Balancing exploration and exploitation in multiobjective evolutionary optimization

An improved immune algorithm with parallel mutation and its application

The objective of this paper is to design a fast and efficient immune algorithm for solving various optimization problems. The immune algorithm (IA), which simulates the principle of the biological immune system, is one of the nature-inspired algorithms and its many advantages have been revealed. Although IA has shown its superiority over the traditional algorithms in many fields, it still suffers from the drawbacks of slow convergence and local minima trapping problems due to its inherent stochastic search property. Many efforts have been done to improve the search performance of immune algorithms, such as adaptive parameter setting and population diversity maintenance. In this paper, an improved immune algorithm (IIA) which utilizes a parallel mutation mechanism (PM) is proposed to solve the Lennard-Jones potential problem (LJPP). In IIA, three distinct mutation operators involving cauchy mutation (CM), gaussian mutation (GM) and lateral mutation (LM) are conditionally selected to be implemented. It is expected that IIA can effectively balance the exploration and exploitation of the search and thus speed up the convergence. To illustrate its validity, IIA is tested on a two-dimension function and some benchmark functions. Then IIA is applied to solve the LJPP to exhibit its applicability to the real-world problems. Experimental results demonstrate the effectiveness of IIA in terms of the convergence speed and the solution quality.

MOEA3H: Multi-objective evolutionary algorithm based on hierarchical decision, heuristic learning and historical environment

Generating feasible solution and selecting valuable solution are the most important issues when dealing with complicated multi-objective problems. Focusing on these issues, the mechanism of multi-objective problem is analyzed by evolutionary history and environmental information. Hierarchical decision based on rank fitness of distance correlation is proposed to guide the evolutionary operator. Heuristic learning by dynamic evolutionary is introduced to deal with static optimization problem. History information acquired from solution landscape is used to achieve a comprehensive search on feasible region. Based on these improvement, multi-objective evolutionary algorithm based on hierarchical decision, heuristic learning and historical environment (MOEA3H) is proposed. The proposed algorithm performs best on 10 and 14 of 19 test problems on IGD and Hvpervolume, respectively.

Swarm Optimization for Energy-Based Acoustic Source Localization: A Comprehensive Study

In the last decades, several swarm-based optimization algorithms have emerged in the scientific literature, followed by a massive increase in terms of their fields of application. Most of the studies and comparisons are restricted to high-level languages (such as MATLAB^®) and testing methods on classical benchmark mathematical functions. Specifically, the employment of swarm-based methods for solving energy-based acoustic localization problems is still in its inception and has not yet been extensively studied. As such, the present work marks the first comprehensive study of swarm-based optimization algorithms applied to the energy-based acoustic localization problem. To this end, a total of 10 different algorithms were subjected to an extensive set of simulations with the following aims: (1) to compare the algorithms' convergence performance and recognize novel, promising methods for solving the problem of interest; (2) to validate the importance (in convergence speed) of an intelligent swarm initialization for any swarm-based algorithm; (3) to analyze the methods' time efficiency when implemented in low-level languages and when executed on embedded processors. The obtained results disclose the high potential of some of the considered swarm-based optimization algorithms for the problem under study, showing that these methods can accurately locate acoustic sources with low latency and bandwidth requirements, making them highly attractive for edge computing paradigms.

Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems

Overlapping solutions occur when more than one solution in the space of decisions maps to the same solution in the space of objectives. This situation threatens the exploration capacity of Multi-Objective Evolutionary Algorithms (MOEAs), preventing them from having a good diversity in their population. The influence of overlapping solutions is intensified on multi-objective combinatorial problems with a low number of objectives. This paper presents a hybrid MOEA for handling overlapping solutions that combines the classic NSGA-II with a strategy based on Objective Space Division (OSD). Basically, in each generation of the algorithm, the objective space is divided into several regions using the nadir solution calculated from the current generation solutions. Furthermore, the solutions in each region are classified into non-dominated fronts using different optimization strategies in each of them. This significantly enhances the achieved diversity of the approximate front of non-dominated solutions. The proposed algorithm (called NSGA-II/OSD) is tested on a classic Operations Research problem: the Multi-Objective Knapsack Problem (0-1 MOKP) with two objectives. Classic NSGA-II, MOEA/D and Global WASF-GA are used to compare the performance of NSGA-II/OSD. In the case of MOEA/D two different versions are implemented, each of them with a different strategy for specifying the reference point. These MOEA/D reference point strategies are thoroughly studied and new insights are provided. This paper analyses in depth the impact of overlapping solutions on MOEAs, studying the number of overlapping solutions, the number of solution repairs, the hypervolume metric, the attainment surfaces and the approximation to the real Pareto front, for different sizes of 0-1 MOKPs with two objectives. The proposed method offers very good performance when compared to the classic NSGA-II, MOEA/D and Global WASF-GA algorithms, all of them well-known in the literature.

A Graph-Based Ant Algorithm for the Winner Determination Problem in Combinatorial Auctions

Iterative combinatorial auctions are known to resolve bidder preference elicitation problems. However, winner determination is a known key bottleneck that has prevented widespread adoption of such auctions, and adding a time-bound to winner determination further complicates the mechanism. As a result, heuristic-based methods have enjoyed an increase in applicability. We add to the growing body of work in heuristic-based winner determination by proposing an ant colony metaheuristic–based anytime algorithm that produces optimal or near-optimal winner determination results within specified time. Our proposed algorithm resolves the speed versus accuracy problem and displays superior performance compared with 20 past state-of-the-art heuristics and two exact algorithms, for 94 open test auction instances that display a wide variety in bid-bundle composition. Furthermore, we contribute to the literature in two predominant ways: first, we represent the winner determination problem as one of finding the maximum weighted path on a directed cyclic graph; second, we improve upon existing ant colony heuristic–based exploration methods by implementing randomized pheromone updating and randomized graph pruning. Finally, to aid auction designers, we implement the anytime property of the algorithm, which allows auctioneers to stop the algorithm and return a valid solution to the winner determination problem even if it is interrupted before computation ends.

Multi-objective grasshopper optimization algorithm based on multi-group and co-evolution

The balance between exploration and exploitation is critical to the performance of a Meta-heuristic optimization method. At different stages, a proper tradeoff between exploration and exploitation can drive the search process towards better performance. This paper develops a multi-objective grasshopper optimization algorithm (MOGOA) with a new proposed framework called the Multi-group and Co-evolution Framework which can archive a fine balance between exploration and exploitation. For the purpose, a grouping mechanism and a co-evolution mechanism are designed and integrated into the framework for ameliorating the convergence and the diversity of multi-objective optimization solutions and keeping the exploration and exploitation of swarm intelligence algorithm in balance. The grouping mechanism is employed to improve the diversity of search agents for increasing coverage of search space. The co-evolution mechanism is used to improve the convergence to the true Pareto optimal front by the interaction of search agents. Quantitative and qualitative outcomes prove that the framework prominently ameliorate the convergence accuracy and convergence speed of MOGOA. The performance of the presented algorithm has been benchmarked by several standard test functions, such as CEC2009, ZDT and DTLZ. The diversity and convergence of the obtained multi-objective optimization solutions are quantitatively and qualitatively compared with the original MOGOA by using two performance indicators (GD and IGD). The results on test suits show that the diversity and convergence of the obtained solutions are significantly improved. On several test functions, some statistical indicators are more than doubled. The validity of the results has been verified by the Wilcoxon rank-sum test.

Multi-objective particle swarm optimization with random immigrants

Complex problems of the current business world need new approaches and new computational algorithms for solution. Majority of the issues need analysis from different angles, and hence, multi-objective solutions are more widely used. One of the recently well-accepted computational algorithms is Multi-objective Particle Swarm Optimization (MOPSO). This is an easily implemented and high time performance nature-inspired approach; however, the best solutions are not found for archiving, solution updating, and fast convergence problems faced in certain cases. This study investigates the previously proposed solutions for creating diversity in using MOPSO and proposes using random immigrants approach. Application of the proposed solution is tested in four different sets using Generational Distance, Spacing, Error Ratio, and Run Time performance measures. The achieved results are statistically tested against mutation-based diversity for all four performance metrics. Advantages of this new approach will support the metaheuristic researchers.