Self-adaptive multi-objective harmony search for optimal design of water distribution networks

In multi-objective optimization computing, it is important to assign suitable parameters to each optimization problem to obtain better solutions. In this study, a self-adaptive multi-objective harmony search (SaMOHS) algorithm is developed to apply the parameter-setting-free technique, which is an example of a self-adaptive methodology. The SaMOHS algorithm attempts to remove some of the inconvenience from parameter setting and selects the most adaptive parameters during the iterative solution search process. To verify the proposed algorithm, an optimal least cost water distribution network design problem is applied to three different target networks. The results are compared with other well-known algorithms such as multi-objective harmony search and the non-dominated sorting genetic algorithm-II. The efficiency of the proposed algorithm is quantified by suitable performance indices. The results indicate that SaMOHS can be efficiently applied to the search for Pareto-optimal solutions in a multi-objective solution space.     

Optimal cost design of water distribution networks using harmony search

This study presents a cost minimization model for the design of water distribution networks. The model uses a recently developed harmony search optimization algorithm while satisfying all the design constraints. The harmony search algorithm mimics a jazz improvisation process in order to find better design solutions, in this case pipe diameters in a water distribution network. The model also interfaces with a popular hydraulic simulator, EPANET, to check the hydraulic constraints. If the design solution vector violates the hydraulic constraints, the amount of violation is considered in the cost function as a penalty. The model was applied to five water distribution networks, and obtained designs that were either the same or cost 0.28–10.26% less than those of competitive meta-heuristic algorithms, such as the genetic algorithm, simulated annealing and tabu search under similar or less favorable conditions. The results show that the harmony search-based model is suitable for water network design.     

A hybrid genetic algorithm for the multi-depot open vehicle routing problem

This paper studies the multi-depot open vehicle routing problem (MDOVRP), a variant of the vehicle routing problem (VRP), in which vehicles start from several depots and are not required to return to the depot. Despite the vast amount of literature about VRPs, the MDOVRP has received very little attention from researchers. In this paper, a new hybrid genetic algorithm is presented for finding the routes that minimize the traveling cost of the vehicles. Computational results on a number of test instances indicate the proposed algorithm dominates the CPLEX solver and the existing approach in the literature. Meanwhile, experiments are conducted on multi-depot VRP benchmarks, and the results are compared with a sophisticated tabu search approach and an exact method.     

带时限与回程的配送中心运输调度问题研究

在优化模型中将配送任务执行时间及每日调用车辆数量及路径作为决策对象,以车辆的固定费用、行驶费用、未按时完成服务产生的惩罚、存储费用等作为优化目标。在遗传算法中采用自然数编码形式以便于优化车辆数量,采用基于扫描算法的启发式算法构造更好的初始解,引入单亲遗传算子、重启机制及并行禁忌搜索以提高种群质量和深度寻优。经不同规模算例间对比测试,显示基于扫描算法的混合遗传算法具有最佳的优化性能。     

All-terminal network reliability optimization via probabilistic solution discovery

This paper presents a new algorithm that can be readily applied to solve the all-terminal network reliability allocation problems. The optimization problem solved considers the minimization of the network design cost subject to a known constraint on all-terminal reliability by assuming that the network contains a known number of functionally equivalent components (with different performance specifications) that can be used to provide redundancy. The algorithm is based on two major steps that use a probabilistic solution discovery approach and Monte Carlo simulation to generate the quasi-optimal network designs. Examples for different sizes of all-terminal networks are used throughout the paper to illustrate the approach. The results obtained for the larger networks with unknown optima show that the quality of the solutions generated by the proposed algorithm is significantly higher with respect to other approaches and that these solutions are obtained from restricted solution search space. Although developed for all-terminal reliability optimization, the algorithm can be easily applied in other resource-constrained allocation problems.     

Optimization of transit network layout and headway with a combined genetic algorithm and simulated annealing method

This article proposes a methodology for optimizing transit networks, including both route structures and headways. Given information on transit demand, transit fleet size and street network in the transit service area, the methodology seeks to minimize transfers and total user cost while maximizing service coverage. The goal is to provide an effective mathematical solution procedure with minimal reliance on heuristics to solve large-scale transit network optimization problems. This article describes the representation of the transit route network and the associated network search spaces, the representation of route network headways and the associated search spaces, the total user cost objective functions, and a stochastic global search scheme based on a combined genetic algorithm and simulated annealing search method. The methodology has been tested with published benchmark problems and applied to a large-scale realistic network optimization problem. The results show that the methodology is capable of producing improved solutions to large-scale transit network design problems.     

Optimal Scheduling of Track Maintenance on a Railway Network

To ensure the safety and continued operation of the railway network system, many maintenance and renewal activities are performed on the track every month. Unplanned maintenance activities are expensive and would cause low service quality. Therefore, the track condition should be monitored, and when it has degraded beyond some acceptable limit, it should be scheduled for maintenance before failure. An optimal timetable of the maintenance activities is needed to be scheduled, planning the monthly workload, to reduce the effect on the transportation service and to reduce the potential costs. Considering the uncertainties of the deterioration process, the safety of transportation service, the lifetime loss of the replaced track, the maintenance cost and the travel cost, this article advances an optimisation model for the maintenance scheduling of a regional railway network. An enhanced genetic algorithm approach is proposed to search for a solution producing maintenance schedule such that the overall cost is minimised in a finite planning horizon. A case study is given to demonstrate the application of the method. The case study results were derived by using an enhanced genetic algorithm method, which is specifically developed to deal with the characteristics of the railway maintenance problem. Copyright © 2012 John Wiley & Sons, Ltd.     

Deterministic network interdiction optimization via an evolutionary approach

This paper introduces an evolutionary optimization approach that can be readily applied to solve deterministic network interdiction problems. The network interdiction problem solved considers the minimization of the maximum flow that can be transmitted between a source node and a sink node for a fixed network design when there is a limited amount of resources available to interdict network links. Furthermore, the model assumes that the nominal capacity of each network link and the cost associated with their interdiction can change from link to link. For this problem, the solution approach developed is based on three steps that use: (1) Monte Carlo simulation, to generate potential network interdiction strategies, (2) Ford-Fulkerson algorithm for maximum s-t flow, to analyze strategies’ maximum source-sink flow and, (3) an evolutionary optimization technique to define, in probabilistic terms, how likely a link is to appear in the final interdiction strategy. Examples for different sizes of networks and network behavior are used throughout the paper to illustrate the approach. In terms of computational effort, the results illustrate that solutions are obtained from a significantly restricted solution search space. Finally, the authors discuss the need for a reliability perspective to network interdiction, so that solutions developed address more realistic scenarios of such problem.     

A Genetic Algorithm to Solve Capacity Assignment Problem in a Flow Network

Computer networks and power transmission networks are treated as capacitated flow networks. A capacitated flow network may partially fail due to maintenance. Therefore, the capacity of each edge should be optimally assigned to face critical situations—i.e., to keep the network functioning normally in the case of failure at one or more edges. The robust design problem (RDP) in a capacitated flow network is to search for the minimum capacity assignment of each edge such that the network still survived even under the edge’s failure. The RDP is known as NP-hard. Thus, capacity assignment problem subject to system reliability and total capacity constraints is studied in this paper. The problem is formulated mathematically, and a genetic algorithm is proposed to determine the optimal solution. The optimal solution found by the proposed algorithm is characterized by maximum reliability and minimum total capacity. Some numerical examples are presented to illustrate the efficiency of the proposed approach.     

An improved harmony search algorithm for emergency inspection scheduling

The ability of nature-inspired search algorithms to efficiently handle combinatorial problems, and their successful implementation in many fields of engineering and applied sciences, have led to the development of new, improved algorithms. In this work, an improved harmony search (IHS) algorithm is presented, while a holistic approach for solving the problem of post-disaster infrastructure management is also proposed. The efficiency of IHS is compared with that of the algorithms of particle swarm optimization, differential evolution, basic harmony search and the pure random search procedure, when solving the districting problem that is the first part of post-disaster infrastructure management. The ant colony optimization algorithm is employed for solving the associated routing problem that constitutes the second part. The comparison is based on the quality of the results obtained, the computational demands and the sensitivity on the algorithmic parameters.     

Models and algorithms for the heterogeneous dial-a-ride problem with driver-related constraints

This paper introduces models and algorithms for a static dial-a-ride problem arising in the transportation of patients by non-profit organizations such as the Austrian Red Cross. This problem is characterized by the presence of heterogeneous vehicles and patients. In our problem, two types of vehicles are used, each providing a different capacity for four different modes of transportation. Patients may request to be transported either seated, on a stretcher or in a wheelchair. In addition, some may require accompanying persons. The problem is to construct a minimum-cost routing plan satisfying service-related criteria, expressed in terms of time windows, as well as driver-related constraints expressed in terms of maximum route duration limits and mandatory lunch breaks. We introduce both a three-index and a set-partitioning formulation of the problem. The linear programming relaxation of the latter is solved by a column generation algorithm. We also propose a variable neighborhood search heuristic. Finally, we integrate the heuristic and the column generation approach into a collaborative framework. The column generation algorithm and the collaborative framework provide tight lower bounds on the optimal solution values for small-to-medium-sized instances. The variable neighborhood search algorithm yields high-quality solutions for realistic test instances.     

A simple metaheuristic approach to the simultaneous scheduling of machines and automated guided vehicles

In this paper we address the problem of simultaneous scheduling of machines and vehicles in flexible manufacturing systems. The studied problem is a job shop where the jobs have to be transported between the machines by automatic guided vehicles. In addition to the processing of jobs, we consider the transportation aspect as an integral part of the optimization process. To deal with this problem, we propose a new solution representation based on vehicles rather than machines. Each solution can thus be evaluated using a discrete event approach. An efficient neighbouring system is then described and implemented into three different metaheuristics: iterated local search, simulated annealing and their hybridisation. Computational results are presented for a benchmark of 40 literature instances. New upper bounds are found for 11 of them, showing the effectiveness of the presented approach.     

Tabu search algorithm for flexible flow path design of unidirectional automated-guided vehicle systems

The unidirectional flow path design problem is one of the most important but difficult problems for the efficient design of automated-guided vehicle systems. As the problem was first formulated by Gaskins and Tanchoco, many researchers have studied the problem. However, the existing solution methods fail to provide an efficient solution approach. In this paper, a mathematical model for the unidirectional flow path design problem is developed. To obtain a near-to-optimal solution in reasonable computation time, a tabu search algorithm is presented. A fast construction algorithm first obtains a feasible initial solution, and a long-term memory structure and a neighbor solution generation approach are adapted to the problem characteristics and embedded in the proposed tabu search algorithm. Computational experiments show that the developed tabu search algorithm outperforms the Ko and Egbelu’s algorithm, Int J Prod Res, 41:2325–2343, (2003).     

A highly optimised tolerance-based approach for multi-stage,multi-product supply chain network design

In this paper we propose an algorithm called Highly Optimised Tolerance (HOT) for solving a multi-stage, multi-product supply chain network design problem. HOT is based on power law and control theory. The proposed approach takes its traits from the local incremental algorithm (LIA), which was initially employed to maximise the design parameter (i.e. yield), particularly in the percolation model. The LIA is somewhat analogous to the evolution by natural selection schema. The proposed methodology explores a wide search space and is computationally viable. The HOT algorithm tries to make the system more robust at each step of the optimisation. The objective of this paper is to reduce the total cost of supply chain distribution by selecting the optimum number of facilities in the network. To examine the effectiveness of the HOT algorithm we compare the results with those obtained by applying simulated annealing on a supply chain network design problem with different problem sizes and the same data sets.     

Mathematical formulation and heuristic algorithms for optimisation of auto-part milk-run logistics network considering forward and reverse flow of pallets

The operational planning of distribution network for automotive industry is complex with many conditions to consider, including heterogeneous fleet, enforcing the feasibility of 3D-packing of pallets into vehicles to address the vehicle's capacity in terms of weight and volume, compatibility of orders in a vehicle, returning empty pallets from assembly-plants backwards to suppliers, and delivery time windows. A mathematical model (MILP) is proposed that takes account of these conditions to minimise total transportation costs. The network structure can be a combination of direct shipment and milk-run for both forward and reverse flow of pallets. The model is solved optimally for small-size problems. For solving larger problems, a heuristic algorithm (in two versions) is proposed that uses a similarity measure to generate a reasonable list of orders. Best/first-fit strategies are employed to generate a feasible solution with the aid of a relaxed version of the proposed MILP. Improvement heuristics are also designed. Unlike most of existing constructive heuristics, our aim for developing the heuristic approach is to force routing decision, with all of its considerations, being made optimal. We also use the proposed best-fit strategy in the body of grouping evolution strategy (GES) algorithm to attain an effective meta-heuristic approach. The effectiveness of heuristics is tested on generated instances which demonstrates they are optimal for small-size problems. They are also tested on the data of daily auto-parts shipments gathered from the largest Iranian automobile company. Results demonstrate there exists a significant potential for cost saving through milk-run strategy compared with the direct shipping strategy.     

Evaluating artificial intelligence heuristics for a flexible Kanban system: simultaneous Kanban controlling and scheduling

This paper evaluates several artificial intelligence heuristics for a simultaneous Kanban controlling and scheduling on a flexible Kanban system. The objective of the problem is to minimise a total production cost that includes due date penalty, inventory, and machining costs. We show that the simultaneous Kanban controlling and scheduling is critical in minimising the total production cost (approximately 30% cost reduction over scheduling without a Kanban controlling). To identify the most effective search method for the simultaneous Kanban controlling and scheduling, we evaluated widely known artificial intelligence heuristics: genetic algorithm, simulated annealing, tabu search, and neighbourhood search. Computational results show that the tabu search performs the best in terms of solution quality. The tabu search also requires a much less computational time than the genetic algorithm and the simulated annealing. To further improve the solution quality and computational time for a simultaneous Kanban controlling and scheduling on a flexible Kanban system, we developed a two-stage tabu search. At the beginning of the tabu search process, an initial solution is constructed by utilising the customer due date information given by a decision support system. The two-stage tabu search performs better than the tabu search with a randomly generated initial solution in both the solution quality and computational time across all problem sizes. The difference in the solution quality is more pronounced at the early stages of the search.     

Considering displacement modes in the fleet management problem

This paper presents two solution approaches for taking into account the displacement mode (forward or in reverse) of vehicles during the solution of the shortest path problem. In the first approach, a graph including all aspects of the problem is constructed and a classical shortest path algorithm is used to solve the problem. In the second approach, a more simple graph is constructed, and all the constraints of the problem are considered during the solution of the shortest path problem. This problem is important for routing a fleet of automated vehicles on a one-lane bidirectional graph.     

Two effective approaches for hydroelectric generation scheduling

Abstract

This paper presents and compares two systematic and effective approaches for the hydroelectric generation scheduling problem (HSP). The objective of the HSP is to determine the best substitution of hydro energy for thermal energy in electric generation so that the fuel cost is minimized while meeting the system load and constraints. In the first approach, HSP is formulated as an optimal control problem, for which a multiplier method‐based differential dynamic programming algorithm developed by Chen et al. [4] is adopted as the solution algorithm. The second approach exploits the network structure of the water balance relation and takes linear approximation of the first formulation to formulate HSP as a minimum cost, linear network flow problem. Bertsekas and Tsengs’ RELAX code is applied to solve such a large‐scale network optimization problem. Numerical results indicate that both approaches generate results close to TPC's empirical schedules, are efficient in computation and suggest predictive operation strategies. We address the differences between the two approaches in solution optimality and computational efficiency and provide necessary information for tradeoffs in selecting a suitable approach.     

Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm

The vehicle routing problem (VRP) is a well-known combinatorial optimisation problem and holds a central place in logistics management. Many exact, heuristic and metaheuristic approaches have been proposed to solve VRP. An important variant of the VRP arises when a ?eet of vehicles is fixed and characterised by different capacities for distribution activities. The problem is known as the heterogeneous fixed fleet VRP (HFFVRP). The HFFVRP is a natural generalisation of the VRP with several vehicle types, each type being defined by a capacity, a fixed cost and a cost per distance unit, and can cover more practical situations in transportation. This problem consists of determining a set of vehicle trips of minimum total length in which a set of customers is to be satisfied in the demand constraints using identical vehicles with limited capacity. If open routes instead of closed ones are considered in the HFFVRP, the problem becomes a heterogeneous fixed fleet Open VRP (HFFOVRP) which has numerous applications in industrial and service problems. In this paper, a bone route algorithm which uses the tabu search as an improved procedure is utilised to solve the HFFOVRP. The proposed algorithm was tested empirically on a 24 of generated VRPs, and compared with elite ant system and ant colony system. In all cases, the proposed algorithm finds the best-known solutions within a reasonable time.     

Vehicle dispatching algorithms for container transshipment hubs

This paper seeks to address the dispatching problem for vehicles (or prime movers) in a transshipment hub by considering the quay cranes and yard cranes capacity. The objective of this paper is to minimize the makespan time at the quay side. This issue is particularly important for a port which uses information technology in making real time decision because the port can exploit information technology to make full use of the data in making good decision. A mixed integer programming (MIP) model is developed to formulate the problem. As the existing solver cannot solve the MIP model in reasonable time, we develop two heuristics to tackle the problem. The first method is based on the neighborhood search, while the second method is based on genetic algorithm (GA) and minimum cost flow (MCF) network model. Unlike the typical GA which usually represents the chromosome using job sequence, we use the ready time for jobs as the representation of the chromosome, and MCF model is then used to decode the chromosome to determine the job sequence for prime movers. The experiment results indicate the superiority of the GA–MCF-based algorithm over the neighborhood search algorithm.