to guarantee an optimal response to a subproblem of these variables. The model and its solver were written in the Julia Programming Language and executed in two test scenarios. In the first, three vehicles with small loads must collect at five points. In the second, a vehicle with greater available capacity must collect at five points. The results obtained show that the mathematical model and the heuristic are adequate to solve the problem. Thus, we understood that the proposed method contributes to the literature, given the criticality of the current scenario concerning the management of WEEE, and it can assist managers and public policymakers when providing inputs for decision-making related to the choice of the best location for installing collection points.

Reusing Newspaper Kiosks for Last-Mile Delivery in Urban Areas

The current increase in e-commerce is generating growing problems in urban areas in terms of both traffic flow (increasing traffic, no parking spaces) and environmental issues (noise, atmospheric pollution, etc.). In parallel, an iconic element of historic districts is disappearing: more and more newspaper kiosks are closing their business as their work dwindles. In this scenario, the objective of this paper is to propose a model for last-mile parcel delivery that exploits the current available newspaper kiosk network by using them as parcel lockers. To demonstrate the benefits of this proposal, we map the kiosk network of the city of Valladolid (Spain), and compare the environmental impact of a traditional (door-to-door) delivery and the proposed model which reuses old kiosks as parcel lockers. The necessary steps to carry out simulations are described in detail so that experiments can be replicated in other cities that face the same issues.

A Data Augmentation Method for Deep Learning Based on Multi-Degree of Freedom (DOF) Automatic Image Acquisition

Deep learning technology is outstanding in visual inspection. However, in actual industrial production, the use of deep learning technology for visual inspection requires a large number of training data with different acquisition scenarios. At present, the acquisition of such datasets is very time-consuming and labor-intensive, which limits the further development of deep learning in industrial production. To solve the problem of image data acquisition difficulty in industrial production with deep learning, this paper proposes a data augmentation method for deep learning based on multi-degree of freedom (DOF) automatic image acquisition and designs a multi-DOF automatic image acquisition system for deep learning. By designing random acquisition angles and random illumination conditions, different acquisition scenes in actual production are simulated. By optimizing the image acquisition path, a large number of accurate data can be obtained in a short time. In order to verify the performance of the dataset collected by the system, the fabric is selected as the research object after the system is built, and the dataset comparison experiment is carried out. The dataset comparison experiment confirms that the dataset obtained by the system is rich and close to the real application environment, which solves the problem of dataset insufficient in the application process of deep learning to a certain extent.

Hybrid Algorithm Based on Ant Colony Optimization and Simulated Annealing Applied to the Dynamic Traveling Salesman Problem

The dynamic traveling salesman problem (DTSP) falls under the category of combinatorial dynamic optimization problems. The DTSP is composed of a primary TSP sub-problem and a series of TSP iterations; each iteration is created by changing the previous iteration. In this article, a novel hybrid metaheuristic algorithm is proposed for the DTSP. This algorithm combines two metaheuristic principles, specifically ant colony optimization (ACO) and simulated annealing (SA). Moreover, the algorithm exploits knowledge about the dynamic changes by transferring the information gathered in previous iterations in the form of a pheromone matrix. The significance of the hybridization, as well as the use of knowledge about the dynamic environment, is examined and validated on benchmark instances including small, medium, and large DTSP problems. The results are compared to the four other state-of-the-art metaheuristic approaches with the conclusion that they are significantly outperformed by the proposed algorithm. Furthermore, the behavior of the algorithm is analyzed from various points of view (including, for example, convergence speed to local optimum, progress of population diversity during optimization, and time dependence and computational complexity).

Capacitated Lot-Sizing Problem with Sequence-Dependent Setup, Setup Carryover and Setup Crossover

Since setup operations have significant impacts on production environments, the capacitated lot-sizing problem considering arbitrary length of setup times helps to develop flexible and efficient production plans. This study discusses a capacitated lot-sizing problem with sequence-dependent setup, setup carryover and setup crossover. A new mixed integer programming formulation is proposed. The formulation is based on three building blocks: the facility location extended formulation; the setup variables with indices for the starting and the completion time periods; and exponential number of generalized subtour elimination constraints (GSECs). A separation routine is adopted to generate the violated GSECs. Computational experiments show that the proposed formulation outperforms models from the literature.

On the Resilience of Ant Algorithms. Experiment with Adapted MMAS on TSP

This paper focuses on the resilience of a nature-inspired class of algorithms. The issues related to resilience fall under a very wide umbrella. The uncertainties that we face in the world require the need of resilient systems in all domains. Software resilience is certainly of critical importance, due to the presence of software applications which are embedded in numerous operational and strategic systems. For Ant Colony Optimization (ACO), one of the most successful heuristic methods inspired by the communication processes in entomology, performance and convergence issues have been intensively studied by the scientific community. Our approach addresses the resilience of MAX–MIN Ant System (MMAS), one of the most efficient ACO algorithms, when studied in relation with Traveling Salesman Problem (TSP). We introduce a set of parameters that allow the management of real-life situations, such as imprecise or missing data and disturbances in the regular computing process. Several metrics are involved, and a statistical analysis is performed. The resilience of the adapted MMAS is analyzed and discussed. A broad outline on future research directions is given in connection with new trends concerning the design of resilient systems.

Robot Path Planning Based on Genetic Algorithm Fused with Continuous Bezier Optimization

In this study, a new method of smooth path planning is proposed based on Bezier curves and is applied to solve the problem of redundant nodes and peak inflection points in the path planning process of traditional algorithms. First, genetic operations are used to obtain the control points of the Bezier curve. Second, a shorter path is selected by an optimization criterion that the length of the Bezier curve is determined by the control points. Finally, a safe distance and adaptive penalty factor are introduced into the fitness function to ensure the safety of the walking process of the robot. Numerous experiments are implemented in two different environments and compared with the existing methods. It is proved that the proposed method is more effective to generate a shorter, smoother, and safer path compared with traditional approaches.

A Proposal for the Organisational Measure in Intelligent Systems

The collaboration within organisations and among organisations is a fundamental concept in the attainment of the overall objectives pursued by an enterprise network in human companies. Swarm systems are intelligent systems that show collaboration within the system; moreover, some models, such as multiple ant colonies, show the collaboration of several systems to achieve a global goal. The collaboration in this type of system optimises the achievement of the overall objectives as in an enterprise network in human organisations. Being able to measure this collaboration allows establishing a relationship between the improvement in the results of the system and the degree of collaboration, both at the level of specialisation of each element of the system and the systems as a whole. The performance of a swarm system depends on the number of members in many cases, so that if we can establish a measure of specialisation and collaboration, we could tipify and classify these systems in terms of the efficiency and the realiability to perform different tasks.

Optimization of a Low-Carbon Two-Echelon Heterogeneous-Fleet Vehicle Routing for Cold Chain Logistics under Mixed Time Window

Due to the rise of social and environmental concerns on global climate change, developing the low-carbon economy is a necessary strategic step to respond to greenhouse effect and incorporate sustainability. As such, there is a new trend for the cold chain industry to establish the low-carbon vehicle routing optimization model which takes costs and carbon emissions as the measurements of performance. This paper studies a low-carbon vehicle routing problem (LC-VRP) derived from a real cold chain logistics network with several practical constraints, which also takes customer satisfaction into account. A low-carbon two-echelon heterogeneous-fleet vehicle routing problem (LC-2EHVRP) model for cold chain third-party logistics servers (3PL) with mixed time window under a carbon trading policy is constructed in this paper and aims at minimizing costs, carbon emissions and maximizing total customer satisfaction simultaneously. To find the optimal solution of such a nondeterministic polynomial (NP) hard problem, we proposed an adaptive genetic algorithm (AGA) approach validated by a numerical benchmark test. Furthermore, a real cold chain case study is presented to demonstrate the influence of the mixed time window’s changing which affect customers’ final satisfaction and the carbon trading settings on LC-2EHVRP model. Experiment of LC-2EHVRP model without customer satisfaction consideration is also designed as a control group. Results show that customer satisfaction is a critical influencer for companies to plan multi-echelon vehicle routing strategy, and current modest carbon price and trading quota settings in China have only a minimal effect on emissions’ control. Several managerial suggestions are given to cold chain logistics enterprises, governments, and even consumers to help improve the development of cold chain logistics.

Optimization of municipal solid waste collection and transportation routes, through linear programming and geographic information system: a case study from Şanlıurfa, Turkey

Solid waste is one of the important causes of the environmental crisis that negatively impacts human health throughout the world and is fast approaching a disaster level that will pose a direct threat to human life. As with all other environmental problems, the increase in solid waste production that goes hand in hand with growing population and rising consumption has become a focus of great concern. Along with these rising levels, the investment, management and maintenance of solid waste collection and transport vehicles is seeing a continual increase in financial outlay. It is clear from the budgets of local authority solid waste management systems, 65 to 80% of which are accounted for by domestic waste, that the collection and transport of solid waste is a high-cost process and that this expenditure can be significantly reduced by the reorganisation of solid waste collection routing schedules and the minimization of collection frequency. This study demonstrates a linear programming model in order to develop an optimal routing schedule for solid waste collection and transportation, thereby reducing costs to a minimum. The neighbourhood of Veysel Karani in the Haliliye District of Şanlıurfa Province, Turkey, was specifically selected for this case study, having the suitable socio-economic and demographic variables to be representative of a metropolitan urban area. Firstly, the data regarding the municipal solid waste collection and transport routes were obtained from the local authority. Analysis and verification of these data were then performed. With the field study, these data were verified on-site, and the missing data were completed. Linear programming and geographic information system (GIS) analysis were used to determine the best route. Consequently, it is concluded that it is possible to save the route by 28% with GIS analysis and 33% with linear programming analysis according to the existing municipal solid waste collection and transportation routes.

Memory Optimization for Bit-Vector-Based Packet Classification on FPGA

High-performance packet classification algorithms have been widely studied during the past decade. Bit-Vector-based algorithms proposed for FPGA can achieve very high throughput by decomposing rules delicately. However, the relatively large memory resources consumption severely hinders applications of the algorithms extensively. It is noteworthy that, in the Bit-Vector-based algorithms, stringent memory resources in FPGA are wasted to store relatively plenty of useless wildcards in the rules. We thus present a memory-optimized packet classification scheme named WeeBV to eliminate the memory occupied by the wildcards. WeeBV consists of a heterogeneous two-dimensional lookup pipeline and an optimized heuristic algorithm for searching all the wildcard positions that can be removed. It can achieve a significant reduction in memory resources without compromising the high throughput of the original Bit-Vector-based algorithms. We implement WeeBV and evaluate its performance by simulation and FPGA prototype. Experimental results show that our approach can save 37% and 41% memory consumption on average for synthetic 5-tuple rules and OpenFlow rules respectively.

A Hybrid PSO-GA Algorithm for Traveling Salesman Problems in Different Environments

In this study particle swarm optimization (PSO) is modified and hybridised with genetic algorithm (GA) using one’s output as the other's input to solve Traveling Salesman Problem(TSP). Here multiple velocity update rules are introduced to modify the PSO and at the time of the movement of a solution, one rule is selected depending on its performances using roulette wheel selection process. Each velocity update rule and the corresponding solution update rule are defined using swap sequence (SS) and swap operation (SO). K-Opt operation is applied in a regular interval of iterations for the movement of any stagnant solution. GA is applied on the final output swarm of the PSO to search the optimal path of the large size TSPs. Roulette wheel selection process, multi-point cyclic crossover and the K-opt operation for the mutation are used in the GA phase. The algorithm is tested in crisp environment using different size benchmark test problems available in the TSPLIB. In the crisp environment the algorithm gives approximately 100% success rate for the test problems up to considerably large sizes. Efficiency of the algorithm is tested with some other existing algorithms in the literature using Friedman test. Some approaches are incorporated with this algorithm for finding solutions of the TSPs in imprecise (fuzzy/rough) environment. Imprecise problems are generated from the crisp problems randomly, solved and obtained results are discussed. It is observed that the performance of the proposed algorithm is better compared to the some other algorithms in the existing literature with respect to the accuracy and the consistency for the symmetric TSPs as well as the Asymmetric TSPs.

SolarView: Low Distortion Radial Embedding with a Focus

We propose a novel type of low distortion radial embedding which focuses on one specific entity and its closest neighbors. Our embedding preserves near-exact distances to the focus entity and aims to minimize distortion between the other entities. We present an interactive exploration tool SolarView which places the focus entity at the center of a "solar system" and embeds its neighbors guided by concentric circles. SolarView provides an implementation of our novel embedding and several state-of-the-art dimensionality reduction and embedding techniques, which we adapted to our setting in various ways. We experimentally evaluated our embedding and compared it to these state-of-the-art techniques. The results show that our embedding competes with these techniques and achieves low distortion in practice. Our method performs particularly well when the visualization, and hence the embedding, adheres to the solar system design principle of our application. Nonetheless-as with all dimensionality reduction techniques-the distortion may be high. We leverage interaction techniques to give clear visual cues that allow users to accurately judge distortion. We illustrate the use of SolarView by exploring the high-dimensional metric space of bibliographic entity similarities.

ExtrIntDetect—A New Universal Method for the Identification of Intelligent Cooperative Multiagent Systems with Extreme Intelligence

In this research, we define a specific type of performance of the intelligent agent-based systems (IABSs) in terms of a difficult problem-solving intelligence measure. Many studies present the successful application of intelligent cooperative multiagent systems (ICMASs) for efficient, flexible and robust solving of difficult real-life problems. Based on a comprehensive study of the scientific literature, we conclude that there is no unanimous view in the scientific literature on machine intelligence, or on what an intelligence metric must measure. Metrics presented in the scientific literature are based on diverse paradigms. In our approach, we assume that the measurement of intelligence is based on the ability to solve difficult problems. In our opinion, the measurement of intelligence in this context is important, as it allows the differentiation between ICMASs based on the degree of intelligence in problem-solving. The recent OutIntSys method presented in the scientific literature can identify systems with outlier high and outlier low intelligence from a set of studied ICMASs. In this paper, a novel universal method called ExtrIntDetect, defined on the basis of a specific series of computing processes and analyses, is proposed for the detection of the ICMASs with statistical outlier low and high problem-solving intelligence from a given set of studied ICMASs. ExtrIntDetect eliminates the disadvantage of the OutIntSys method with respect to its limited robustness. The recent symmetric MetrIntSimil metric presented in the literature is capable of measuring and comparing the intelligence of large numbers of ICMASs and based on their respective problem-solving intelligences in order to classify them into intelligence classes. Systems whose intelligence does not statistically differ are classified as belonging to the same class of intelligent systems. Systems classified in the same intelligence class are therefore able to solve difficult problems using similar levels of intelligence. One disadvantage of the symmetric MetrIntSimil lies in the fact that it is not able to detect outlier intelligence. Based on this fact, the ExtrIntDetect method could be used as an extension of the MetrIntSimil metric. To validate and evaluate the ExtrIntDetect method, an experimental evaluation study on six ICMASs is presented and discussed.

Replica symmetry and replica symmetry breaking for the traveling salesperson problem

We study the energy landscape of the traveling salesperson problem (TSP) using exact ground states and a novel linear programming approach to generate excited states with closely defined properties. We look at four different ensembles, notably the classic finite dimensional Euclidean TSP and the mean-field-like (1,2)-TSP, which has its origin directly in the mapping of the Hamiltonian circuit problem on the TSP. Our data supports previous conjectures that the Euclidean TSP does not show signatures of replica symmetry breaking neither in two nor in higher dimension. On the other hand the (1,2)-TSP exhibits some signature which does not exclude broken replica symmetry, making it a candidate for further studies in the future.

A Heuristic Algorithm for the Routing and Scheduling Problem with Time Windows: A Case Study of the Automotive Industry in Mexico

This paper investigates a real-world distribution problem arising in the vehicle production industry, particularly in a logistics company, in which cars and vans must be loaded on auto-carriers and then delivered to dealerships. A solution to the problem involves the loading and optimal routing, without violating the capacity and time window constraints for each auto-carrier. A two-phase heuristic algorithm was implemented to solve the problem. In the first phase the heuristic builds a route with an optimal insertion procedure, and in the second phase the determination of a feasible loading. The experimental results show that the purposed algorithm can be used to tackle the transportation problem in terms of minimizing total traveling distance, loading/unloading operations and transportation costs, facilitating a decision-making process for the logistics company.

IntraClusTSP—An Incremental Intra-Cluster Refinement Heuristic Algorithm for Symmetric Travelling Salesman Problem

The Symmetric Traveling Salesman Problem (sTSP) is an intensively studied NP-hard problem. It has many important real-life applications such as logistics, planning, manufacturing of microchips and DNA sequencing. In this paper we propose a cluster level incremental tour construction method called Intra-cluster Refinement Heuristic (IntraClusTSP). The proposed method can be used both to extend the tour with a new node and to improve the existing tour. The refinement step generates a local optimal tour for a cluster of neighbouring nodes and this local optimal tour is then merged into the global optimal tour. Based on the performed evaluation tests the proposed IntraClusTSP method provides an efficient incremental tour generation and it can improve the tour efficiency for every tested state-of-the-art methods including the most efficient Chained Lin-Kernighan refinement algorithm. As an application example, we apply IntraClusTSP to automatically determine the optimal number of clusters in a cluster analysis problem. The standard methods like Silhouette index, Elbow method or Gap statistic method, to estimate the number of clusters support only partitional (single level) clustering, while in many application areas, the hierarchical (multi-level) clustering provides a better clustering model. Our proposed method can discover hierarchical clustering structure and provides an outstanding performance both in accuracy and execution time.

Solution to travelling salesman problem by clusters and a modified multi-restart iterated local search metaheuristic

This article finds feasible solutions to the travelling salesman problem, obtaining the route with the shortest distance to visit n cities just once, returning to the starting city. The problem addressed is clustering the cities, then using the NEH heuristic, which provides an initial solution that is refined using a modification of the metaheuristic Multi-Restart Iterated Local Search MRSILS; finally, clusters are joined to end the route with the minimum distance to the travelling salesman problem. The contribution of this research is the use of the metaheuristic MRSILS, that in our knowledge had not been used to solve the travelling salesman problem using clusters. The main objective of this article is to demonstrate that the proposed algorithm is more efficient than Genetic Algorithms when clusters are used. To demonstrate the above, both algorithms are compared with some cases taken from the literature, also a comparison with the best-known results is done. In addition, statistical studies are made in the same conditions to demonstrate this fact. Our method obtains better results in all the 10 cases compared.

A goal programming model for a sustainable biomass supply chain network

Purpose

The design of a biomass supply chain is a problem where multiple stakeholders with often conflicting objectives are involved. To accommodate the aspects stakeholder, the supply chain design should incorporate multiple objectives. In addition to the supply chain design, the management of energy from biomass is a demanding task, as the operation of production of biomass products needs to be aligned with the rest of the operations of the biomass supply chain. The purpose of the paper is to propose a mathematical framework for the optimal design of biomass supply chain.

Design/methodology/approach

An integrated mathematical framework that models biomass production, transportation and warehousing throughout the nodes of a biomass supply chain is presented. Owing to conflicting objectives, weights are imposed on each aspect, and a 0-1 weighted goal programming mixed-integer linear programming (WGP MILP) programming model is formulated and used for all possible weight representations under environmental, economic and social criteria.

Findings

The results of the study show that emphasis on the environmental aspect, expressed with high values in the environmental criterion, significantly reduces the level of CO2 emissions derived from the transportation of biomass through the various nodes of the supply chain. Environmental and economic criteria seem to be moving in the same direction for high weight values in the corresponding aspect. From the results, social criterion seems to move to the opposite direction from environmental and economic criteria.

Originality/value

An integrated mathematical framework is presented modeling biomass production, transportation and warehousing. To the best of the authors’ knowledge, such a model that integrates multiple objectives with supply chain design has not yet been published.

Crossover versus mutation: a comparative analysis of the evolutionary strategy of genetic algorithms applied to combinatorial optimization problems

Since their first formulation, genetic algorithms (GAs) have been one of the most widely used techniques to solve combinatorial optimization problems. The basic structure of the GAs is known by the scientific community, and thanks to their easy application and good performance, GAs are the focus of a lot of research works annually. Although throughout history there have been many studies analyzing various concepts of GAs, in the literature there are few studies that analyze objectively the influence of using blind crossover operators for combinatorial optimization problems. For this reason, in this paper a deep study on the influence of using them is conducted. The study is based on a comparison of nine techniques applied to four well-known combinatorial optimization problems. Six of the techniques are GAs with different configurations, and the remaining three are evolutionary algorithms that focus exclusively on the mutation process. Finally, to perform a reliable comparison of these results, a statistical study of them is made, performing the normal distribution z-test.

Advances in mixed-integer programming methods for chemical production scheduling

The goal of this paper is to critically review advances in the area of chemical production scheduling over the past three decades and then present two recently proposed solution methods that have led to dramatic computational enhancements. First, we present a general framework and problem classification and discuss modeling and solution methods with an emphasis on mixed-integer programming (MIP) techniques. Second, we present two solution methods: (a) a constraint propagation algorithm that allows us to compute parameters that are then used to tighten MIP scheduling models and (b) a reformulation that introduces new variables, thus leading to effective branching. We also present computational results and an example illustrating how these methods are implemented, as well as the resulting enhancements. We close with a discussion of open research challenges and future research directions.

DIMMA-Implemented Metaheuristics for Finding Shortest Hamiltonian Path Between Iranian Cities Using Sequential DOE Approach for Parameters Tuning

A Hamiltonian path is a path in an undirected graph, which visits each node exactly once and returns to the starting node. Finding such paths in graphs is the Hamiltonian path problem, which is NP-complete. In this paper, for the first time, a comparative study on metaheuristic algorithms for finding the shortest Hamiltonian path for 1071 Iranian cities is conducted. These are the main cities of Iran based on social-economic characteristics. For solving this problem, four hybrid efficient and effective metaheuristics, consisting of simulated annealing, ant colony optimization, genetic algorithm, and tabu search algorithms, are combined with the local search methods. The algorithms’ parameters are tuned by sequential design of experiments (DOE) approach, and the most appropriate values for the parameters are adjusted. To evaluate the proposed algorithms, the standard problems with different sizes are used. The performance of the proposed algorithms is analyzed by the quality of solution and CPU time measures. The results are compared based on efficiency and effectiveness of the algorithms.

Column generation algorithms for exact modularity maximization in networks

Finding modules, or clusters, in networks currently attracts much attention in several domains. The most studied criterion for doing so, due to Newman and Girvan [Phys. Rev. E 69, 026113 (2004)], is modularity maximization. Many heuristics have been proposed for maximizing modularity and yield rapidly near optimal solution or sometimes optimal ones but without a guarantee of optimality. There are few exact algorithms, prominent among which is a paper by Xu [Eur. Phys. J. B 60, 231 (2007)]. Modularity maximization can also be expressed as a clique partitioning problem and the row generation algorithm of Grötschel and Wakabayashi [Math. Program. 45, 59 (1989)] applied. We propose to extend both of these algorithms using the powerful column generation methods for linear and non linear integer programming. Performance of the four resulting algorithms is compared on problems from the literature. Instances with up to 512 entities are solved exactly. Moreover, the computing time of previously solved problems are reduced substantially.

Combinatorial and probabilistic fusion of noisy correlation measurements for untracked freehand 3-D ultrasound

In freehand 3-D ultrasound (US), the relative positions of US images are usually measured using a position tracking device despite its cumbersome nature. The probe trajectory can instead be estimated from image data, using registration techniques to recover in-plane motion and speckle decorrelation to recover out-of-plane transformations. The relationship between speckle decorrelation and elevational separation is typically represented by a single curve, estimated from calibration data. Distances read off such a curve are corrupted by bias and uncertainty, and only provide an absolute estimate of elevational displacement. This paper presents a probabilistic model of the relationship between correlation measurements and elevational separation. This representation captures the skewed distribution of distance estimates based on high correlations and the uncertainties attached to each measurement. Multiple redundant correlation measurements can then be integrated within a maximum likelihood estimation framework. This paper also introduces a new method based on the traveling salesman problem for resolving sign ambiguities in data sets resulting from nonmonotonic probe motion and frame intersections. Experiments with real and synthetic US data show that by combining these new methods, out-of-plane US probe motion is recovered with improved accuracy over baseline methods using a deterministic model and fewer measurements.