Solving Multi-Criteria Optimization Problems with Population-Based ACO

In this paper a Population-based Ant Colony Optimization approach is proposed to solve multi-criteria optimization problems where the population of solutions is chosen from the set of all non-dominated solutions found so far. We investigate different maximum sizes for this population. The algorithm employs one pheromone matrix for each type of optimization criterion. The matrices are derived from the chosen population of solutions, and can cope with an arbitrary number of criteria. As a test problem, Single Machine Total Tardiness with changeover costs is used

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

Multi-rendezvous Spacecraft Trajectory Optimization with Beam P-ACO

The design of spacecraft trajectories for missions visiting multiple celestial bodies is here framed as a multi-objective bilevel optimization problem. A comparative study is performed to assess the performance of different Beam Search algorithms at tackling the combinatorial problem of finding the ideal sequence of bodies. Special focus is placed on the development of a new hybridization between Beam Search and the Population-based Ant Colony Optimization algorithm. An experimental evaluation shows all algorithms achieving exceptional performance on a hard benchmark problem. It is found that a properly tuned deterministic Beam Search always outperforms the remaining variants. Beam P-ACO, however, demonstrates lower parameter sensitivity, while offering superior worst-case performance. Being an anytime algorithm, it is then found to be the preferable choice for certain practical applications.Comment: Code available at https://github.com/lfsimoes/beam_paco__gtoc

Adaptive multimodal continuous ant colony optimization

Seeking multiple optima simultaneously, which multimodal optimization aims at, has attracted increasing attention but remains challenging. Taking advantage of ant colony optimization algorithms in preserving high diversity, this paper intends to extend ant colony optimization algorithms to deal with multimodal optimization. First, combined with current niching methods, an adaptive multimodal continuous ant colony optimization algorithm is introduced. In this algorithm, an adaptive parameter adjustment is developed, which takes the difference among niches into consideration. Second, to accelerate convergence, a differential evolution mutation operator is alternatively utilized to build base vectors for ants to construct new solutions. Then, to enhance the exploitation, a local search scheme based on Gaussian distribution is self-adaptively performed around the seeds of niches. Together, the proposed algorithm affords a good balance between exploration and exploitation. Extensive experiments on 20 widely used benchmark multimodal functions are conducted to investigate the influence of each algorithmic component and results are compared with several state-of-the-art multimodal algorithms and winners of competitions on multimodal optimization. These comparisons demonstrate the competitive efficiency and effectiveness of the proposed algorithm, especially in dealing with complex problems with high numbers of local optima

Multi-objective discrete particle swarm optimisation algorithm for integrated assembly sequence planning and assembly line balancing

In assembly optimisation, assembly sequence planning and assembly line balancing have been extensively studied because both activities are directly linked with assembly efficiency that influences the final assembly costs. Both activities are categorised as NP-hard and usually performed separately. Assembly sequence planning and assembly line balancing optimisation presents a good opportunity to be integrated, considering the benefits such as larger search space that leads to better solution quality, reduces error rate in planning and speeds up time-to-market for a product. In order to optimise an integrated assembly sequence planning and assembly line balancing, this work proposes a multi-objective discrete particle swarm optimisation algorithm that used discrete procedures to update its position and velocity in finding Pareto optimal solution. A computational experiment with 51 test problems at different difficulty levels was used to test the multi-objective discrete particle swarm optimisation performance compared with the existing algorithms. A statistical test of the algorithm performance indicates that the proposed multi-objective discrete particle swarm optimisation algorithm presents significant improvement in terms of the quality of the solution set towards the Pareto optimal set

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