Multi-objective Network Design Problem Research Articles

Pareto-Optimal Sustainable Transportation Network Design under Spatial Queuing

This paper presents a multi-objective network design problem with environmental considerations for urban networks with queues. A spatial queuing link model is introduced to take account of the spatial effect of queuing. With this more realistic link performance function capturing spatial queuing, the network equilibrium flow patterns can be more accurately identified. Furthermore, to better estimate vehicle emissions, this paper proposes a refined emission estimation model, which distinguishes between travel speeds in free-running state and queue-forming state over a link. A multi-objective bi-level programming is then developed, in which the upper-level problem optimizes the investment decisions, whereas the lower-level problem characterizes the user equilibrium with spatial queuing delays. The metaheuristic of non-dominated sorting genetic algorithm II (NSGA-II) is adopted to solve the multi-objective network design problem. Numerical tests on the Sioux Falls network and the Barcelona network confirm the effectiveness of our proposed model and algorithm in identifying queuing equilibrium flows and Pareto optimal solutions. The refined models and valuable information about trade-offs among objectives are particularly helpful for environmentally sustainable transport network planning.

A node-depth phylogenetic-based artificial immune system for multi-objective Network Design Problems

Abstract Network Design Problems (NDP) constitute a traditional class of combinatorial optimization problems. They usually rely on finding an optimal tree on a graph that respects the particular constraints of the problem at hand. When using evolutionary algorithms to solve NDP, one can use specific encodings to represent a tree. A newly proposed tree encoding in the literature is the Node-depth Phylogenetic-based encoding (NPE), which possess small time and space complexity, among other desirable characteristics. In this work, we propose the first metaheuristic on the literature that implements the NPE, the Node-depth Phylogenetic-based Non-dominated Sorting Artificial Immune System (NPE-NSAIS). We assess the quality of the proposed algorithm by solving a bi-objective NDP, the Minimum-Cost Bounded-Error Calibration Tree problem (MBCT). Our results reveal that the NPE-NSAIS outperforms the state-of-the-art algorithm for the MBCT. Moreover, we show that the NPE-NSAIS outperforms three other NSAIS algorithms that employ different encodings, the NSGA-II, and the SPEA2.

A model for multi-class road network recovery scheduling of regional road networks

In this paper, an optimisation model for recovery planning of road networks is presented in which both social and economic resilience is aimed to be achieved. The model is formulated as a bi-level multi-objective discrete network design problem which forms a non-convex mixed integer non-linear problem. Solved by a Branch and Bound method, the solution algorithm employs an outer approximation method to estimate the lower bound of each node in the Branch and Bound search tree. The solution algorithm exploits a unique approach for lower-bound computation dealing with a disrupted multi-class network that may not be able to satisfy the demand between all OD pairs due to damaged links. The model is assessed by applying it on the Sioux Falls network. It is also illustrated how the Pareto-optimal solutions achieved by the multi-objective optimisation can vary depending on the emphasis placed on different classes of vehicles.

The multi-objective network design problem using minimizing externalities as objectives: comparison of a genetic algorithm and simulated annealing framework

Incorporation of externalities in the Multi-Objective Network Design Problem (MO NDP) as objectives is an important step in designing sustainable networks. In this research the problem is defined as a bi-level optimization problem in which minimizing externalities are the objectives and link types which are associated with certain link characteristics are the discrete decision variables. Two distinct solution approaches for this multi-objective optimization problem are compared. The first heuristic is the non-dominated sorting genetic algorithm II (NSGA-II) and the second heuristic is the dominance based multi objective simulated annealing (DBMO-SA). Both heuristics have been applied on a small hypothetical test network as well as a realistic case of the city of Almelo in the Netherlands. The results show that both heuristics are capable of solving the MO NDP. However, the NSGA-II outperforms DBMO-SA, because it is more efficient in finding more non-dominated optimal solutions within the same computation time and maximum number of assessed solutions.

Performance of a Genetic Algorithm for Solving the Multi-Objective, Multimodal Transportation Network Design Problem

The optimization of infrastructure planning in a multimodal network is defined as a multi-objective network design problem, with accessibility, use of urban space by parking, operating deficit and climate impact as objectives. Decision variables are the location of park and ride facilities, train stations and the frequency of public transport lines. For a case study the Pareto set is estimated by the Non-dominated Sorting Genetic Algorithm (NSGA-II). Such a Pareto set is one specific outcome of the optimization process, for a specific value of the parameters generation size, number of generations and mutation rate and for a specific outcome of the Monte Carlo simulation within NSGA-II. Similar issues exist for many other metaheuristics. However, when applied in practice, a policy maker desires a result that is robust for these unknown aspects of the method. In this paper Pareto sets from various runs of the NSGA-II algorithm are analyzed and compared. To compare the values of the decision variables in the Pareto sets, new methods are necessary, so these are defined and applied. The results show that the differences concerning decision variables are considerably larger than the differences concerning objectives. This indicates that the randomness of the algorithm may be a problem when determining the decisions to be made. Furthermore, it is concluded that variations caused by different parameters are comparable with the variations caused by randomness within the algorithm.

Handling multiple objectives in optimization of externalities as objectives for dynamic traffic management

Dynamic traffic management (DTM) is acknowledged in various policy documents as an important instrument to improve network performance. This network performance is not only a matter of accessibility, since the externalities of traffic are becoming more and more important objectives as well. Optimization of network performance using DTM measures is a specific example of a network design problem (NDP) and incorporation of externality objectives results in a multi objective network design problem (MO NDP)). Solving this problem resorts in a Pareto optimal set of solutions. A framework is presented with the non-dominated sorting algorithm (NSGAII), the Streamline dynamic traffic assignment model and several externality models, that is used to solve this MO NDP. With a numerical experiment it is shown that the Pareto optimal set provides important information for the decision making process, which would not have been available if the optimization problem was simplified by incorporation of a compensation principle in advance. However, in the end a solution has to be chosen as the best compromise. Since the Pareto optimal set can be difficult to comprehend, ranking it may be necessary to assist the decision makers. Cost benefit analysis which uses the economic compensation principle is a method that is often used for ranking the alternatives. This research shows, that travel time costs are by far the most dominant objective. Therefore other ranking methods should be considered. Differences between these methods are explained and it is illustrated that the outcomes and therefore the eventual decisions taken can be different.

A fuzzy goal programming approach to solve multi-objective supply chain network design problems

A fuzzy goal programming approach to solve multi-objective supply chain network design problems

Genetic Algorithm Performance with Different Selection Methods in Solving Multi-Objective Network Design Problem

Selection is one of the key operations of genetic algorithm (GA). This paper presents a comparative analysis of GA performance in solving multi-objective network design problem (MONDP) using different parent selection methods. Three problem instances were tested and results show that on the average tournament selection is the most effective and most efficient for 10-node network design problem, while Ranking & Scaling is the least effective and least efficient. For 21-node and 36-node network problems, Roulette Wheel is the least effective but most efficient while Ranking & Scaling equals and outperformed tournament in effectiveness and efficiency respectively.

Solution of preemptive multi-objective network design problems applying Benders decomposition method

This paper deals with preemptive priority based multi-objective network design problems in which construction times together with travel costs are taken into account. These cost and time objective functions are ordered lexicographically with respect to manager’s strategies in order to decrease total cost and total construction time of the network. To solve this preemptive problem, instead of the standard sequential approach, a modified Benders decomposition algorithm is developed. It is proved that this algorithm decreases the (expected) number of computations and so this algorithm is efficient for large-scale network design problems.

Acceleration of Solving the Dynamic Multi-Objective Network Design Problem Using Response Surface Methods

Optimization of externalities and accessibility using dynamic traffic management measures on a strategic level is a specific example of solving a multi-objective network design problem. Solving this optimization problem is time consuming, because heuristics like evolutionary multi objective algorithms are needed and solving the lower level requires solving the dynamic user equilibrium problem. Using function approximation like response surface methods (RSM) in combination with evolutionary algorithms could accelerate the determination of the Pareto optimal set. Three algorithms in which RSM are used in different ways in combination with the Strength Pareto Evolutionary Algorithm 2+ (SPEA2+) are compared with employing the SPEA2+ without the use of these methods. The results show that the algorithms using RSM methods accelerate the search considerably at the start, but tend to converge more quickly, possibly to a local optimum, and therefore loose their head start. Therefore, usage of function approximation is mainly of interest if a limited number of exact evaluations can be done or this can be used as a pre phase in a hybrid approach.

Pruning and ranking the Pareto optimal set, application for the dynamic multi‐objective network design problem

SUMMARYSolving the multi‐objective network design problem (MONDP) resorts to a Pareto optimal set. This set can provide additional information like trade‐offs between objectives for the decision making process, which is not available if the compensation principle would be chosen in advance. However, the Pareto optimal set of solutions can become large, especially if the objectives are mainly opposed. As a consequence, the Pareto optimal set may become difficult to analyze and to comprehend. In this case, pruning and ranking becomes attractive to reduce the Pareto optimal set and to rank the solutions to assist the decision maker. Because the method used, may influence the eventual decisions taken, it is important to choose a method that corresponds best with the underlying decision process and is in accordance with the qualities of the data used. We provided a review of some methods to prune and rank the Pareto optimal set to illustrate the advantages and disadvantages of these methods. The methods are applied using the outcome of solving the dynamic MONDP in which minimizing externalities of traffic are the objectives, and dynamic traffic management measures are the decision variables. For this, we solved the dynamic MONDP for a realistic network of the city Almelo in the Netherlands using the non‐dominated sorting genetic algorithm II. For ranking, we propose to use a fuzzy outranking method that can take uncertainties regarding the data quality and the perception of decision makers into account; and for pruning, a method that explicitly reckons with significant trade‐offs has been identified as the more suitable method to assist the decision making process. Copyright © 2012 John Wiley & Sons, Ltd.

Effects of Optimizing Externalities Using Cooperating Dynamic Traffic Management Measures on Network Level

Optimization of traffic network performance using dynamic traffic management (DTM) measures can be viewed as a specific example of solving a network design problem (NDP). Decision variables are the specific settings of DTM measures. DTM measures have been identified as powerful instruments not only to increase network efficiency, but also to improve externalities. As a result, in the optimization the focus is not only on efficiency, but also on climate, air quality, traffic safety, and noise. These assessment criteria are determined using the output of a dynamic traffic assignment model. This results in a dynamic multi-objective NDP, which is solved as a bilevel optimization problem; it results in a Pareto optimal set. This set provides valuable information for the decision-making process, which would not have been available if the compensation principle would have been chosen in advance. Knowledge obtained by optimization of realistic cases can be used to attain knowledge about incorporation of externalities as an objective when optimizing traffic systems using DTM measures. A case study for a realistic network of the city of Almelo shows that the objectives efficiency, climate, and air quality are mainly aligned and mainly opposed to traffic safety and noise. However, there is not a single solution that optimizes all three aligned objectives. Based on the Pareto optimal set, the trade-offs are determined and using cluster analysis the solutions and results are further analyzed for network segments.

Comparison of Multiobjective Evolutionary Algorithms for Optimization of Externalities by Using Dynamic Traffic Management Measures

The externalities of traffic are increasingly important for policy decisions related to design of a road network. Optimization of externalities with dynamic traffic management measures influencing the supply of infrastructure is a multiobjective network design problem, which in turn is a bi-level optimization problem. The presence of conflicting objectives makes the solution to the optimization problem a challenge. Evolutionary multiobjective algorithms have proved successful in solving such problems. However, like all optimization methods, these are subject to the no-free-lunch theorem. Therefore, this paper compares the nondominated sorting genetic algorithm II (NSGA-II), the strength Pareto evolutionary algorithm 2 (SPEA2), and the strength Pareto evolutionary algorithm 2+ (SPEA2+) to find a Pareto optimal solution set for this problem. Because incorporation of traffic dynamics is important, the lower level should be solved through a dynamic traffic assignment model, which increases needed CPU time. Therefore, algorithm performance is compared within a certain budget. The approaches are compared in a numerical experiment through different metrics. The externalities optimized are noise, climate, and congestion. The results show that climate and congestion are aligned and that both are opposed to noise in the case study. On average, SPEA2+ outperforms SPEA2 in this problem on all used measures. Results of NSGA-II and SPEA2+ are inconclusive. A larger population results on average in a larger space coverage, while a smaller population results in higher performance on spacing and diversity. Most performance measures are relatively insensitive for the mutation rate.

Pareto Optimal Multiobjective Optimization for Robust Transportation Network Design Problem

A study was done to formulate and solve the multiobjective network design problem with uncertain demand. Various samples of demand are realized for optimal improvements in the network while the objectives of the expected total system travel time and the higher moment for total system travel time are minimized. A formulation is proposed for multi-objective robust network design, and a solution methodology is developed on the basis of a revised fast and elitist nondominated sorting genetic algorithm. The developed methodology has been tested on the Nguyen-Dupuis network, and various Pareto optimal solutions are compared with earlier work on the single-objective robust network design problem. A real medium-size network was solved to prove efficacy of the model. The results show better solutions for the multiobjective robust network design problem with relatively less computational effort.

Multiobjective transportation network design and routing problems: Taxonomy and annotation

In this paper we update an earlier review of multiobjective network design and routing problems. Forty-one articles are annotated. The diversity of objectives presented demonstrates the multiobjective nature of such problems and the difficulty of measuring these objectives in commensurate units. The variety of problems addressed reflects the importance and complexity of transportation network analysis.