Multi-objective Routing Problem Research Articles

Hybridization of Evolutionary Algorithm and Deep Reinforcement Learning for Multiobjective Orienteering Optimization

Multi-objective orienteering problems (MO-OPs) are classical multi-objective routing problems and have received much attention in recent decades. This study seeks to solve MO-OPs through a problem-decomposition framework, that is, an MO-OP is decomposed into a multi-objective knapsack problem (MOKP) and a traveling salesman problem (TSP). The MOKP and TSP are then solved by a multi-objective evolutionary algorithm (MOEA) and a deep reinforcement learning (DRL) method, respectively. While the MOEA module is for selecting cities, the DRL module is for planning a Hamiltonian path for these cities. An iterative use of these two modules drives the population towards the Pareto front of MO-OPs. The effectiveness of the proposed method is compared against NSGA-II and NSGA-III on various types of MO-OP instances. Experimental results show that our method performs best on almost all the test instances, and has shown strong generalization ability.

A robust multi-objective routing problem for heavy-duty electric trucks with uncertain energy consumption

In the Vehicle Routing Problem (VRP), utilizing Battery Electric Vehicles (BEVs) adds some challenges such as limited driving range and long recharging time to the problem. The energy consumption in BEVs plays an important role in determining their range coverage and the frequency of recharging. This paper introduces a new robust mathematical model for the EVRP with Heavy-duty Battery Electric Trucks to handle the energy consumption uncertainty in the short-haul delivery problems. Moreover, the on-time delivery factor that results in customers’ satisfaction is addressed by minimizing the delay and the earliness during distribution. Hence, the presented EVRP is a bi-objective problem that simultaneously minimizes transportation costs and maximizes customers’ satisfaction. To solve the problem, two metaheuristic algorithms are developed, including a Nondominated Sorting Genetic Algorithm II (NSGA-II), and Adaptive Large Neighborhood Search (ALNS) combined with multi-objective solution approaches (e.g., weighted-sum,ε-constraint, and hybrid methods). The results show that the ALNS algorithm combined with the weighted-sum method performed better than the other approaches.Moreover, a simulation study is conducted to analyze the robust solutions obtained for different levels of uncertainty to provide managerial insights for decision-makers.

Modelling a Learning-Based Dynamic Tree Routing Model for Wireless Mesh Access Networks

Link asymmetry in wireless mesh access networks (WMAN) of Mobile ad-hoc Networks (MANETs) is due mesh routers’ transmission range. It is depicted as significant research challenges that pose during the design of network protocol in wireless networks. Based on the extensive review, it is noted that the substantial link percentage is symmetric, i.e., many links are unidirectional. It is identified that the synchronous acknowledgement reliability is higher than the asynchronous message. Therefore, the process of establishing bidirectional link quality through asynchronous beacons underrates the link reliability of asymmetric links. It paves the way to exploit an investigation on asymmetric links to enhance network functions through link estimation. Here, a novel Learning-based Dynamic Tree routing (LDTR) model is proposed to improve network performance and delay. For the evaluation of delay measures, asymmetric link, interference, probability of transmission failure is evaluated. The proportion of energy consumed is used for monitoring energy conditions based on the total energy capacity. This learning model is a productive way for resolving the routing issues over the network model during uncertainty. The asymmetric path is chosen to achieve exploitation and exploration iteratively. The learning-based Dynamic Tree routing model is utilized to resolve the multi-objective routing problem. Here, the simulation is done with MATLAB 2020a simulation environment and path with energy-efficiency and lesser E2E delay is evaluated and compared with existing approaches like the Dyna-Q-network model (DQN), asymmetric MAC model (AMAC), and cooperative asymmetric MAC model (CAMAC) model. The simulation outcomes demonstrate that the anticipated LDTR model attains superior network performance compared to others. The average energy consumption is 250 J, packet energy consumption is 6.5 J, PRR is 50 bits/sec, 95% PDR, average delay percentage is 20%.

A multi-objective Dyna-Q based routing in wireless mesh network

Routing is an essential part for network deployment to maintain and improve the network performance. With the rapid demands of various wireless applications, delay and energy efficiency are two fundamentally important aspects in the next-generation communication. A multi-objective Dyna-Q based routing (MODQR) approach to improve both delay and energy performances is proposed in this paper. For delay, the interference, asymmetrical link condition and probability of transmission failure (PTF) are considered. When deriving the PTF, the gray physical interference model is used. For energy, the ratio of consumed energy to energy capacity is used to monitor energy condition. Reinforcement learning is an effective way to solve the routing problem in a network with uncertain conditions. A path can be chosen by iterative exploration and exploitation. Dyna-Q is an effective reinforcement learning algorithm which can increase the convergence speed. To the best of our knowledge, Dyna-Q is used to solve the multi-objective routing problem for the first time. The path with least end-to-end delay and largest energy efficiency will be selected. Simulation results show that MODQR can obtain up to 80.97%, 83.48% and 86.15% better network performance than three other state-of-the-art routing methods.

Multiobjective routing protocol for wireless sensor network optimization using ant colony conveyance algorithm

SummaryThe widely deployed wireless sensor networks, incorporated with the capabilities of sensing, processing, and communicating, require more effective routing to maintain the balance between the performance parameters and to be prevented from the security attacks. The cryptographic methods used were effective but consumed more energy on the authentication, the encryption, and the decryption. So the routing addressing the security problems, with the reduced energy consumption, latency, and PDR losses, maximizing the network lifetime is proposed in the paper. This multiobjective routing problem of the sensor networks is handled using the ant colony routing techniques, taking into consideration the remaining energy of the nodes, the distance between the nodes, and the trust credentials of the nodes, to reduce the energy consumption and enhance the lifetime of the sensor networks. The further performance evaluation using the network simulator‐2 reveals the efficiency and the quality of the service of proposed routing technique over existing techniques on the grounds of energy utilization, PDR, lifetime of sensor networks, and the security enhancement rate.

Robust multiobjective optimization with application to Internet routing

Robust optimization addressing decision making under uncertainty has been very well developed for problems with a single objective function and applied to areas of human activity such as portfolio selection, investment decisions, signal processing, and telecommunication-network planning. As these decision problems typically have several decisions or goals, we extend robust single objective optimization to the multiobjective case. The column-wise uncertainty model can be carried over to the multiobjective case without any additional assumptions. For the row-wise uncertainty model, we show under additional assumptions that robust efficient solutions are efficient to specific instance problems and can be found as the efficient solutions of another deterministic problem. Being motivated by the fact that Internet traffic must be maintained in a reliable yet affordable manner in situations of complex and dynamic usage, we apply the row-wise model to an intradomain multiobjective routing problem with polyhedral traffic uncertainty. We consider traditional objective functions corresponding to link utilizations and implement the biobjective case using the parametric simplex algorithm to compute robust efficient routings. We also present computational results for the Abilene network and analyze their meaning in the context of the application.

A multiobjective GRASP–VND algorithm to solve the waste collection problem

AbstractIn this paper, the waste collection problem (WCP) of a city in the south of Spain is addressed as a multiobjective routing problem that considers three objectives. From the company's perspective, the minimization of the travel cost is desired as well as that of the total number of vehicles. Additionally, from the employee's point of view, a set of balanced routes is also sought. Four variants of a multiobjective hybrid algorithm are proposed. Specifically, a GRASP (greedy randomized adaptive search procedure) with a VND (variable neighborhood descent) is combined. The best GRASP–VND algorithm found is applied in order to solve the real‐world WCP of a city in the south of Spain.

Decision Support System for Solving Multi-Objective Routing Problem

Decision Support System for Solving Multi-Objective Routing Problem

A multi-objective evolutionary algorithm based QoS routing in wireless mesh networks

The huge demand for real time services in wireless mesh networks (WMN) creates many challenging issues for providing quality of service (QoS). Designing of QoS routing protocols, which optimize the multiple objectives is computationally intractable. This paper proposes a new model for routing in WMN by using Modified Non-dominated Sorting Genetic Algorithm-II (MNSGA-II). The objectives which are considered here are the minimization of expected transmission count and the transmission delay. In order to retain the diversity in the non-dominated solutions, dynamic crowding distance (DCD) procedure is implemented in NSGA-II. The simulation is carried out in Network Simulator 2 (NS-2) and comparison is made using the metrics, expected transmission count and transmission delay by varying node mobility and by increasing number of nodes. It is observed that MNSGA-II improves the throughput and minimizes the transmission delay for varying number of nodes and higher mobility scenarios. The simulation clearly shows that MNSGA-II algorithm is certainly more suitable for solving multiobjective routing problem. A decision-making procedure based on analytic hierarchy process (AHP) has been adopted to find the best compromise solution from the set of Pareto-solutions obtained through MNSGA-II. The performance of MNSGA-II is compared with reference point based NSGA-II (R-NSGA-II) in terms of spread.

Performance Comparison between the Multi-Colony and Multi-Pheromone ACO Algorithms for Solving the Multi-objective Routing Problem in a Public Transportation Network

Routing in a multimodal urban public transportation network, according to the user's preferences, can be considered as a multi-objective optimisation problem. Solving this problem is a complicated task due to the different and incompatible objective functions, various modes in the network, and the large size of the network. In this research, two optimisation algorithms are considered for solving this problem. The multi-colony and multi-pheromone Ant Colony Optimisation (ACO) algorithms are two different modes of the Multi-Objective ACO (MOACO) algorithm. Moreover, according to the acquired information, the algorithms implemented in the public transportation network of Tehran consist of four modes. In addition, three objective functions have been simultaneously considered as the problem's objectives. The algorithms are run with different initial parameters and afterwards, the results are compared and evaluated based on the different obtained routes and with the aid of the convergence and repeatability tests, diversity and convergence metrics.

Hybrid evolutionary algorithms for the Multiobjective Traveling Salesman Problem

In the Multiobjective Traveling Salesman Problem (moTSP) simultaneous optimization of more than one objective functions is required. In this paper, three hybrid evolutionary algorithms with common characteristics are proposed and analyzed for the solution of the Multiobjective Traveling Salesman Problem. The two hybrid evolutionary algorithms are based on Differential Evolution algorithm and the third one is a hybridized version of the NSGA II. One of the challenges of the proposed algorithms is the efficient application of an algorithm, the Differential Evolution algorithm, which is suitable for continuous optimization problems, in a combinatorial optimization problem. Thus, we test two different versions of the algorithm, the one with the use of an external archive (denoted as MODE) and the other using the crowding distance (denoted as NSDE). Also, another novelty of the proposed algorithms is the use of three different mutation operators in each of the two versions of the Differential Evolution algorithm leading to six different algorithms (MODE1, MODE2 and MODE3 for the first version and NSDE1, NSDE2 and NSDE3 for the second version). We use in each algorithm a Variable Neighborhood Search (VNS) procedure in each solution separately in order to increase the exploitation abilities of the algorithms. In order to give the quality of the algorithms, experiments are conducted using classic Euclidean Traveling Salesman Problem benchmark instances taken from the TSP library. Also, we use a number of different evaluation measures in order to conclude which of the three algorithms is the most suitable for the solution of the selected problem. In general, the proposed algorithms can easily be applied in all multiobjective routing problems by changing the objective function and the constraints of the problem and they have the ability to use more than two objective functions (in the paper we test the algorithm with up to five different objective functions). The hybridized use of the global search algorithm, the Differential Evolution, with the Variable Neighborhood Search increases the exploration and the exploitation abilities of the algorithms giving very effective evolutionary multiobjective optimization algorithms.

Discrete multi-objective differential evolution algorithm for routing in wireless mesh network

The wireless mesh network (WMN) is a challenging technology that offers high quality services to the end users. With growing demand for real-time services in the wireless networks, quality-of-service-based routing offers vital challenges in WMNs. In this paper, a discrete multi-objective differential evolution (DMODE) approach for finding optimal route from a given source to a destination with multiple and competing objectives is proposed. The objective functions are maximization of packet delivery ratio and minimization of delay. For maintaining good diversity, the concepts of weight mapping crossover (WMX)-based recombination and dynamic crowding distances are implemented in the DMODE algorithm. The simulation is carried out in NS-2 and it is observed that DMODE substantially improves the packet delivery ratio and significantly minimizes the delay for various scenarios. The performance of DMODE, DEPT and NSGA-II is compared with respect to multi-objective performance measures namely as `spread'. The results demonstrate that DMODE generates true and well-distributed Pareto-optimal solutions for the multi-objective routing problem in a single run.

Non-Dominated Quantum Iterative Routing Optimization for Wireless Multihop Networks

Routing in wireless multihop networks (WMHNs) relies on a delicate balance of diverse and often conflicting parameters, when aiming for maximizing the WMHN performance. Classified as a non-deterministic polynomial-time hard problem, routing in WMHNs requires sophisticated methods. As a benefit of observing numerous variables in parallel, quantum computing offers a promising range of algorithms for complexity reduction by exploiting the principle of quantum parallelism (QP), while achieving the optimum full-search-based performance. In fact, the so-called non-dominated quantum optimization (NDQO) algorithm has been proposed for addressing the multiobjective routing problem with the goal of achieving a near-optimal performance, while imposing a complexity of the order of $O(N)$ and $O(N\sqrt {N})$ in the best and worst case scenarios, respectively. However, as the number of nodes in the WMHN increases, the total number of routes increases exponentially, making its employment infeasible despite the complexity reduction offered. Therefore, we propose a novel optimal quantum-assisted algorithm, namely, the non-dominated quantum iterative optimization (NDQIO) algorithm, which exploits the synergy between the hardware and the QP for the sake of achieving a further complexity reduction, which is on the order of $O(\sqrt {N})$ and $O(N\sqrt {N})$ in the best and worst case scenarios, respectively. In addition, we provide simulation results for demonstrating that our NDQIO algorithm achieves an average complexity reduction of almost an order of magnitude compared with the near-optimal NDQO algorithm, while having the same order of power consumption.

Two-step Solving Algorithm for Hazmat Transportation Routing and Dispatch Problem

This paper focus on the multi-objective routing and dispatch problem for a given hazardous materials shipment with multiple time windows and time varying attributes. Section 1 consists of background and purpose of the research. Section 2 proposes a mathematical model for this problem by introducing the punishing functions to convert time windows into penalty variables of model. Section 3 develops a two-step solving algorithm for model, of which the first step is to identify the non-dominated paths with specific dispatch time based on the improved dynamic programming method, and the second step is to choose the optimal alternatives from non-dominated paths by the application of the grey correlation analysis method. Section 4 carries out a case study to test the methodology proposed in the paper. The results show that the model and the two-step algorithm can effectively solve road hazardous materials transportation routing and dispatch problem.

Optimal Routing with Multiple Objectives: Efficient Algorithm and Application to the Hazardous Materials Transportation Problem

Abstract:  This article presents an efficient parametric optimization method for the biobjective optimal routing problem. The core process is a bounded greedy single‐objective shortest path approximation algorithm. This method avoids the computationally intensive dominance check with labeling methods and overcomes the deficiency with existing parametric methods that can only find extreme nondominated paths. Moreover, we propose a decomposition scheme to convert a multiobjective routing problem into a number of biobjective problems. We then compare its computational performance against the classic label‐correcting method over a set of synthetically generated random networks and illustrate its algorithmic advances and solution behaviors by an example application of routing hazardous materials in a U.S. northeastern highway network.

Tabu search for a multi-objective routing problem

Multi-objective optimization problems deal with the presence of different conflicting objectives. Given that it is not possible to obtain a single solution by optimizing all the objectives simultaneously, a common way to face these problems is to obtain a set of efficient solutions called the non-dominated frontier. In this paper, we address the problem of routing school buses with two objectives: minimize the number of buses, and minimize the longest time a student would have to stay in the bus. The trade-off in this problem is between service level, which is represented by the maximum route length, and operational cost, which is represented by the number of buses in the solution. We present different constructive solution methods and a tabu search procedure to obtain non-dominated solutions. The procedure is coupled with an intensification phase based on the path relinking methodology: a strategy proposed several years ago, which has been rarely used in actual implementations. Computational experiments with real data, in the context of routing school buses in a rural area, establish the effectiveness of our procedure in relation to the approach previously identified to be the best.

An effective genetic algorithm approach to multiobjective routing problems (MORPs)

Dynamic programming (DP) is a mathematical procedure designed primarily to improve the computational efficiency of solving select mathematical programming problems by decomposing them into smaller, and hence computationally simpler, subproblems. In solving multiple objectives dynamic programming problem (MODP), classical approaches reduce the multiple objectives into a single objective of minimizing a weighted sum of objectives. The determination of these weights indicate the relative importance of the various objective. Also, if the problem scale increases, it becomes difficult to be dealt with even in the case of single objective because of the rapid expansion of the number of states to be considered. In this paper, we investigated the possibility of using genetic algorithms (GAs) to solve multiobjective routing problems (MORPs). This procedure eliminates the need of any user defined weight factor for each objective. Also, the proposed approach is developed to deal with the problems with both single or multiple objectives. The simulation results for MORPs shows that genetic algorithms (GAs) may hopefully be a new approach for such kinds of difficult-to-solve problems.

Multiobjective routing problems

Many network routing problems, particularly where the transportation of hazardous materials is involved, are multiobjective in nature; that is, it is desired to optimise not only physical path length but other features as well. Several such problems are defined here and a general framework for multiobjective routing problems is proposed. The notion of “efficient solution” is defined and it is demonstrated, by means of an example, that a problem may have very many solutions which are efficient. Next, potentially useful solution methods for multiobjective routing problems are discussed with emphasis being placed on the use of shortest/k-shortest path techniques. Finally, some directions for possible further research are indicated.

A fuzzy approach to multi-objective routing problem with applications to process planning in manufacturing systems

In this paper a method is developed for the selection of an efficient path in a fuzzy multi-objective network. The application of the methodology developed is illustrated by a process plan selection problem in a manufacturing environment.

Multi‐Objective Programming Approach for Routing Hazardous Materials

This paper examines the systemwide routing, of hazardous materials as a means of reducing the threat to the population residing along the links of an entire transportation network. A multi‐objective decision‐making model is used for the mathematical formulation of the routing problem. The proposed model includes the following objectives: (1) Minimization of risk; (2) minimization of risk of special population categories; (3) minimization of travel time; and (4) minimization of property damages. A capacitated and a noncapacitated version of the multiobjective routing problem are presented. A hypothetical network is used to display the applicability of the proposed model. For the example under consideration it is shown that the imposition of capacity constraints on the links of the network tends to distribute the risk in an equitable manner while it increases the total risk by 35%.