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

Submodular memetic approximation for multiobjective parallel test paper generation

Parallel test paper generation is a biobjective distributed resource optimization problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified assessment criteria. Generating high-quality parallel test papers is challenging due to its NP-hardness in both of the collective objective functions. In this paper, we propose a submodular memetic approximation algorithm for solving this problem. The proposed algorithm is an adaptive memetic algorithm (MA), which exploits the submodular property of the collective objective functions to design greedy-based approximation algorithms for enhancing steps of the multiobjective MA. Synergizing the intensification of submodular local search mechanism with the diversification of the population-based submodular crossover operator, our algorithm can jointly optimize the total quality maximization objective and the fairness quality maximization objective. Our MA can achieve provable near-optimal solutions in a huge search space of large datasets in efficient polynomial runtime. Performance results on various datasets have shown that our algorithm has drastically outperformed the current techniques in terms of paper quality and runtime efficiency

Hyper-volume evolutionary algorithm

We propose a multi-objective evolutionary algorithm (MOEA), named the Hyper-volume Evolutionary Algorithm (HVEA). The algorithm is characterised by three components. First, individual fitness evaluation depends on the current Pareto front, specifically on the ratio of its dominated hyper-volume to the current Pareto front hyper-volume, hence giving an indication of how close the individual is to the current Pareto front. Second, a ranking strategy classifies individuals based on their fitness instead of Pareto dominance, individuals within the same rank are non-guaranteed to be mutually non-dominated. Third, a crowding assignment mechanism that adapts according to the individual’s neighbouring area, controlled by the neighbouring area radius parameter, and the archive of non-dominated solutions. We perform extensive experiments on the multiple 0/1 knapsack problem using different greedy repair methods to compare the performance of HVEA to other MOEAs including NSGA2, SEAMO2, SPEA2, IBEA and MOEA/D. This paper shows that by tuning the neighbouring area radius parameter, the performance of the proposed HVEA can be pushed towards better convergence, diversity or coverage and this could be beneficial to different types of problems

Combinatorial optimization and metaheuristics

Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods

Neuroevolution for solving multiobjective knapsack problems

The multiobjective knapsack problem (MOKP) is an important combinatorial problem that arises in various applications, including resource allocation, computer science and finance. When tackling this problem by evolutionary multiobjective optimization algorithms (EMOAs), it has been demonstrated that traditional recombination operators acting on binary solution representations are susceptible to a loss of diversity and poor scalability. To address those issues, we propose to use artificial neural networks for generating solutions by performing a binary classification of items using the information about their profits and weights. As gradient-based learning cannot be used when target values are unknown, neuroevolution is adapted to adjust the neural network parameters. The main contribution of this study resides in developing a solution encoding and genotype-phenotype mapping for EMOAs to solve MOKPs. The proposal is implemented within a state-of-the-art EMOA and benchmarked against traditional variation operators based on binary crossovers. The obtained experimental results indicate a superior performance of the proposed approach. Furthermore, it is advantageous in terms of scalability and can be readily incorporated into different EMOAs.Portuguese “Fundação para a Ciência e Tecnologia” under grant PEst-C/CTM/LA0025/2013 (Projecto Estratégico - LA 25 - 2013-2014 - Strategic Project - LA 25 - 2013-2014