Optimised crossover genetic algorithm for capacitated vehicle routing problem

This paper presents a genetic algorithm for solving capacitated vehicle routing problem, which is mainly characterised by using vehicles of the same capacity based at a central depot that will be optimally routed to supply customers with known demands. The proposed algorithm uses an optimised crossover operator designed by a complete undirected bipartite graph to find an optimal set of delivery routes satisfying the requirements and giving minimal total cost. We tested our algorithm with benchmark instances and compared it with some other heuristics in the literature. Computational results showed that the proposed algorithm is competitive in terms of the quality of the solutions found.     

A genetic algorithm for the problem of configuring a hub-and-spoke network for a LTL trucking company in Brazil

A heuristic based on genetic algorithms is proposed to the problem of configuring hub-and-spoke networks for trucking companies that operate less-than-truckload (LTL) services in Brazil. The problem consists of determining the number of consolidation terminals (also known as hubs), their locations and the assignment of the spokes to the hubs, aiming to minimize the total cost, which is composed of fixed and variable costs. The proposed formulation differs from similar formulations found in the literature in the sense that it allows variable scale-reduction factors for the transportation costs according to the total amount of freight between hub terminals, as occurs to less-than-truckload (LTL) freight carriers in Brazil. Our genetic algorithm approach incorporates an efficient local improvement procedure that is applied to each generated individual of the population. Computational results for benchmark problems are presented. A practical application to a real world problem involving one of the top-ten trucking companies in Brazil is also described.     

A hybrid genetic algorithm for the repetition free longest common subsequence problem

Computing the longest common subsequence of two sequences is one of the most studied algorithmic problems. In this work we focus on a particular variant of the problem, called repetition free longest common subsequence (RF-LCS$\text{<small-caps>RF-LCS</small-caps>}$), which has been proved to be NP-hard. We propose a hybrid genetic algorithm, which combines standard genetic algorithms and estimation of distribution algorithms, to solve this problem. An experimental comparison with some well-known approximation algorithms shows the suitability of the proposed technique.     

A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge

This paper considers a two-stage distribution problem of a supply chain that is associated with a fixed charge. Two kinds of cost are involved in this problem: a continuous cost that linearly increases with the amount transported between a source and a destination, and secondly, a fixed charge, that incurs whenever there exists a transportation of a non-zero quantity between a source and a destination. The objective criterion is the minimisation of the total cost of distribution. A genetic algorithm (GA) that belongs to evolutionary search heuristics is proposed and illustrated. The proposed methodology is evaluated for its solution quality by comparing it with the approximate and lower bound solutions. Thus, the comparison reveals that the GA generates better solution than the approximation method and is capable of providing solution either equal or closer to the lower bound solution of the problem.     

A genetic algorithm for a single product network design model with lead time and safety stock considerations

We consider a two-stage supply chain with a production facility that replenishes a single product at retailers. The objective is to locate distribution centers in the network such that the sum of facility location, pipeline inventory, and safety stock costs is minimized. We explicitly model the relationship between the flows in the network, lead times, and safety stock levels. We use genetic algorithms to solve the model and compare their performance to that of a Lagrangian heuristic developed in earlier work. A novel chromosome representation that combines binary vectors with random keys provides solutions of similar quality to those from the Lagrangian heuristic. The model is then extended to incorporate arbitrary demand variance at the retailers. This modification destroys the structure upon which the Lagrangian heuristic is based, but is easily incorporated into the genetic algorithm. The genetic algorithm yields significantly better solutions than a greedy heuristic for this modification and has reasonable computational requirements.     

A genetic algorithm for cellular manufacturing design and layout

Cellular manufacturing (CM) is an approach that can be used to enhance both flexibility and efficiency in today’s small-to-medium lot production environment. The design of a CM system (CMS) often involves three major decisions: cell formation, group layout, and group schedule. Ideally, these decisions should be addressed simultaneously in order to obtain the best results. However, due to the complexity and NP-complete nature of each decision and the limitations of traditional approaches, most researchers have only addressed these decisions sequentially or independently. In this study, a hierarchical genetic algorithm is developed to simultaneously form manufacturing cells and determine the group layout of a CMS. The intrinsic features of our proposed algorithm include a hierarchical chromosome structure to encode two important cell design decisions, a new selection scheme to dynamically consider two correlated fitness functions, and a group mutation operator to increase the probability of mutation. From the computational analyses, these proposed structure and operators are found to be effective in improving solution quality as well as accelerating convergence.     

A genetic k-medoids clustering algorithm

We propose a hybrid genetic algorithm for k-medoids clustering. A novel heuristic operator is designed and integrated with the genetic algorithm to fine-tune the search. Further, variable length individuals that encode different number of medoids (clusters) are used for evolution with a modified Davies-Bouldin index as a measure of the fitness of the corresponding partitionings. As a result the proposed algorithm can efficiently evolve appropriate partitionings while making no a priori assumption about the number of clusters present in the datasets. In the experiments, we show the effectiveness of the proposed algorithm and compare it with other related clustering methods.     

A new crossover approach for solving the multiple travelling salesmen problem using genetic algorithms

This paper proposes a new crossover operator called two-part chromosome crossover (TCX) for solving the multiple travelling salesmen problem (MTSP) using a genetic algorithm (GA) for near-optimal solutions. We adopt the two-part chromosome representation technique which has been proven to minimise the size of the problem search space. Nevertheless, the existing crossover method for the two-part chromosome representation has two limitations. Firstly, it has extremely limited diversity in the second part of the chromosome, which greatly restricts the search ability of the GA. Secondly, the existing crossover approach tends to break useful building blocks in the first part of the chromosome, which reduces the GA’s effectiveness and solution quality. Therefore, in order to improve the GA search performance with the two-part chromosome representation, we propose TCX to overcome these two limitations and improve solution quality. Moreover, we evaluate and compare the proposed TCX with three different crossover methods for two MTSP objective functions, namely, minimising total travel distance and minimising longest tour. The experimental results show that TCX can improve the solution quality of the GA compared to three existing crossover approaches.     

A genetic algorithm for resource investment project scheduling problem,tardiness permitted with penalty

In this paper a genetic algorithm for solving a class of project scheduling problems, called Resource Investment Problem, is presented. Tardiness of project is permitted with defined penalty. Elements of algorithm such as chromosome structure, unfitness function, crossover, mutation, immigration and local search operations are explained.     

The equilibrium generalized assignment problem and genetic algorithm

The well-known generalized assignment problem (GAP) is to minimize the costs of assigning n jobs to m capacity constrained agents (or machines) such that each job is assigned to exactly one agent. This problem is known to be NP-hard and it is hard from a computational point of view as well. In this paper, follows from practical point of view in real systems, the GAP is extended to the equilibrium generalized assignment problem (EGAP) and the equilibrium constrained generalized assignment problem (ECGAP). A heuristic equilibrium strategy based genetic algorithm (GA) is designed for solving the proposed EGAP. Finally, to verify the computational efficiency of the designed GA, some numerical experiments are performed on some known benchmarks. The test results show that the designed GA is very valid for solving EGAP.     

Product line selection and pricing analysis: Impact of genetic relaxations

A model for the product line selection and pricing problem (PLSP) is presented andthree solution procedures based on a genetic algorithm are developed to analyze the results based on consumer preference patterns. Since the PLSP model is nonlinear and integer, two of the solution procedures use genetic encoding to “relax” the NP hard model. The relaxations result in linear integer and shortest path models for the fitness evaluation which are solved using branch and bound and labeling algorithms, respectively. Performance of the quality of solutions generated by the procedures is evaluated for various problem sizes and customer preference structures. The results show that the genetic relaxations provide efficient and effective solution methodologies for the problem, when compared to the pure artificial intelligence technique of genetic search. The impact of the preference structure on the product line and the managerial implications of the solution characteristics generated by the genetic relaxations are also discussed. The models can be used to explicitly consider tradeoffs between marketing and operations concerns in designing a product line.     

A model and solution method for multi-period sales promotion design

This research addresses the optimal design of a series of promotions (which might offer free gifts, discounts, or special services) periodically mailed to potential customers. A model and methodology are presented which maximize the multiple purchases of these customers over time using opinions from both promotion designers and customers. A Genetic Algorithm-based heuristic is developed to efficiently arrive at good promotion designs, and the methodology is applied to a problem using real data.     

A new bilevel formulation for the vehicle routing problem and a solution method using a genetic algorithm

The Vehicle Routing Problem (VRP) is one of the most well studied problems in operations research, both in real life problems and for scientific research purposes. During the last 50 years a number of different formulations have been proposed, together with an even greater number of algorithms for the solution of the problem. In this paper, the VRP is formulated as a problem of two decision levels. In the first level, the decision maker assigns customers to the vehicles checking the feasibility of the constructed routes (vehicle capacity constraints) and without taking into account the sequence by which the vehicles will visit the customers. In the second level, the decision maker finds the optimal routes of these assignments. The decision maker of the first level, once the cost of each routing has been calculated in the second level, estimates which assignment is the better one to choose. Based on this formulation, a bilevel genetic algorithm is proposed. In the first level of the proposed algorithm, a genetic algorithm is used for calculating the population of the most promising assignments of customers to vehicles. In the second level of the proposed algorithm, a Traveling Salesman Problem (TSP) is solved, independently for each member of the population and for each assignment to vehicles. The algorithm was tested on two sets of benchmark instances and gave very satisfactory results. In both sets of instances the average quality is less than 1%. More specifically in the set with the 14 classic instances proposed by Christofides, the quality is 0.479% and in the second set with the 20 large scale vehicle routing problems, the quality is 0.826%. The algorithm is ranked in the tenth place among the 36 most known and effective algorithms in the literature for the first set of instances and in the sixth place among the 16 algorithms for the second set of instances. The computational time of the algorithm is decreased significantly compared to other heuristic and metaheuristic algorithms due to the fact that the Expanding Neighborhood Search Strategy is used.     

A hybrid genetic algorithm for the two-dimensional single large object placement problem

In the two-dimensional single large object placement problem, we are given a rectangular master surface which has to be cut into a set of smaller rectangular items, with the aim of maximizing the total value of the pieces cut. We consider the special case in which the items cannot be rotated and must be cut with their edges always parallel to the edges of the surface. We present new greedy algorithms and a hybrid genetic approach with elitist theory, immigration rate, heuristics on-line and tailored crossover operators. Extensive computational results for a large number of small and large benchmark test problems are presented. The results show that our approach outperforms existing heuristic algorithms.     

A competitive magnet-based genetic algorithm for solving the resource-constrained project scheduling problem

This paper presents a genetic algorithm for solving the resource-constrained project scheduling problem. The innovative component of the algorithm is the use of a magnet-based crossover operator that can preserve up to two contiguous parts from the receiver and one contiguous part from the donator genotype. For this purpose, a number of genes in the receiver genotype absorb one another to have the same order and contiguity they have in the donator genotype. The ability of maintaining up to three contiguous parts from two parents distinguishes this crossover operator from the powerful and famous two-point crossover operator, which can maintain only two contiguous parts, both from the same parent. Comparing the performance of the new procedure with that of other procedures indicates its effectiveness and competence.     

A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem

In this paper we address a two-dimensional (2D) orthogonal packing problem, where a fixed set of small rectangles has to be placed on a larger stock rectangle in such a way that the amount of trim loss is minimized. The algorithm we propose hybridizes a placement procedure with a genetic algorithm based on random keys. The approach is tested on a set of instances taken from the literature and compared with other approaches. The computation results validate the quality of the solutions and the effectiveness of the proposed algorithm.     

A note on a symmetrical set covering problem: The lottery problem

In a lottery, n numbers are drawn from a set of m numbers. On a lottery ticket we fill out n numbers. Consider the following problem: what is the minimum number of tickets so that there is at least one ticket with at least p matching numbers? We provide a set-covering formulation for this problem and characterize its LP solution. The existence of many symmetrical alternative solutions, makes this a very difficult problem to solve, as our computational results indicate.     

A new implementation of an algorithm for the optimal assignment problem: An improved version of Munkres' algorithm

Existing implementations of Munkres' algorithm for the optimal assignment problem are shown to requireO(n ⁴) time in the worstn×n case. A new implementation is presented which runs in worst-case timeO(n ³) and compares favorably in performance with the algorithm of Edmonds and Karp for this problem.The results of this paper were obtained by the author while at the Department of Computer Science, Cornell University. This work was supported in part by a Vanderbilt University Research Council Grant.     

An approximation algorithm for network design problems with downwards-monotone demand functions

Building on an existing 2-approximate algorithm for the class of network design problems with downwards-monotone demand functions, many of which are NP-hard, we present an algorithm that produces solutions that are at least as good as and typically better than solutions produced by the existing algorithm.