A Novel Genetic Algorithm using Helper Objectives for the 0-1 Knapsack Problem

The 0-1 knapsack problem is a well-known combinatorial optimisation problem. Approximation algorithms have been designed for solving it and they return provably good solutions within polynomial time. On the other hand, genetic algorithms are well suited for solving the knapsack problem and they find reasonably good solutions quickly. A naturally arising question is whether genetic algorithms are able to find solutions as good as approximation algorithms do. This paper presents a novel multi-objective optimisation genetic algorithm for solving the 0-1 knapsack problem. Experiment results show that the new algorithm outperforms its rivals, the greedy algorithm, mixed strategy genetic algorithm, and greedy algorithm + mixed strategy genetic algorithm

The ant colony metaphor for multiple knapsack problem

This paper presents an Ant Colony (AC) model for the Multiple Knapsack Problem (MKP). The ant colony metaphor, as well as other evolutionary metaphors, was applied successfully to diverse heavily constrained problems. An AC system is also considered a class of multiagent distributed algorithm for combinatorial optimisation. The principle of an AC system is adapted to the MKP. We present some results regarding its performance against known optimum for different instances of MKP. The obtained results show the potential power of this particular evolutionary approach for optimisation problems.Eje: Workshop sobre Aspectos Teoricos de la Inteligencia ArtificialRed de Universidades con Carreras en Informática (RedUNCI

Parallel ant system applied to the multiple knapsack problem

Interesting real world combinatorial problems are NP-complete and many of them are hard to solve by using traditional methods. However, several heuristic methods have been developed in order to obtain timely suboptimal solutions. Most of those heuristic methods are also naturally suitable for a parallel implementation and consequently, an additional improvement on the response time can be obtained. One way of increasing the computational power is by using multiple processors operating together on a single problem. The overall problem is split into parts, each of which is operated by a separate processor in parallel. Unfortunately problems cannot be divided perfectly into separate parts and interaction is necessary between the parts like data transfer and process synchronization. However, substantial improvement can be achieved, depending on the problem and the amount of parallelism in the problem. Our work aims to exploit the capability of a distributed computing environment by using PVM and implementing a parallel version of an Ant System for solving the Multiple Knapsack Problem (MKP). An Ant System (a distributed algorithm) is a set of agents working independently and cooperating sporadically in a common problem solving activity. Regarding the above characteristics, an Ant System can be naturally considered as a nearly embarrassingly parallel computation. The proposed parallel implementations of an Ant System are based on two different approaches, static and dynamic task assignment. The computational study involves processors of different velocities and several MKP test cases of different sizes and difficulties (tight and loose constraints). The performance on the response time is measured by two indexes, Speedup Factor and Efficiency when is compared to a serial version of an Ant System. The results obtained show the potential power of exploiting the parallelism underlying in an Ant System regarding the good quality of the results and a remarkable decreasing on the computation time.Sistemas InteligentesRed de Universidades con Carreras en Informática (RedUNCI

Natural Selection of Paths in Networks

We present a novel algorithm that exhibits natural selection of paths in a network. If each node and weighted directed edge has a unique identifier, a path in the network is defined as an ordered list of these unique identifiers. We take a population perspective and view each path as a genotype. If each node has a node phenotype then a path phenotype is defined as the list of node phenotypes in order of traversal. We show that given appropriate path traversal, weight change and structural plasticity rules, a path is a unit of evolution because it can exhibit multiplicative growth (i.e. change it’s probability of being traversed), and have variation and heredity. Thus, a unit of evolution need not be a spatially distinct physical individual. The total set of paths in a network consists of all possible paths from the start node to a finish node. Each path phenotype is associated with a reward that determines whether the edges of that path will be multiplicatively strengthened (or weakened). A pair-wise tournament selection algorithm is implemented which compares the reward obtained by two paths. The directed edges of the winning path are strengthened, whilst the directed edges of the losing path are weakened. Edges shared by both paths are not changed (or weakened if diversity is desired). Each time a node is activated there is a probability that the path will mutate, i.e. find an alternative route that bypasses that node. This generates the potential for a novel but correlated path with a novel but correlated phenotype. By this process the more frequently traversed paths are responsible for most of the exploration. Nodes that are inactive for some period of time are lost (which is equivalent to connections to and from them being broken). This network-based natural selection compares favourably with a standard pair-wise tournament-selection based genetic algorithm on a range of combinatorial optimization problems and continuous parametric optimization problems. The network also exhibits memory of past selective environments and can store previously discovered characters for reuse in later optimization tasks. The pathway evolution algorithm has several possible implementations and permits natural selection with unlimited heredity without template replication

Application of Pigeon Inspired Optimization for Multidimensional Knapsack Problem

The multidimensional knapsack problem (MKP) is a generalization of the classical knapsack problem, a problem for allocating a resource by selecting a subset of objects that seek for the highest profit while satisfying the capacity of knapsack constraint. The MKP have many practical applications in different areas and classified as a NP-hard problem. An exact method like branch and bound and dynamic programming can solve the problem, but its time computation increases exponentially with the size of the problem. Whereas some approximation method has been developed to produce a near-optimal solution within reasonable computational times. In this paper a pigeon inspired optimization (PIO) is proposed for solving MKP. PIO is one of the metaheuristic algorithms that is classified in population-based swarm intelligent that is developed based on the behavior of the pigeon to find its home although it had gone far away from it home. In this paper, PIO implementation to solve MKP is applied to two different characteristic cases in total 10 cases. The result of the implementation of the two-best combination of parameter values for 10 cases compared to particle swarm optimization, intelligent water drop algorithm and the genetic algorithm gives satisfactory results

Solving the Multidimensional Knapsack Problem Using an Evolutionary Algorithm Hybridized with Branch and Bound

Abstract. A hybridization of an evolutionary algorithm (EA) with the branch and bound method (B&B) is presented in this paper. Both tech-niques cooperate by exchanging information, namely lower bounds in the case of the EA, and partial promising solutions in the case of the B&B. The multidimensional knapsack problem has been chosen as a bench-mark. To be precise, the algorithms have been tested on large problems instances from the OR-library. As it will be shown, the hybrid approach can provide high quality results, better than those obtained by the EA and the B&B on their own.

Agrupamiento homogéneo de elementos con múltiples atributos mediante algoritmos genéticos

Este artículo describe el problema general de agrupamiento, particularmente aquel en el que se busca conformar grupos de igual tamaño y equitativos respecto a más de un atributo, como un problema de optimización multi-objetivo, cuya solución por medio de una búsqueda exhaustiva no siempre será conveniente dada la explosión combinatoria que puede presentarse. Como alternativa a esta situación, se propone un método basado en algoritmos genéticos donde las soluciones posibles se codifican en estructuras tipo cromosoma a manera de matrices y donde por medio de un proceso iterativo en el que intervienen los operadores genéticos de selección, cruce y mutación, se guía el proceso de búsqueda hasta dar con una solución satisfactoria

Algoritmo multiobjetivo NSGA-II aplicado al problema de la mochila.

Este trabajo presenta la filosofía del algoritmo multiobjetivo elitista NSGA-II, explicando su esquema de funcionamiento y los mecanismos especiales que permiten la preservación y la evolución de soluciones Pareto óptimas. Este algoritmo se aplica sobre el problema de optimización clásico correspondiente al problema de la mochila adaptado para optimización multiobjetivo. También se desarrolla una propuesta alternativa para ser comparada con el esquema básico del NSGA-II

The ant colony metaphor for multiple knapsack problem

This paper presents an Ant Colony (AC) model for the Multiple Knapsack Problem (MKP). The ant colony metaphor, as well as other evolutionary metaphors, was applied successfully to diverse heavily constrained problems. An AC system is also considered a class of multiagent distributed algorithm for combinatorial optimisation. The principle of an AC system is adapted to the MKP. We present some results regarding its performance against known optimum for different instances of MKP. The obtained results show the potential power of this particular evolutionary approach for optimisation problems.Eje: Workshop sobre Aspectos Teoricos de la Inteligencia ArtificialRed de Universidades con Carreras en Informática (RedUNCI

Parallel ant system applied to the multiple knapsack problem

Interesting real world combinatorial problems are NP-complete and many of them are hard to solve by using traditional methods. However, several heuristic methods have been developed in order to obtain timely suboptimal solutions. Most of those heuristic methods are also naturally suitable for a parallel implementation and consequently, an additional improvement on the response time can be obtained. One way of increasing the computational power is by using multiple processors operating together on a single problem. The overall problem is split into parts, each of which is operated by a separate processor in parallel. Unfortunately problems cannot be divided perfectly into separate parts and interaction is necessary between the parts like data transfer and process synchronization. However, substantial improvement can be achieved, depending on the problem and the amount of parallelism in the problem. Our work aims to exploit the capability of a distributed computing environment by using PVM and implementing a parallel version of an Ant System for solving the Multiple Knapsack Problem (MKP). An Ant System (a distributed algorithm) is a set of agents working independently and cooperating sporadically in a common problem solving activity. Regarding the above characteristics, an Ant System can be naturally considered as a nearly embarrassingly parallel computation. The proposed parallel implementations of an Ant System are based on two different approaches, static and dynamic task assignment. The computational study involves processors of different velocities and several MKP test cases of different sizes and difficulties (tight and loose constraints). The performance on the response time is measured by two indexes, Speedup Factor and Efficiency when is compared to a serial version of an Ant System. The results obtained show the potential power of exploiting the parallelism underlying in an Ant System regarding the good quality of the results and a remarkable decreasing on the computation time.Sistemas InteligentesRed de Universidades con Carreras en Informática (RedUNCI