New Genetic Algorithms Based Approaches to Continuous <Emphasis Type="Italic">p</Emphasis>-Median Problem

We proposed new genetic algorithms (GAs) to address well-known p-median problem in continuous space. Two GA approaches with different replacement procedures are developed to solve this problem. To make the approaches more efficient in finding near-optimal solution two hybrid algorithms are developed combining the new GAs and a traditional local search heuristic. The performance of the newly developed models is compared to that of the traditional alternating location-allocation heuristics by numerical simulation and it is found that the models are effective in finding optimum facility locations.     

New heuristic algorithms for solving the planar p-median problem

In this paper we propose effective heuristics for the solution of the planar p-median problem. We develop a new distribution based variable neighborhood search and a new genetic algorithm, and also test a hybrid algorithm that combines these two approaches. The best results were obtained by the hybrid approach. The best known solution was found in 466 out of 470 runs, and the average solution was only 0.000016% above the best known solution on 47 well explored test instances of 654 and 1060 demand points and up to 150 facilities.     

Initialization strategies to enhancing the performance of genetic algorithms for the p-median problem

Finding solutions to the p-median problem is an important research topic in location science. A number of meta-heuristic methods have been developed in the literature to find optimal or near optimal solutions to large-scale p-median problems within an acceptable computational time. Among these methods, the recent literature has demonstrated the effectiveness of genetic algorithms (GAs) and hybrid GAs. In this paper, we focus on the strategies of generating the initial population of a genetic algorithm and examine the impact of such strategies on the overall GA performance in terms of solution quality and computational time. Our initialization approach first produces a near optimal solution with low computational complexity, and then uses this solution as a seed to generate a set of solutions as the initial GA population, which is then used in an existing hybrid GA to test the performance of the proposed approach. Experiments based on the forty p-median problems in the OR Library are conducted. Results demonstrate that the proposed approach can significantly reduce computational time without compromising the quality of resulting solutions in almost all cases, and the excellence of the proposed approach increases with the problem scale. Furthermore, a geo-referenced dataset is also tested and the resulting solution maps visualize and validate the principle of the proposed approach.     

Stochastic Local Search Algorithms for Graph Set <Emphasis Type="Italic">T</Emphasis>-colouring and Frequency Assignment

The graph set T-colouring problem (GSTCP) generalises the classical graph colouring problem; it asks for the assignment of sets of integers to the vertices of a graph such that constraints on the separation of any two numbers assigned to a single vertex or to adjacent vertices are satisfied and some objective function is optimised. Among the objective functions of interest is the minimisation of the difference between the largest and the smallest integers used (the span). In this article, we present an experimental study of local search algorithms for solving general and large size instances of the GSTCP. We compare the performance of previously known as well as new algorithms covering both simple construction heuristics and elaborated stochastic local search algorithms. We investigate systematically different models and search strategies in the algorithms and determine the best choices for different types of instance. The study is an example of design of effective local search for constraint optimisation problems.     

Local Search Heuristics for Capacitated p-Median Problems

The search for p-median vertices on a network (graph) is a classical location problem. The p facilities (medians) must be located so as to minimize the sum of the distances from each demand vertex to its nearest facility. The Capacitated p-Median Problem (CPMP) considers capacities for the service to be given by each median. The total service demanded by vertices identified by p-median clusters cannot exceed their service capacity. Primal-dual based heuristics are very competitive and provide simultaneously upper and lower bounds to optimal solutions. The Lagrangean/surrogate relaxation has been used recently to accelerate subgradient like methods. The dual lower bound have the same quality of the usual Lagrangean relaxation dual but is obtained using modest computational times. This paper explores improvements on upper bounds applying local search heuristics to solutions made feasible by the Lagrangean/surrogate optimization process. These heuristics are based on location-allocation procedures that swap medians and vertices inside the clusters, reallocate vertices, and iterate until no improvements occur. Computational results consider instances from the literature and real data obtained using a geographical information system.     

Artificial intelligence heuristics in solving vehicle routing problems with time window constraints

This paper describes the authors’ research on various heuristics in solving vehicle routing problem with time window constraints (VRPTW) to near optimal solutions. VRPTW is NP-hard problem and best solved to near optimum by heuristics. In the vehicle routing problem, a set of geographically dispersed customers with known demands and predefined time windows are to be served by a fleet of vehicles with limited capacity. The optimized routines for each vehicle are scheduled as to achieve the minimal total cost without violating the capacity and time window constraints. In this paper, we explore different hybridizations of artificial intelligence based techniques including simulated annealing, tabu search and genetic algorithm for better performance in VRPTW. All the implemented hybrid heuristics are applied to solve the Solomon's 56 VRPTW with 100-customer instances, and yield 23 solutions competitive to the best solutions published in literature according to the authors’ best knowledge.     

Solving bus terminal location problems using evolutionary algorithms

Bus terminal assignment with the objective of maximizing public transportation service is known as bus terminal location problem (BTLP). We formulate the BTLP, a problem of concern in transportation industry, as a p-uncapacitated facility location problem (p-UFLP) with distance constraint. The p-UFLP being NP-hard (Krarup and Pruzan, 1990), we propose evolutionary algorithms for its solution. According to the No Free Lunch theorem and the good efficiency of the distinctive preserve recombination (DPX) operator, we design a new recombination operator for solving a BTLP by new evolutionary and memetic algorithms namely, genetic local search algorithms (GLS). We also define the potential objective function (POF) for the nodes and design a new mutation operator based on POF. To make the memetic algorithm faster, we estimate the variation of the objective function based on POF in the local search as part of an operator in memetic algorithms. Finally, we explore numerically the performance of nine proposed algorithms on over a thousand randomly generated problems and select the best two algorithms for further testing. The comparative studies show that our new hybrid algorithm composing the evolutionary algorithm with the GLS outperforms the multistart simulated annealing algorithm.     

Solving the feeder bus network design problem by genetic algorithms and ant colony optimization

This paper proposes the design and analysis of two metaheuristics, genetic algorithms and ant colony optimization, for solving the feeder bus network design problem. A study of how these proposed heuristics perform is carried out on several randomly generated test problems to evaluate their computational efficiency and the quality of solutions obtained by them. The results are also compared to those published in the literature. Computational experiments have shown that both heuristics are comparable to the state-of-the-art algorithms such as simulated annealing and tabu search.     

Optimization of one-dimensional Bin Packing Problem with island parallel grouping genetic algorithms

The well-known one-dimensional Bin Packing Problem (BPP) of whose variants arise in many real life situations is a challenging NP-Hard combinatorial optimization problem. Metaheuristics are widely used optimization tools to find (near-) optimal solutions for solving large problem instances of BPP in reasonable running times. With this study, we propose a set of robust and scalable hybrid parallel algorithms that take advantage of parallel computation techniques, evolutionary grouping genetic metaheuristics, and bin-oriented heuristics to obtain solutions for large scale one-dimensional BPP instances. A total number of 1318 benchmark problems are examined with the proposed algorithms and it is shown that optimal solutions for 88.5% of these instances can be obtained with practical optimization times while solving the rest of the problems with no more than one extra bin. When the results are compared with the existing state-of-the-art heuristics, the developed parallel hybrid grouping genetic algorithms can be considered as one of the best one-dimensional BPP algorithms in terms of computation time and solution quality.     

An experimental evaluation of local search heuristics for graph partitioning

A common problem that arises in many applications is to partition the vertices of a graph intok subsets, each containing a bounded number of vertices, such that the number of graph edges with endpoints in different subsets is minimized. This paper describes an empirical study of the performance of various local search heuristics for thisk-way graph partitioning problem. The heuristics examined are local optimization, simulated annealing, tabu search, and genetic algorithms. In addition, the hierarchical hybrid approach is introduced, in which the problem is recursively decomposed into small pieces, to which local search heuristics are then applied.     

Evolutionary algorithms for scheduling m-machine flow shop with lot streaming

This paper addresses the problem of making sequencing and scheduling decisions for n jobs–m-machines flow shops under lot sizing environment. Lot streaming (Lot sizing) is the process of creating sub lots to move the completed portion of a production sub lots to down stream machines. There is a scope for efficient algorithms for scheduling problems in m-machine flow shop with lot streaming. In recent years, much attention is given to heuristics and search techniques. Evolutionary algorithms that belong to search heuristics find more applications in recent research. Genetic algorithm (GA) and hybrid genetic algorithm (HEA) also known as hybrid evolutionary algorithm fall under evolutionary heuristics. On this concern this paper proposes two evolutionary algorithms namely, GA and HEA to evolve best sequence for makespan/total flow time criterion for m-machine flow shop involved with lot streaming and set-up time. The following two algorithms are used to evaluate the performance of the proposed GA and HEA: (i) Baker's algorithm (BA), an optimal solution procedure for two-machine flow shop problem with lot streaming and makespan objective criterion and (ii) simulated annealing algorithm (SA) for m-machine flow shop problem with lot streaming and makespan and total flow time criteria.     

Genetic scheduling for parallel processor systems: comparativestudies and performance issues

Task scheduling is essential for the proper functioning of parallel processor systems. Scheduling of tasks onto networks of parallel processors is an interesting problem that is well-defined and documented in the literature. However, most of the available techniques are based on heuristics that solve certain instances of the scheduling problem very efficiently and in reasonable amounts of time. This paper investigates an alternative paradigm, based on genetic algorithms, to efficiently solve the scheduling problem without the need to apply any restricted assumptions that are problem-specific, such is the case when using heuristics. Genetic algorithms are powerful search techniques based on the principles of evolution and natural selection. The performance of the genetic approach will be compared to the well-known list scheduling heuristics. The conditions under which a genetic algorithm performs best will also be highlighted. This will be accompanied by a number of examples and case studies     

A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems

This paper investigates the first hybrid scatter search and path relinking meta-heuristic for the Delay-Constrained Least-Cost (DCLC) multicast routing problem. The underpinning mathematic model of the DCLC multicast routing problem is the constrained Steiner tree problem in graphs, a well known NP-complete problem. After combining a path relinking method as the solution combination method in scatter search, we further explore two improvement strategies: tabu search and variable neighborhood search, to intensify the search in the hybrid scatter search algorithm. A large number of simulations on some benchmark instances from the OR-library and a group of random graphs of different characteristics demonstrate that the improvement strategy greatly affects the performance of the proposed scatter search algorithm. The hybrid scatter search algorithm intensified by a variable neighborhood descent search is highly efficient in solving the DCLC multicast routing problem in comparison with other algorithms and heuristics in the literature.     

Mathematical modeling and heuristic approaches to flexible job shop scheduling problems

Scheduling for the flexible job shop is very important in both fields of production management and combinatorial optimization. However, it is quite difficult to achieve an optimal solution to this problem in medium and actual size problem with traditional optimization approaches owing to the high computational complexity. For solving the realistic case with more than two jobs, two types of approaches have been used: hierarchical approaches and integrated approaches. In hierarchical approaches assignment of operations to machines and the sequencing of operations on the resources or machines are treated separately, i.e., assignment and sequencing are considered independently, where in integrated approaches, assignment and sequencing are not differentiated. In this paper, a mathematical model and heuristic approaches for flexible job shop scheduling problems (FJSP) are considered. Mathematical model is used to achieve optimal solution for small size problems. Since FJSP is NP-hard problem, two heuristics approaches involve of integrated and hierarchical approaches are developed to solve the real size problems. Six different hybrid searching structures depending on used searching approach and heuristics are presented in this paper. Numerical experiments are used to evaluate the performance of the developed algorithms. It is concluded that, the hierarchical algorithms have better performance than integrated algorithms and the algorithm which use tabu search and simulated annealing heuristics for assignment and sequencing problems consecutively is more suitable than the other algorithms. Also the numerical experiments validate the quality of the proposed algorithms.     

A genetic algorithm and a particle swarm optimizer hybridized with Nelder–Mead simplex search

This paper integrates Nelder–Mead simplex search method (NM) with genetic algorithm (GA) and particle swarm optimization (PSO), respectively, in an attempt to locate the global optimal solutions for the nonlinear continuous variable functions mainly focusing on response surface methodology (RSM). Both the hybrid NM–GA and NM–PSO algorithms incorporate concepts from the NM, GA or PSO, which are readily to implement in practice and the computation of functional derivatives is not necessary. The hybrid methods were first illustrated through four test functions from the RSM literature and were compared with original NM, GA and PSO algorithms. In each test scheme, the effectiveness, efficiency and robustness of these methods were evaluated via associated performance statistics, and the proposed hybrid approaches prove to be very suitable for solving the optimization problems of RSM-type. The hybrid methods were then tested by ten difficult nonlinear continuous functions and were compared with the best known heuristics in the literature. The results show that both hybrid algorithms were able to reach the global optimum in all runs within a comparably computational expense.     

Crew pairing optimization based on hybrid approaches

The crew pairing problem (CPP) deals with generating crew pairings due to law and restrictions and selecting a set of crew pairings with minimal cost that covers all the flight legs. In this study, we present three different algorithms to solve CPP. The knowledge based random algorithm (KBRA) and the hybrid algorithm (HA) both combine heuristics and exact methods. While KBRA generates a reduced solution space by using the knowledge received from the past, HA starts to generate a reduced search space including high quality legal pairings by using some mechanisms in components of genetic algorithm (GA). Zero-one integer programming model of the set covering problem (SCP) which is an NP-hard problem is then used to select the minimal cost pairings among solutions in the reduced search space. Column generation (CG) which is the most commonly used technique in the CPP literature is used as the third solution technique. While the master problem is formulated as SCP, legal pairings are generated in the pricing problem by solving a shortest path problem on a structured network. In addition, the performance of CG integrated by KBRA (CG_KBRA) and HA (CG_HA) is investigated on randomly generated test problems. Computational results show that HA and CG_HA can be considered as effective and efficient solution algorithms for solving CPP in terms of the computational cost and solution quality.     

Hybrid Evolutionary Metaheuristics for Concurrent Multi-Objective Design of Urban Road and Public Transit Networks

This paper addresses a bi-modal multi-objective discrete urban road network design problem with automobile and bus flow interaction. The problem considers the concurrent urban road and bus network design in which the authorities play a major role in designing bus network topology. The road network design deals with the decision making for new street constructions, lane additions to existing streets, lane allocations for two-way streets, and the orientations and locations of one-way streets. The bus network design is performed by keeping the terminal stations of the existing bus lines unchanged and redesigning the forth and back routes of each line. Four measures, namely user benefit, the demand coverage of the bus network, the demand share of the bus mode, and the average travel generalized cost of bus passengers, are used to evaluate the network design scenarios. The problem is formulated as a multi-objective optimization model in which a modal-split/assignment model is included to depict the mode and route choice behaviors of travelers. The model is solved by the hybrid genetic algorithm and the hybrid clonal selection algorithm. The performance of these algorithms is presented and investigated by solving a number of test networks.     

Robust hyper-heuristic algorithms for the offline oriented/non-oriented 2D bin packing problems

The offline 2D bin packing problem (2DBPP) is an NP-hard combinatorial optimization problem in which objects with various width and length sizes are packed into minimized number of 2D bins. Various versions of this well-known industrial engineering problem can be faced frequently. Several heuristics have been proposed for the solution of 2DBPP but it has not been possible to find the exact solutions for large problem instances. Next fit, first fit, best fit, unified tabu search, genetic and memetic algorithms are some of the state-of-the-art methods successfully applied to this important problem. In this study, we propose a set of novel hyper-heuristic algorithms that select/combine the state-of-the-art heuristics and local search techniques for minimizing the number of 2D bins. The proposed algorithms introduce new crossover and mutation operators for the selection of the heuristics. Through the results of exhaustive experiments on a set of offline 2DBPP benchmark problem instances, we conclude that the proposed algorithms are robust with their ability to obtain high percentage of the optimal solutions.     

BEAMR: An exact and approximate model for the p-median problem

The p-median problem is perhaps one of the most well-known location–allocation models in the location science literature. It was originally defined by Hakimi in 1964 and 1965 and involves the location of p facilities on a network in such a manner that the total weighted distance of serving all demand is minimized. This problem has since been the subject of considerable research involving the development of specialized solution approaches as well as the development of many different types of extended model formats. One element of past research that has remained almost constant is the original ReVelle–Swain formulation [ReVelle CS, Swain R. Central facilities location. Geographical Analysis 1970;2:30–42]. With few exceptions as detailed in the paper, virtually no new formulations have been proposed for general use in solving the classic p-median problem. This paper proposes a new model formulation for the p-median problem that contains both exact and approximate features. This new p-median formulation is called Both Exact and Approximate Model Representation (BEAMR). We show that BEAMR can result in a substantially smaller integer-linear formulation for a given application of the p-median problem and can be used to solve for either an exact optimum or a bounded, close to optimal solution. We also present a methodological framework in which the BEAMR model can be used. Computational results for problems found in the OR_library of Beasley [A note on solving large p-median problems. European Journal of Operational Research 1985;21:270–3] indicate that BEAMR not only extends the application frontier for the p-median problem using general-purpose software, but for many problems represents an efficient, competitive solution approach.     

A Memetic Approach to the Nurse Rostering Problem

Constructing timetables of work for personnel in healthcare institutions is known to be a highly constrained and difficult problem to solve. In this paper, we discuss a commercial system, together with the model it uses, for this rostering problem. We show that tabu search heuristics can be made effective, particularly for obtaining reasonably good solutions quickly for smaller rostering problems. We discuss the robustness issues, which arise in practice, for tabu search heuristics. This paper introduces a range of new memetic approaches for the problem, which use a steepest descent improvement heuristic within a genetic algorithm framework. We provide empirical evidence to demonstrate the best features of a memetic algorithm for the rostering problem, particularly the nature of an effective recombination operator, and show that these memetic approaches can handle initialisation parameters and a range of instances more robustly than tabu search algorithms, at the expense of longer solution times. Having presented tabu search and memetic approaches (both with benefits and drawbacks) we finally present an algorithm that is a hybrid of both approaches. This technique produces better solutions than either of the earlier approaches and it is relatively unaffected by initialisation and parameter changes, combining some of the best features of each approach to create a hybrid which is greater than the sum of its component algorithms.