Two And Three-Point Block Methods For Solving First Order Ordinary Differential Equations In Parallel

This thesis concerns mainly in deriving new 2-point and 3-point block methods for solving a single equation of first order ODE directly using constant step size in both explicit and implicit methods. These methods, which calculate the numerical solution at more than one point simultaneously, are suitable for parallel implementations.The programs of the methods employed are run on a shared memory Sequent Symmetry SE30 parallel computer. The numerical results show that the new methods reduce the total number of steps and execution time.The accuracy of the parallel block and I-point methods is comparable particularly when finer step size are used.The stability of the new methods also had been investigated

A genetic algorithm on single machine family scheduling problem to minimise total weighted completion time

In this paper, we address a single machine family scheduling problem where jobs, each characterised by a processing time and an associated positive weight, are partitioned into families and setup time is required between these families. For this problem, we propose a genetic algorithm using an optimised crossover operator designed by an undirected bipartite graph to find an optimal schedule which minimises the total weighted completion time of the jobs in the presence of the sequence independent family setup times. The proposed algorithm finds the best offspring solution among an exponentially large number of potential offspring. Extensive computational experiments are conducted to assess the efficiency of the proposed algorithm compared to other variants of genetic algorithms. The computational results indicate the effectiveness of the proposed algorithm in generating better quality solutions compared to other algorithms

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

Solving single machine scheduling problem with maximum lateness using a genetic algorithm

We develop an optimised crossover operator designed by an undirected bipartite graph within a genetic algorithm for solving a single machine family scheduling problem, where jobs are partitioned into families and setup time is required between these families. The objective is to find a schedule which minimises the maximum lateness of the jobs in the presence of the sequence independent family setup times. The results showed that the proposed algorithm is generating better quality solutions compared to other variants of genetic algorithm

Heuristic placement routines for two-dimensional bin packing problem.

Problem statement: Cutting and packing (C and P) problems are optimization problems that are concerned in finding a good arrangement of multiple small items into one or more larger objects. Bin packing problem is a type of C AND P problems. Bin packing problem is an important industrial problem where the general objective is to reduce the production costs by maximizing the utilization of the larger objects and minimizing the material used. Approach: In this study, we considered both oriented and non-oriented cases of Two-Dimensional Bin Packing Problem (2DBPP) where a given set of small rectangles (items), was packed without overlaps into a minimum number of identical large rectangles (bins). We proposed heuristic placement routines called the Improved Lowest Gap Fill, LGFi and LGFiOF for solving non-oriented and oriented cases of 2DBPP respectively. Extensive computational experiments using benchmark data sets collected from the literature were conducted to assess the effectiveness of the proposed routines. Results: The computational results were compared with some well known heuristic placement routines. The results showed that the LGFi and LGFiOF are competitive when compared with other heuristic placement routines. Conclusion: Both LGFi and LGFiOF produced better packing quality compared to other heuristic placement routines

Metaheuristic approaches for urban transit scheduling problem: a review

Urban Transit Network Design Problem (UTNDP) focuses on deriving useful set of routes, manageable timetabling for each transit route and transit scheduling based on available resources. UTNDP is commonly subdivided into Urban Transit Routing Problem (UTRP) and Urban Transit Scheduling Problem (UTSP), respectively. There are various approaches applied to solve the UTSP. The aim of this paper is to give a comprehensive list of studies on UTSP that deals with metaheuristic approaches such as Tabu Search, Simulated Annealing, Genetic Algorithm and their hybrid methods. This review also addressed possible gaps of the approaches and the limitations of the overall problem. It can be concluded that only some of the metaheuristic approaches and sub-problems are highly studied in UTSP. This review will be useful for researchers who are interested in expanding their knowledge and conduct research in UTSP using metaheuristic approaches

Urban transit network design problems: a review of population-based metaheuristics

The urban transit network design problem (UTNDP) involves the development of a transit route set and associated schedules for an urban public transit system. The design of efficient public transit systems is widely considered as a viable option for the economic, social, and physical structure of an urban setting. This paper reviews four well-known population-based metaheuristics that have been employed and deemed potentially viable for tackling the UTNDP. The aim is to give a thorough review of the algorithms and identify the gaps for future research directions

Heuristics and metaheuristics approaches for facility layout problems: a survey

Facility Layout Problem (FLP) is a NP-hard problem concerned with the arrangement of facilities as to minimize the distance travelled between all pairs of facilities. Many exact and approximate approaches have been proposed with an extensive applicability to deal with this problem. This paper studies the fundamentals of some well-known heuristics and metaheuristics used in solving the FLPs. It is hoped that this paper will trigger researchers for in-depth studies in FLPs looking into more specific interest such as equal or unequal FLPs

Differential evolution for urban transit routing problem

The urban transit routing problem (UTRP) involves the construction of route sets on existing road networks to cater for the transit demand efficiently. This is an NP-hard problem, where the generation of candidate route sets can lead to a number of potential routes being discarded on the grounds of infeasibility. This paper presents a new repair mechanism to complement the existing terminal repair and the make-small-change operators in dealing with the infeasibility of the candidate route set. When solving the UTRP, the general aim is to determine a set of transit route networks that achieves a minimum total cost for both the passenger and the operator. With this in mind, we propose a differential evolution (DE) algorithm for solving the UTRP with a specific objective of minimizing the average travel time of all served passengers. Computational experiments are performed on the basis of benchmark Mandl’s Swiss network. Computational results from the proposed repair mechanism are comparable with the existing repair mechanisms. Furthermore, the combined repair mechanisms of all three operators produced very promising results. In addition, the proposed DE algorithm outperformed most of the published results in the literature

Hybrid genetic algorithm for university examination timetabling problem

This paper considers a Hybrid Genetic Algorithm (HGA) for University Examination Timetabling Problem (UETP). UETP is defined as the assignment of a given number of exams and their candidates to a number of available timeslots while satisfying a given set of constraints. Solutions for uncapacitated UETP are presented where five domain-specific knowledge in the form of low-level heuristics are used to guide the construction of the timetable in the initial population. The main components of the genetic operators in a GA will be tested and the best combination of the genetic operators will be adopted to construct a Pure Genetic Algorithm (PGA). The PGA will then hybridised with three new local optimisation techniques, which will make up the HGA; to improve the solutions found. These new local optimisation techniques will arrange the timeslots and exams using new explicit equations, if and only if, the modification will reduce the penalty cost function. The performance of the proposed HGA is compared with other metaheuristics from literature using the Carter’s benchmark dataset which comprises of real-world timetabling problem from various universities. The computational results show that the proposed HGA outperformed some of the metaheuristic approaches and is comparable to most of the well-known metaheuristic approaches