Heuristic algorithms for the travelling deliveryman problem

Algoritmi euristici per la risoluzione del Travelling DEliveryman Problem

L'algoritmo bionomico per il Traveling Salesman Problem

In questa tesi viene presentato un nuovo metaeuristico per la risoluzione del Traveling Salesman Problem (TSP) simmetrico. Tale metodo, detto algoritmo bionomico, è una variante dell'algoritmo genetico che usa un metodo innovativo di generazione del parents set. Nella tesi vengono proposti diversi metodi di crossover specifici per il TSP ma che possono essere facilmente estesi per altri problemi di ottimizzazione combinatoria. Tali metodi sono stati sperimentati su un insieme di problemi test, i risultati computazionali mostrano l'efficienza dei metodi proposti. In particolare uno dei metodi domina gli altri sia per la miglior qualità delle soluzioni prodotte che per il minor tempo di calcolo impiegato.

New method of solution of the traveling salesman problem /

"Supported in part jointly by the Atomic Energy Commission and the Advanced Research Projects Agency (ARPA) under AEC Contract AT(11-1)-1018."

A new three phase method (SDP method) for the multi-objective vehicle routing problem with simultaneous delvery and pickup (VRPSDP)

Transportation service operators are witnessing a growing demand for bi-directional movement of goods. Given this, the following thesis considers an extension to the vehicle routing problem (VRP) known as the delivery and pickup transportation problem (DPP), where delivery and pickup demands may occupy the same route. The problem is formulated here as the vehicle routing problem with simultaneous delivery and pickup (VRPSDP), which requires the concurrent service of the demands at the customer location. This formulation provides the greatest opportunity for cost savings for both the service provider and recipient. The aims of this research are to propose a new theoretical design to solve the multi-objective VRPSDP, provide software support for the suggested design and validate the method through a set of experiments. A new real-life based multi-objective VRPSDP is studied here, which requires the minimisation of the often conflicting objectives: operated vehicle fleet size, total routing distance and the maximum variation between route distances (workload variation). The former two objectives are commonly encountered in the domain and the latter is introduced here because it is essential for real-life routing problems. The VRPSDP is defined as a hard combinatorial optimisation problem, therefore an approximation method, Simultaneous Delivery and Pickup method (SDPmethod) is proposed to solve it. The SDPmethod consists of three phases. The first phase constructs a set of diverse partial solutions, where one is expected to form part of the near-optimal solution. The second phase determines assignment possibilities for each sub-problem. The third phase solves the sub-problems using a parallel genetic algorithm. The suggested genetic algorithm is improved by the introduction of a set of tools: genetic operator switching mechanism via diversity thresholds, accuracy analysis tool and a new fitness evaluation mechanism. This three phase method is proposed to address the shortcoming that exists in the domain, where an initial solution is built only then to be completely dismantled and redesigned in the optimisation phase. In addition, a new routing heuristic, RouteAlg, is proposed to solve the VRPSDP sub-problem, the travelling salesman problem with simultaneous delivery and pickup (TSPSDP). The experimental studies are conducted using the well known benchmark Salhi and Nagy (1999) test problems, where the SDPmethod and RouteAlg solutions are compared with the prominent works in the VRPSDP domain. The SDPmethod has demonstrated to be an effective method for solving the multi-objective VRPSDP and the RouteAlg for the TSPSDP.

On the kidney exchange problem: cardinality constrained cycle and chain problems on directed graphs: a survey of integer programming approaches

The Kidney Exchange Problem (KEP) is a combinatorial optimization problem and has attracted the attention from the community of integer programming/combinatorial optimisation in the past few years. Defined on a directed graph, the KEP has two variations: one concerns cycles only, and the other, cycles as well as chains on the same graph. We call the former a Cardinality Constrained Multi-cycle Problem (CCMcP) and the latter a Cardinality Constrained Cycles and Chains Problem (CCCCP). The cardinality for cycles is restricted in both CCMcP and CCCCP. As for chains, some studies in the literature considered cardinality restrictions, whereas others did not. The CCMcP can be viewed as an Asymmetric Travelling Salesman Problem that does allow subtours, however these subtours are constrained by cardinality, and that it is not necessary to visit all vertices. In existing literature of the KEP, the cardinality constraint for cycles is usually considered to be small (to the best of our knowledge, no more than six). In a CCCCP, each vertex on the directed graph can be included in at most one cycle or chain, but not both. The CCMcP and the CCCCP are interesting and challenging combinatorial optimization problems in their own rights, particularly due to their similarities to some travelling salesman- and vehicle routing-family of problems. In this paper, our main focus is to review the existing mathematical programming models and solution methods in the literature, analyse the performance of these models, and identify future research directions. Further, we propose a polynomial-sized and an exponential-sized mixed-integer linear programming model, discuss a number of stronger constraints for cardinality-infeasible-cycle elimination for the latter, and present some preliminary numerical results.

Computational experiments involving population size for FPGA-based implementation of a GA for the TSP

The feasibility of using an in-hardware implementation of a genetic algorithm (GA) to solve the computationally expensive travelling salesman problem (TSP) is explored, especially in regard to hardware resource requirements for problem and population sizes. We investigate via numerical experiments whether a small population size might prove sufficient to obtain reasonable quality solutions for the TSP, thereby permitting relatively resource efficient hardware implementation on field programmable gate arrays (FPGAs). Software experiments on two TSP benchmarks involving 48 and 532 cities were used to explore the extent to which population size can be reduced without compromising solution quality, and results show that a GA allowed to run for a large number of generations with a smaller population size can yield solutions of comparable quality to those obtained using a larger population. This finding is then used to investigate feasible problem sizes on a targeted Virtex-7 vx485T-2 FPGA platform via exploration of hardware resource requirements for memory and data flow operations.

Design methodologies and architectures of hardware-based evolutionary algorithms for aerospace optimisation applications on FPGAS

This thesis is a study of new design methods for allowing evolutionary algorithms to be more effectively utilised in aerospace optimisation applications where computation needs are high and computation platform space may be restrictive. It examines the applicability of special hardware computational platforms known as field programmable gate arrays and shows that with the right implementation methods they can offer significant benefits. This research is a step forward towards the advancement of efficient and highly automated aircraft systems for meeting compact physical constraints in aerospace platforms and providing effective performance speedups over traditional methods.

Multilevel refinement for combinatorial optimisation problems

We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (sometimes for the original problem, sometimes the coarsest) and then iteratively refined at each level. As a general solution strategy, the multilevel paradigm has been in use for many years and has been applied to many problem areas (most notably in the form of multigrid techniques). However, with the exception of the graph partitioning problem, multilevel techniques have not been widely applied to combinatorial optimisation problems. In this paper we address the issue of multilevel refinement for such problems and, with the aid of examples and results in graph partitioning, graph colouring and the travelling salesman problem, make a case for its use as a metaheuristic. The results provide compelling evidence that, although the multilevel framework cannot be considered as a panacea for combinatorial problems, it can provide an extremely useful addition to the combinatorial optimisation toolkit. We also give a possible explanation for the underlying process and extract some generic guidelines for its future use on other combinatorial problems.

Optimization through quantum annealing: theory and some applications

Quantum annealing is a promising tool for solving optimization problems, similar in some ways to the traditional ( classical) simulated annealing of Kirkpatrick et al. Simulated annealing takes advantage of thermal fluctuations in order to explore the optimization landscape of the problem at hand, whereas quantum annealing employs quantum fluctuations. Intriguingly, quantum annealing has been proved to be more effective than its classical counterpart in many applications. We illustrate the theory and the practical implementation of both classical and quantum annealing - highlighting the crucial differences between these two methods - by means of results recently obtained in experiments, in simple toy-models, and more challenging combinatorial optimization problems ( namely, Random Ising model and Travelling Salesman Problem). The techniques used to implement quantum and classical annealing are either deterministic evolutions, for the simplest models, or Monte Carlo approaches, for harder optimization tasks. We discuss the pro and cons of these approaches and their possible connections to the landscape of the problem addressed.

A Study of Ordered Gene Problems Featuring DNA Error Correction and DNA Fragment Assembly with a Variety of Heuristics, Genetic Algorithm Variations, and Dynamic Representations

Ordered gene problems are a very common classification of optimization problems. Because of their popularity countless algorithms have been developed in an attempt to find high quality solutions to the problems. It is also common to see many different types of problems reduced to ordered gene style problems as there are many popular heuristics and metaheuristics for them due to their popularity. Multiple ordered gene problems are studied, namely, the travelling salesman problem, bin packing problem, and graph colouring problem. In addition, two bioinformatics problems not traditionally seen as ordered gene problems are studied: DNA error correction and DNA fragment assembly. These problems are studied with multiple variations and combinations of heuristics and metaheuristics with two distinct types or representations. The majority of the algorithms are built around the Recentering- Restarting Genetic Algorithm. The algorithm variations were successful on all problems studied, and particularly for the two bioinformatics problems. For DNA Error Correction multiple cases were found with 100% of the codes being corrected. The algorithm variations were also able to beat all other state-of-the-art DNA Fragment Assemblers on 13 out of 16 benchmark problem instances.

Optimal Path Searching through Specified Routes using different Algorithms

To connect different electrical, network and data devices with the minimum cost and shortest path, is a complex job. In huge buildings, where the devices are placed at different locations on different floors and only some specific routes are available to pass the cables and buses, the shortest path search becomes more complex. The aim of this thesis project is, to develop an application which indentifies the best path to connect all objects or devices by following the specific routes.To address the above issue we adopted three algorithms Greedy Algorithm, Simulated Annealing and Exhaustive search and analyzed their results. The given problem is similar to Travelling Salesman Problem. Exhaustive search is a best algorithm to solve this problem as it checks each and every possibility and give the accurate result but it is an impractical solution because of huge time consumption. If no. of objects increased from 12 it takes hours to search the shortest path. Simulated annealing is emerged with some promising results with lower time cost. As of probabilistic nature, Simulated annealing could be non optimal but it gives a near optimal solution in a reasonable duration. Greedy algorithm is not a good choice for this problem. So, simulated annealing is proved best algorithm for this problem. The project has been implemented in C-language which takes input and store output in an Excel Workbook

A modified Intelligent Water Drops algorithm and its application to optimization problems

The Intelligent Water Drop (IWD) algorithm is a recent stochastic swarm-based method that is useful for solving combinatorial and function optimization problems. In this paper, we investigate the effectiveness of the selection method in the solution construction phase of the IWD algorithm. Instead of the fitness proportionate selection method in the original IWD algorithm, two ranking-based selection methods, namely linear ranking and exponential ranking, are proposed. Both ranking-based selection methods aim to solve the identified limitations of the fitness proportionate selection method as well as to enable the IWD algorithm to escape from local optima and ensure its search diversity. To evaluate the usefulness of the proposed ranking-based selection methods, a series of experiments pertaining to three combinatorial optimization problems, i.e., rough set feature subset selection, multiple knapsack and travelling salesman problems, is conducted. The results demonstrate that the exponential ranking selection method is able to preserve the search diversity, therefore improving the performance of the IWD algorithm. © 2014 Elsevier Ltd. All rights reserved.

A universal optimization strategy for ant colony optimization algorithms based on the Physarum-inspired mathematical model

Ant colony optimization (ACO) algorithms often fall into the local optimal solution and have lower search efficiency for solving the travelling salesman problem (TSP). According to these shortcomings, this paper proposes a universal optimization strategy for updating the pheromone matrix in the ACO algorithms. The new optimization strategy takes advantages of the unique feature of critical paths reserved in the process of evolving adaptive networks of the Physarum-inspired mathematical model (PMM). The optimized algorithms, denoted as PMACO algorithms, can enhance the amount of pheromone in the critical paths and promote the exploitation of the optimal solution. Experimental results in synthetic and real networks show that the PMACO algorithms are more efficient and robust than the traditional ACO algorithms, which are adaptable to solve the TSP with single or multiple objectives. Meanwhile, we further analyse the influence of parameters on the performance of the PMACO algorithms. Based on these analyses, the best values of these parameters are worked out for the TSP.