An algorithm for multi-objective assignment problem.

Tse Hok Man.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 68-69).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 2 --- Background Study --- p.4Chapter 2.1 --- Channel Assignment in Multicarrier CDMA Systems --- p.4Chapter 2.1.1 --- Channel Throughput --- p.5Chapter 2.1.2 --- Greedy Approach to Channel Assignment --- p.6Chapter 2.2 --- Generalised Assignment Problem --- p.7Chapter 2.2.1 --- Branch and Bound Approach for GAP --- p.8Chapter 2.2.2 --- Genetic Algorithm for GAP --- p.10Chapter 2.3 --- Negative Cycle Detection --- p.11Chapter 2.3.1 --- Labeling Method --- p.11Chapter 2.3.2 --- Bellman-Ford-Moore algorithm --- p.13Chapter 2.3.3 --- Amortized Search --- p.14Chapter 3 --- Multi-objective Assignment Problem --- p.15Chapter 3.1 --- Multi-objective Assignment Problem --- p.16Chapter 3.2 --- NP-Hardness --- p.18Chapter 3.3 --- Transformation of the Multi-objective Assignment Problem --- p.19Chapter 3.4 --- Algorithm --- p.23Chapter 3.5 --- Example --- p.25Chapter 3.6 --- A Special Case - Linear Objective Function --- p.32Chapter 3.7 --- Performance on the assignment problem --- p.33Chapter 4 --- Goal Programming Model for Channel Assignment Problem --- p.35Chapter 4.1 --- Motivation --- p.35Chapter 4.2 --- System Model --- p.36Chapter 4.3 --- Goal Programming Model for Channel Assignment Problem --- p.38Chapter 4.4 --- Simulation --- p.39Chapter 4.4.1 --- Throughput Optimization --- p.40Chapter 4.4.2 --- Best-First-Assign Algorithm --- p.41Chapter 4.4.3 --- Channel Swapping Algorithm --- p.41Chapter 4.4.4 --- Lower Bound --- p.43Chapter 4.4.5 --- Result --- p.43Chapter 4.5 --- Future Works --- p.50Chapter 5 --- Extended Application on the General Problem --- p.51Chapter 5.1 --- Latency Minimization --- p.52Chapter 5.2 --- Generalised Assignment Problem --- p.53Chapter 5.3 --- Quadratic Assignment Problem --- p.60Chapter 6 --- Conclusion --- p.65Bibliography --- p.6

Population extremal optimisation for discrete multi-objective optimisation problems

The power to solve intractable optimisation problems is often found through population based evolutionary methods. These include, but are not limited to, genetic algorithms, particle swarm optimisation, differential evolution and ant colony optimisation. While showing much promise as an effective optimiser, extremal optimisation uses only a single solution in its canonical form – and there are no standard population mechanics. In this paper, two population models for extremal optimisation are proposed and applied to a multi-objective version of the generalised assignment problem. These models use novel intervention/interaction strategies as well as collective memory in order to allow individual population members to work together. Additionally, a general non-dominated local search algorithm is developed and tested. Overall, the results show that improved attainment surfaces can be produced using population based interactions over not using them. The new EO approach is also shown to be highly competitive with an implementation of NSGA-II.No Full Tex

Methods for many-objective optimization: an analysis

Decomposition-based methods are often cited as the solution to problems related with many-objective optimization. Decomposition-based methods employ a scalarizing function to reduce a many-objective problem into a set of single objective problems, which upon solution yields a good approximation of the set of optimal solutions. This set is commonly referred to as Pareto front. In this work we explore the implications of using decomposition-based methods over Pareto-based methods from a probabilistic point of view. Namely, we investigate whether there is an advantage of using a decomposition-based method, for example using the Chebyshev scalarizing function, over Paretobased methods

Adaptive approach heuristics for the generalized assignment problem

The Generalized Assignment Problem consists in assigning a set of tasks to a set of agents with minimum cost. Each agent has a limited amount of a single resource and each task must be assigned to one and only one agent, requiring a certain amount of the resource of the agent. We present new metaheuristics for the generalized assignment problem based on hybrid approaches. One metaheuristic is a MAX-MIN Ant System (MMAS), an improved version of the Ant System, which was recently proposed by Stutzle and Hoos to combinatorial optimization problems, and it can be seen has an adaptive sampling algorithm that takes in consideration the experience gathered in earlier iterations of the algorithm. Moreover, the latter heuristic is combined with local search and tabu search heuristics to improve the search. A greedy randomized adaptive search heuristic (GRASP) is also proposed. Several neighborhoods are studied, including one based on ejection chains that produces good moves without increasing the computational effort. We present computational results of the comparative performance, followed by concluding remarks and ideas on future research in generalized assignment related problems.Metaheuristics, generalized assignment, local search, GRASP, tabu search, ant systems

Modelling epistasis in genetic disease using Petri nets, evolutionary computation and frequent itemset mining

Petri nets are useful for mathematically modelling disease-causing genetic epistasis. A Petri net model of an interaction has the potential to lead to biological insight into the cause of a genetic disease. However, defining a Petri net by hand for a particular interaction is extremely difficult because of the sheer complexity of the problem and degrees of freedom inherent in a Petri net’s architecture. We propose therefore a novel method, based on evolutionary computation and data mining, for automatically constructing Petri net models of non-linear gene interactions. The method comprises two main steps. Firstly, an initial partial Petri net is set up with several repeated sub-nets that model individual genes and a set of constraints, comprising relevant common sense and biological knowledge, is also defined. These constraints characterise the class of Petri nets that are desired. Secondly, this initial Petri net structure and the constraints are used as the input to a genetic algorithm. The genetic algorithm searches for a Petri net architecture that is both a superset of the initial net, and also conforms to all of the given constraints. The genetic algorithm evaluation function that we employ gives equal weighting to both the accuracy of the net and also its parsimony. We demonstrate our method using an epistatic model related to the presence of digital ulcers in systemic sclerosis patients that was recently reported in the literature. Our results show that although individual “perfect” Petri nets can frequently be discovered for this interaction, the true value of this approach lies in generating many different perfect nets, and applying data mining techniques to them in order to elucidate common and statistically significant patterns of interaction

An enhanced classifier system for autonomous robot navigation in dynamic environments

In many cases, a real robot application requires the navigation in dynamic environments. The navigation problem involves two main tasks: to avoid obstacles and to reach a goal. Generally, this problem could be faced considering reactions and sequences of actions. For solving the navigation problem a complete controller, including actions and reactions, is needed. Machine learning techniques has been applied to learn these controllers. Classifier Systems (CS) have proven their ability of continuos learning in these domains. However, CS have some problems in reactive systems. In this paper, a modified CS is proposed to overcome these problems. Two special mechanisms are included in the developed CS to allow the learning of both reactions and sequences of actions. The learning process has been divided in two main tasks: first, the discrimination between a predefined set of rules and second, the discovery of new rules to obtain a successful operation in dynamic environments. Different experiments have been carried out using a mini-robot Khepera to find a generalised solution. The results show the ability of the system to continuous learning and adaptation to new situations.Publicad

Geometric generalisation of surrogate model-based optimisation to combinatorial and program spaces

Open access journalSurrogate models (SMs) can profitably be employed, often in conjunction with evolutionary algorithms, in optimisation in which it is expensive to test candidate solutions. The spatial intuition behind SMs makes them naturally suited to continuous problems, and the only combinatorial problems that have been previously addressed are those with solutions that can be encoded as integer vectors. We show how radial basis functions can provide a generalised SM for combinatorial problems which have a geometric solution representation, through the conversion of that representation to a different metric space. This approach allows an SM to be cast in a natural way for the problem at hand, without ad hoc adaptation to a specific representation. We test this adaptation process on problems involving binary strings, permutations, and tree-based genetic programs. © 2014 Yong-Hyuk Kim et al