3 research outputs found

### 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

### Mixed strategy may outperform pure strategy: An initial study

In pure strategy meta-heuristics, only one search strategy is applied for all
time. In mixed strategy meta-heuristics, each time one search strategy is
chosen from a strategy pool with a probability and then is applied. An example
is classical genetic algorithms, where either a mutation or crossover operator
is chosen with a probability each time. The aim of this paper is to compare the
performance between mixed strategy and pure strategy meta-heuristic algorithms.
First an experimental study is implemented and results demonstrate that mixed
strategy evolutionary algorithms may outperform pure strategy evolutionary
algorithms on the 0-1 knapsack problem in up to 77.8% instances. Then
Complementary Strategy Theorem is rigorously proven for applying mixed strategy
at the population level. The theorem asserts that given two meta-heuristic
algorithms where one uses pure strategy 1 and another uses pure strategy 2, the
condition of pure strategy 2 being complementary to pure strategy 1 is
sufficient and necessary if there exists a mixed strategy meta-heuristics
derived from these two pure strategies and its expected number of generations
to find an optimal solution is no more than that of using pure strategy 1 for
any initial population, and less than that of using pure strategy 1 for some
initial population