Prize-collecting Vehicle Routing Problem Research Articles

A knowledge-based NSGA-II algorithm for multi-objective hot rolling production scheduling under flexible time-of-use electricity pricing

With the increasing demand and shortage of energy, the iron and steel industry has focused on achieving low-carbon and smart manufacturing. This study investigates an energy-oriented scheduling problem arising from hot rolling production under flexible time-of-use (TOU) electricity tariffs, where the electric power comes from both the enterprise-owned power plant and the state-owned power grid. First, we model the studied scheduling problem as a multi-objective prize-collecting vehicle routing problem with special constraints. This model selects slabs from the order pool and sequences them to form rolling units, aiming to simultaneously minimize the transition costs in specifications, penalty costs, and electricity costs. Next, we develop a knowledge-based NSGA-II algorithm (KB-NSGA-II) by introducing a self-adaptive recombination procedure and a shortest path search (SPS)-based local intensification procedure. Furthermore, the comparative experimental results indicate that the KB-NSGA-II outperforms other competing algorithms in terms of the following indicators: (1) the hypervolume indicator is improved by approximately 57%; (2) the Spacing indicator is decreased by approximately 40%; and (3) the success ratio indicator of KB-NSGA-II is at least 60% higher than that of other competing algorithms. Finally, we apply a multi-criteria decision-making method named VIKOR to a case study under flexible TOU pricing strategies. These comparison results and the case study confirm that the KB-NSGA-II algorithm obtained better computational performance than the other competing algorithms and provided more flexible solutions under TOU pricing.

An Improved NSGA-II for Energy-oriented Hot Rolling Production Scheduling Problems

With the sharply increasing energy demand and the shortage of energy, the scheduling goal of hot rolling production (HRP) is to select and sequence slabs to reduce cost and energy consumption. A multi-objective HRP optimal scheduling model is formulated and transferred as a multi-objective prize collecting vehicle routing problem (MO-PCVRP) with special constraints that simultaneously minimizes the jump cost of width, thickness, and hardness between adjacent slabs, the total length of unselected slabs, and the energy cost. Furthermore, this paper introduces a greedy strategy to intensify the local search of the standard NSGA-II algorithm, and names it local-intensification NSGA-II (LI-NSGA-II). The comparison experiments show that the LI-NSGA-II algorithm obtains better comprehensive performance than other compared algorithms in solving multi-objective scheduling problems of HRP.

Picker routing optimization of storage stacker based on improved multi-objective iterative local search algorithm

<p style='text-indent:20px;'>In the process of warehouse automation, the efficient picker routing strategy is one of the key factors to improve warehouse efficiency. According to the order and the picking characteristics of the warehouse stacker, the picker routing of the stacker is regarded as the prize-collecting vehicle routing problem (PCVRP). According to the path and order for stacker picking, we designed a picker routing optimization strategy based on improved multi-objective iterative local search (IMOILS) algorithm. An elite pool strategy was set to save the high-quality solutions in the iterative process, and the nondominated solutions in the iterative evolution were stored and updated. Adding the adaptive enhanced perturbation strategy was beneficial to the current solution to escape from local optimum. In the local search procedure, to limit the excessively large search space, the epsilon constraint was adopted to limit the significant deterioration in another objective direction. The computational results showed that the proposed algorithm is superior to the comparison algorithms in the number of nondominated solutions, the hypervolume, and the spacing metric, and the stability of the algorithm is also good, which not only verifies the effectiveness of the proposed algorithm, but also provides a feasible optimization scheme for the storage stacker's picker routing problem.</p>

Multi-Objective Prize-Collecting Vehicle Routing Problem with Multiple Depots: A Variable Neighborhood Search-Based Procedure

Multi-Objective Prize-Collecting Vehicle Routing Problem with Multiple Depots: A Variable Neighborhood Search-Based Procedure

A teaching–learning-based optimization algorithm for the environmental prize-collecting vehicle routing problem

A teaching–learning-based optimization algorithm for the environmental prize-collecting vehicle routing problem

Tourist group itinerary design: When the firefly algorithm meets the n-person Battle of Sexes

The presented research focuses on generating tourist trip itineraries for a group with different individual preferences on various points of interest. A set of walking routes among selected points of interest is provided by the Prize-Collecting Vehicle Routing Problem solution, considering several imposed constraints. However, the members of a tourist group request to stay together during their trip, despite their different preferences. Thus, to accommodate preferential heterogeneity in group itinerary design, the n-person Prize-Collecting Vehicle Routing Problem is proposed in this research, along with a novel, combined game theory and metaheuristic approach to solve it. Notably, the n-person Battle of Sexes game is utilized to configure a priori the set of locations to be visited, which results in three distinctive sets, depending on whether their visit is prohibited, mandatory, or optional. Consecutively, the metaheuristic firefly algorithm is employed to determine the tourist routes, enhanced with the coordinates-related encoding/decoding process. This process enables the original algorithm to solve discrete optimization problems without altering or hybridizing the original algorithmic framework. Compared with other metaheuristic algorithms, the proposed approach generates efficient and satisfactory tourist trip itineraries for heterogeneous groups.

The aquaculture service vessel routing problem with time dependent travel times and synchronization constraints

This paper studies the Aquaculture Service Vessel Routing Problem (ASVRP), which is an important planning problem arising in sea-based fish farming. In the ASVRP, there is a set of fish farms located in the sea, where each fish farm has one or more service tasks to be performed by a given heterogeneous fleet of service vessels with different capabilities. Some service tasks require simultaneous operation of more than one vessel and might also have time windows and precedence requirements. Furthermore, varying weather conditions make the sailing times and the service times of the tasks time dependent. The objective of the ASVRP is to maximize the value of the service tasks performed within a given planning horizon. We propose a time discrete optimization model for the ASVRP, formulated as a time dependent, prize collecting vehicle routing problem with synchronization constraints and time windows. Furthermore, we present an Adaptive Large Neighborhood Search (ALNS) heuristic for solving the problem. Results on a number of test instances based on real world data show that both the ALNS heuristic and a commercial solver are able to find high quality solutions for small problem instances, while the ALNS heuristic is superior when the problem size increases.

Research on hot rolling scheduling problem based on Two-phase Pareto algorithm.

Under the background of excess capacity and energy saving in iron and steel enterprises, the hot rolling batch scheduling problem based on energy saving is a multi-objective and multi constraint optimization problem. In this paper, a hybrid multi-objective prize-collecting vehicle routing problem (Hybrid Price Collect Vehicle Routing Problem, HPCVRP) model is established to ensure minimum energy consumption, meet process rules, and maximize resource utilization. A two-phase Pareto search algorithm (2PPLS) is designed to solve this model. The improved MOEA/D with a penalty based boundary intersection distance (PBI) algorithm (MOEA/D-PBI) is introduced to decompose the HPCVRP in the first phase. In the second phase, the multi-objective ant colony system (MOACS) and Pareto local search (PLS) algorithm is used to generate approximate Pareto-optimal solutions. The final solution is then selected according to the actual demand and preference. In the simulation experiment, the 2PPLS is compared with five other algorithms, which shows the superiority of 2PPLS. Finally, the experiment was carried out on actual slab data from a steel plant in Shanghai. The results show that the model and algorithm can effectively reduce the energy consumption in the process of hot rolling batch scheduling.

An interactive preference-guided firefly algorithm for personalized tourist itineraries

The present research proposes an interactive optimization framework to aid tourists to organize their trip by generating personalized walking itineraries among several Points of Interest (POIs). The solution of the multi-objective Prize-Collecting Vehicle Routing Problem (MO-PCVRP) is used to simulate this tourist trip design problem. The objectives of the proposed formulation are the minimization of the total distance walked among selected POIs, the minimization of a fixed cost related to the number of the created itineraries, and the maximization of the total satisfaction gained by visiting the selected POIs. The optimization of the MO-PCVRP is conducted by the proposed Preference-Guided Firefly Algorithm (PGFA), which allows for preferences articulated by a decision-maker (DM) to guide the search. The PGFA is incorporated into an interactive framework, where a DM provides his/her preferential information, progressively during the optimization process, by ranking a small representative set of Pareto optimal solutions. The DM’s articulated preferences are elicited utilizing a preference disaggregation method, the UTASTAR, which results in a preference model, which is ultimately used to guide the search towards the DM’s Region of Interest (ROI) in the Pareto front. The effectiveness and robustness of the proposed interactive PGFA framework are demonstrated over experimental scenarios.

A firefly algorithm for the environmental prize-collecting vehicle routing problem

In the present research, a new variant of the Vehicle Routing Problem (VRP), the Environmental Prize-Collecting Vehicle Routing Problem (E-PCVRP), is introduced. The E-PCVRP is a selective routing problem that focuses on the maximization of the aggregated prize values collected from the visited nodes while minimizing the fixed and variable cost of the formed routes. In terms of variable cost, the CO2 emissions of the vehicles performing the routes are considered as a load-distance function. The presented solution approach is based on the Firefly Algorithm (FA). The FA is an optimization algorithm, designed for the solution of continuous problems, while the proposed E-PCVRP, requires a discrete solution approach. Addressing the above discrepancy, the Firefly Algorithm based on Coordinates (FAC) is introduced, which incorporates the proposed “Coordinates Related” (CR) encoding/decoding process in the original FA scheme. The CR is a novel process that allows for algorithms designed for continuous optimization to by employed in the solution of discrete problems, such as the VRP. Specifically, the CR utilizes auxiliary vectors for solution representation, containing the Cartesian coordinates of each node, that allows for the original movement equation of the FA to be applied directly. The effectiveness of the FAC algorithm is showed over computational experiments and statistical analysis, in comparison to the performance of other bio-inspired algorithms and a mathematical solver. • The Environmental Prize-Collecting Vehicle Routing Problem is presented. • The objective function considers prize maximization and CO2 emissions minimization. • As the basis of the solution approach, the Firefly Algorithm has been chosen. • The novel CR encoding/decoding process is proposed and incorporated into FA's scheme. • Statistical analysis proves the significance of results obtained by the proposed FAC.

A hybrid multi-objective genetic local search algorithm for the prize-collecting vehicle routing problem

This paper studies the prize-collecting vehicle routing problem (PCVRP), which is a new variant of the vehicle routing problem. In the PCVRP, besides the vehicle assignment and visiting sequencing, customer selection also must be determined because the available vehicles are insufficient to visit all the customers. Two types of PCVRP are often encountered in the real world, namely the PCVRP in which the number of vehicles is predetermined (PCVRP-P) and that in which the number of vehicles is not predetermined (PCVRP-NP). In general, multiple optimization objectives are required to be considered in both the PCVRP-P and PCVRP-NP. Unlike the commonly used weighted-sum method, a Pareto-based evolutionary algorithm featuring a genetic algorithm combined with a local search strategy (denoted as HGLS) is proposed for solving the multi-objective PCVRP-P. Subsequently, based on the proposed HGLS, a decomposition strategy is designed to solve the multi-objective PCVRP-NP problem by decomposing it into multiple PCVRP-P problems. In order to determine the number of PCVRP-P problems in the decomposition strategy, a vehicle-number-range determination approach is proposed to obtain a tight upper bound and lower bound of the number of vehicles. The superiority of the proposed algorithm is demonstrated by conducting several experiments on the benchmark problems.

A two-level self-adaptive variable neighborhood search algorithm for the prize-collecting vehicle routing problem

This paper investigates the prize-collecting vehicle routing problem (PCVRP), which has a strong background in practical industries. In the PCVRP, the capacities of all available vehicles are not sufficient to satisfy the demands of all customers. Consequently it is not a compulsory requirement that all customers should be visited. However, a prize can be collected once a customer is visited. In addition, it is required that the total demands of visited customers should reach a pre-specified value at least. The objective is to establish a schedule of vehicle routes so as to minimize the total transportation cost and at the same time maximize the prize collected by all vehicles. The total transportation cost consists of the total distance of vehicle routes and the sum of vehicles used in the schedule. To solve the PCVRP, a two-level self-adaptive variable neighborhood search (TLSAVNS) algorithm is developed according to the two levels of decisions in the PCVRP, namely the selection of customers to visit and the visiting sequence of selected customers in each vehicle route. The proposed TLSAVNS algorithm is self-adaptive because the neighborhoods and their search sequence are determined automatically by the algorithm itself based on the analysis of its search history. In addition, a graph extension method is adopted to obtain the lower bound for PCVRP by transforming the proposed mixed integer programming model of PCVRP into an equivalent traveling salesman problem (TSP) model, and the obtained lower bound is used to evaluate the proposed TLSAVNS algorithm. Computational results on benchmark problems show that the proposed TLSAVNS algorithm is efficient for PCVRP.

The prize-collecting vehicle routing problem with single and multiple depots and non-linear cost

In this paper, we propose a new routing problem to model a highly relevant planning task in small package shipping. We consider the Prize-Collecting Vehicle Routing Problem with Non-Linear cost in its single and multi-depot version, which integrates the option of outsourcing customers to subcontractors instead of serving them with the private fleet. Thereby, a lower bound on the total customer demand to be served by the private fleet guarantees a high utilization of the fleet capacity. To represent the practical situation, where a discount is given by a subcontractor if larger amounts of packages are outsourced, subcontracting costs follow a non-linear function. The considered problem is NP-hard and we propose an Adaptive Variable Neighborhood Search algorithm to solve instances of realistic size. We propose new benchmark sets for the single and the multi-depot problem, which are adapted from test instances of the capacitated VRP and the closely related Multi-Depot VRP with Private fleet and Common carrier. In numerical studies, we investigate the performance of our algorithm on the newly generated test instances and on standard benchmark problems of related problems. Moreover, we study the effect of different cost functions and different values of the minimal demand to be served by the private fleet on the routing solutions obtained.

A multi-objective optimisation algorithm for the hot rolling batch scheduling problem

The hot rolling batch scheduling problem is a hard problem in the steel industry. In this paper, the problem is formulated as a multi-objective prize collecting vehicle routing problem (PCVRP) model. In order to avoid the selection of weight coefficients encountered in single objective optimisation, a multi-objective optimisation algorithm based on Pareto-dominance is used to solve this model. Firstly, the Pareto ℳ𝒜𝒳–ℳℐ𝒩 Ant System (P-ℳℳAS), which is a brand new multi-objective ant colony optimisation algorithm, is proposed to minimise the penalties caused by jumps between adjacent slabs, and simultaneously maximise the prizes collected. Then a multi-objective decision-making approach based on TOPSIS is used to select a final rolling batch from the Pareto-optimal solutions provided by P-ℳℳAS. The experimental results using practical production data from Shanghai Baoshan Iron & Steel Co., Ltd. have indicated that the proposed model and algorithm are effective and efficient.

Modeling and Solution for the Coil Sequencing Problem in Steel Color-Coating Production

This paper studies the problem of selecting coils and sequencing them to form a production plan by considering production practical requirements, which arises on the color coating line in the steel industry. The problem can be modeled as a generalization of the prize collecting vehicle routing problem which should make both sequencing and selecting decisions. We propose tabu search-based algorithm (TS) to solve the problem. After each move in the searching procedure, the sequencing decision is adjusted to optimal by a dynamic programming algorithm which can solve up to the industrial sized problem quickly. Thus, TS procedure essentially makes the selecting decision. To further improve the TS algorithm, composite neighborhoods involving block moves are proposed. In addition, compound moves are implemented by choosing improvement strategy from variable neighborhoods alternately at each iteration. To evaluate the performance of the TS algorithm, by reformulating the problem as a set covering model with double-side inequality capacity constraints, the lower bound is constructed using a column generation algorithm where the pricing problem is solved by dynamic programming method based on derived dominance rules. From the computation results based on randomly generated instances, the average deviation between the feasible solution and lower bound is 4.2334%, thus the performance of the proposed TS algorithm and column generation is demonstrated. Alternately, another TS algorithm without DP is proposed for the possible larger scale instances.

Two-stage Method for Solving Large-scale Hot Rolling Planning Problem in Steel Production

AbstractHot rolling (HR) planning is a multi-objective and multi-constraint large-scale combinatorial optimization problem. A prize-collecting vehicle routing problem (PCVRP) based model for HR planning is presented according to the demand of HR. The model considers many practical constraints and reasonable arrangement of warm-up materials and staple materials, but considers objectives such as product quality, productivity and ensuring the normal production of downstream production lines etc. A two-stage method for solving HR planning, namely planning rolling units firstly according to the demand of single mode rolling unit and then planning rolling units according to the demand of mix mode rolling unit, is proposed. A simulated annealing (SA) and ant colony optimization (ACO) based hybrid algorithm is used for solving the first stage problem. A variable neighborhood tabu search (VNTS) algorithm is used for solving the second stage problem. Computational results show the effectiveness of the proposed method.

Guided local search algorithm for hot strip mill scheduling problem with considering hot charge rolling

This study investigates the hot strip mill scheduling problem which is one of the most important planning problems in the steel industry. The problem is formulated using the prize collecting vehicle routing problem. The new proposed formulation considers more details and more realistic constraints than those used in previous studies. The hot charge technique leads to considerable savings in energy and other benefits in the process of steel production. In our proposed formulation, the necessary provisions required for obtaining an initial level of hot charge have been taken into consideration. A search algorithm has been developed that consists of three major phases including separation of slabs that can be scheduled, generation of an initial solution, and improvement of the solution. Generation of the initial solution is accomplished using a greedy constraint satisfaction algorithm and solution improvement through a guided local search. Proposed model and search algorithm have been tested on random and collected instances from practical production data in Mobarakeh Steel Complex. The experimental results show the high accuracy and efficiency of the proposed model and search algorithm.

The hot-rolling batch scheduling method based on the prize collecting vehicle routing problem

This paper studies a hot-rolling batch scheduling problem, which is a challenging problem commonly arising in the iron-steel industry. This problem deals with forming steel strips into rolling units and determining the rolling sequences while minimizing changes in characteristics (e.g., width, thickness and rigidity) of all neighbor steel strips and maximizing the machine utilization. Based on technical rules used in iron-steel production practice, we formulate this problem as a prize collecting vehicle routing problem, which is a hard combinatorial multi-objective optimization problem. We develop a new heuristic approach to solve this problem by enhancing the framework of particle swarm optimization (PSO). The key features of our approach are the utilization of number mapping function, which allows the PSO algorithm to deal with discrete problems, and the employment of tabu search at the end of every PSO iteration. We investigate and measure the performance of the proposed approach using three real life datasets obtained from a well-known iron-steel production company in China. The results suggest that our approach is very efficient and effective in providing high-quality and practical solutions, and our approach outperforms traditional PSO and tabu search algorithms based on these datasets.

Iterated local search algorithm based on very large-scale neighborhood for prize-collecting vehicle routing problem

This paper presents a new variant of the vehicle routing problem (VRP), the prize-collecting vehicle routing problem (PCVRP), which is derived from the hot rolling production of the iron and steel industry. One major characteristic of the PCVRP is that the customers need not be visited compulsorily but a prize can be collected from each customer when visited. Besides the capacity constraint, a task completion constraint is introduced and requires that the total demand of the visited customers should be no less than a predetermined amount. The main objective is a linear combination of three objectives: minimization of total distance traveled, minimization of vehicles used, and maximization of prizes collected. An iterated local search algorithm (ILS) based on very large-scale neighborhood (VLSN) using cyclic transfer is proposed for the PCVRP. Computational results of problem instances with up to 100 customers show the algorithm is efficient and effective.