Algorithm For Multi-objective Optimization Problems Research Articles

A new VPS-based algorithm for multi-objective optimization problems

In this paper, a multi-objective variant of the vibrating particles system (MOVPS) is introduced. The new algorithm uses an external archive to keep the non-dominated solutions. Besides, the maximin strategy and crowding distance concept are employed for the selection of candidates to achieve the diversity and convergence of the solutions in the objective function space. MOVPS is evaluated using seven mathematical optimization problems and three structural design problems with continuous and discrete variables. The results are compared with competitive multi-objective optimization algorithms and show that the MOVPS can effectively find acceptable approximations of Pareto fronts for the multi-objective optimization problems.

Ensemble of multi-objective metaheuristic algorithms for multi-objective unconstrained binary quadratic programming problem

Metaheuristics have been widely utilized for solving NP-hard optimization problems. However, these algorithms usually perform differently from one problem to another, i.e., one may be effective on a problem but performs badly on another problem. Therefore, it is difficult to choose the best algorithm in advance for a given problem. In contrast to selecting the best algorithm for a problem, selection hyper-heuristics aim at performing well on a set of problems (instances). This paper proposes a selection hyper-heuristic based algorithm for multi-objective optimization problems. In the proposed algorithm, multiple metaheuristics exhibiting different search behaviors are managed and controlled as low-level metaheuristics in an algorithm pool, and the most appropriate metaheuristic is selected by means of a performance indicator at each search stage. To assess the performance of the proposed algorithm, an implementation of the algorithm containing four metaheuristics is proposed and tested for solving multi-objective unconstrained binary quadratic programming problem. Experimental results on 50 benchmark instances show that the proposed algorithm can provide better overall performance than single metaheuristics, which demonstrates the effectiveness of the proposed algorithm.

Integer cat swarm optimization algorithm for multiobjective integer problems

In the literature, several variants of cat swarm optimization (CSO) algorithm are reported. However, CSO for integer multiobjective optimization problems (MOPs) has not yet been investigated. Owing to the frequent occurrence of integer MOPs and their importance in practical design problems, in this work, we investigate a new CSO approach for solving purely integer MOPs. This new approach named as multiobjective integer cat swarm optimization (MO-ICSO) algorithm incorporates the modified version of the CSO algorithm for MOPs. This approach is comprised of the concepts of rounding the floating points to the nearest integer numbers and the probabilistic updating (PU) technique. It uses the idea of Pareto dominance for finding the non-dominated solutions and an external archive for storing these solutions. We demonstrate the power of this new approach via its quantitative analysis and sensitivity test of its several parameters using different performance metrics performed over multiobjective multidimensional knapsack problem and several standard test functions. The simulation results argue that the proposed MO-ICSO approach can be a better candidate for solving the integer MOPs.

Multi-indicators Brain Storm Optimization Algorithm for Multi-objective Optimization Problems

The brains storming optimization (BSO) is a novel swarm intelligence algorithm, which is inspired from the intelligence of the human brainstorming process. In BSO, the convergent operation and divergent operation are implemented to drive the evolution of individuals towards a global optimal region in the single-objective space. In order to extend BSO to resolve multi-objective optimization problems, this paper presents a multi-objective brainstorming algorithm based on multiple indicators, called MIBSO. In MIBSO, the two indicators are used to measure the dispersion and convergence degrees of the obtained solutions, respectively. Experimental results show the effectiveness and efficiency of the proposed algorithm.

A Novel Coupling Algorithm Based on Glowworm Swarm Optimization and Bacterial Foraging Algorithm for Solving Multi-Objective Optimization Problems

In the real word, optimization problems in multi-objective optimization (MOP) and dynamic optimization can be seen everywhere. During the last decade, among various swarm intelligence algorithms for multi-objective optimization problems, glowworm swarm optimization (GSO) and bacterial foraging algorithm (BFO) have attracted increasing attention from scholars. Although many scholars have proposed improvement strategies for GSO and BFO to keep a good balance between convergence and diversity, there are still many problems to be solved carefully. In this paper, a new coupling algorithm based on GSO and BFO (MGSOBFO) is proposed for solving dynamic multi-objective optimization problems (dMOP). MGSOBFO is proposed to achieve a good balance between exploration and exploitation by dividing into two parts. Part I is in charge of exploitation by GSO and Part II is in charge of exploration by BFO. At the same time, the simulation binary crossover (SBX) and polynomial mutation are introduced into the MGSOBFO to enhance the convergence and diversity ability of the algorithm. In order to show the excellent performance of the algorithm, we experimentally compare MGSOBFO with three algorithms on the benchmark function. The results suggests that such a coupling algorithm has good performance and outperforms other algorithms which deal with dMOP.

A Novel Double-Strand DNA Genetic Algorithm for Multi-Objective Optimization

Multi-objective optimization is important for many businesses, science, and engineering applications. Existing evolutionary algorithms for multi-objective optimization problems based on single chain encoding still have difficulties in obtaining high-quality results. This paper presents a new DNA genetic algorithm that uses a novel double-strand DNA encoding, a set of new genetic operators, and two new ranking criteria to obtain solutions that closely approximate the Pareto-optimal front. The extensive experiments were performed using a set of comprehensive benchmark bi-objective and tri-objective test problems. The experimental results show that this algorithm outperforms a set of the state-of-the-art evolutionary algorithms on several well-accepted performance metrics.

A unified view of parallel multi-objective evolutionary algorithms

This paper describes a unified view of parallel evolutionary algorithms for multi-objective optimization problems. The parallel optimization algorithms are detailed from both design and implementation aspects. The proposed taxonomy is based on three hierarchical parallel models. Moreover, various parallel architectures are taken into account. The performance assessment issue of parallel multi-objective evolutionary algorithms (MOEA) is also presented. This work can be extended to any population-based metaheuristics such as particle swarm and scatter search.

A new learning-based adaptive multi-objective evolutionary algorithm

Abstract In this paper, we propose an adaptive multi-objective evolutionary algorithm for multi-objective optimization problems (MOPs). In the algorithm, a clustering approach is employed to learn the Pareto optimal set's manifold structure adaptively, in accordance with the regularity property of MOPs, along the evolution. An advanced sampling strategy is developed for the generation of promising offspring from the learned structure. To generate trial solution, each non-dominated solution at present generation is Gaussian-perturbed using the variance-covariance matrix within its cluster. The other new features include 1) an adaptive hybridization of the developed sampling strategy with a differential evolution (DE) operator which aims to combine local and global information; 2) a reusing scheme which is to reduce the computational cost on modeling (clustering); and 3) an adaptive strength Pareto based approach which is to adaptively determine the contribution of the developed sampling strategy and the DE operator for balancing exploration and exploitation. The developed algorithm was empirically compared with four well-known MOEAs on a number of test instances with complex Pareto optimal set structure and complicated Pareto fronts. Experimental results suggest that it outperforms the compared algorithms on these test instances in terms of two commonly-used measure metrics. The effectiveness of the developed sampling strategy, the reusing scheme, the hybrid strategy, and the adaptive strategy was also empirically validated.

An Improved Non-dominated Sorting Genetic Algorithm-II (INSGA-II) applied to the design of DNA codewords

DNA codewords design is critical for many research fields, from DNA computing, to DNA hybridization arrays, to DNA nanotechnology. Results in the literature rely on a wide variety of design criteria adapted to the particular requirements of each application. Since DNA codewords design can be regarded as a multi-objective optimization problem, and nondominated sorting genetic algorithm II (NSGA-II) has been demonstrated as one of the most efficient algorithms for multi-objective optimization problems, in this paper, we proposed an improved nondominated sorting genetic algorithm II (INSGA-II) for the design of DNA codewords. The novelty of our method is that introduced the constraints to the non-dominated sorting process. The performance of our method is compared with other DNA codewords design methods, and the experiment results in silico showed that the INSGA-II has a higher convergence speed and better population diversity than those of other algorithms, and can provide reliable and effective codewords for the controllable DNA computing.

Grasshopper optimization algorithm for multi-objective optimization problems

This work proposes a new multi-objective algorithm inspired from the navigation of grass hopper swarms in nature. A mathematical model is first employed to model the interaction of individuals in the swam including attraction force, repulsion force, and comfort zone. A mechanism is then proposed to use the model in approximating the global optimum in a single-objective search space. Afterwards, an archive and target selection technique are integrated to the algorithm to estimate the Pareto optimal front for multi-objective problems. To benchmark the performance of the algorithm proposed, a set of diverse standard multi-objective test problems is utilized. The results are compared with the most well-regarded and recent algorithms in the literature of evolutionary multi-objective optimization using three performance indicators quantitatively and graphs qualitatively. The results show that the proposed algorithm is able to provide very competitive results in terms of accuracy of obtained Pareto optimal solutions and their distribution.

Multi-objective particle swarm optimization using Pareto-based set and aggregation approach

Multi-objective optimization problems (MOPs) need to be solved in real world recently. In this paper, a multi-objective particle swarm optimization based on Pareto set and aggregation approach was proposed to deal with MOPs. Firstly, velocities and positions were updated similar to PSO. Then, global-best set was defined in particle swarm optimizer to preserve Pareto-based set obtained by the population. Specifically, a hybrid updating strategy based on Pareto set and aggregation approach was introduced to update the global-best set and local search was carried on global-best set. Thirdly, personal-best positions were updated in decomposition way, and global-best position was selected from global-best set. Finally, ZDT instances and DTLZ instances were selected to evaluate the performance of MULPSO and the results show validity of the proposed algorithm for MOPs.

Simulated annealing-based immunodominance algorithm for multi-objective optimization problems

Based on the simulated annealing strategy and immunodominance in the artificial immune system, a simulated annealing-based immunodominance algorithm (SAIA) for multi-objective optimization (MOO) is proposed in this paper. In SAIA, all immunodominant antibodies are divided into two classes: the active antibodies and the hibernate antibodies at each temperature. Clonal proliferation and recombination are employed to enhance local search on those active antibodies while the hibernate antibodies have no function, but they could become active during the following temperature. Thus, all antibodies in the search space can be exploited effectively and sufficiently. Simulated annealing-based adaptive hypermutation, population pruning, and simulated annealing selection are proposed in SAIA to evolve and obtain a set of antibodies as the trade-off solutions. Complexity analysis of SAIA is also provided. The performance comparison of SAIA with some state-of-the-art MOO algorithms in solving 14 well-known multi-objective optimization problems (MOPs) including four many objectives test problems and twelve multi-objective 0/1 knapsack problems shows that SAIA is superior in converging to approximate Pareto front with a standout distribution.

A Kriging-assisted multiobjective evolutionary algorithm

A surrogate-assisted (SA) evolutionary algorithm for Multiobjective Optimization Problems (MOOPs) is presented as a contribution to Soft Computing (SC) in Artificial Intelligence (AI). Such algorithm is grounded on the cooperation between a “pure” evolutionary algorithm and a Kriging based algorithm featuring the Expected Hyper-Volume Improvement (EHVI) metric. Comparison with state-of-art pure and Kriging-assisted algorithms over two- and three-objective test functions have demonstrated that the proposed algorithm can achieve high performance in the approximation of the Pareto-optimal front mitigating the drawbacks of its parent algorithms.

Hyper multi-objective evolutionary algorithm for multi-objective optimization problems

Multi-objective optimization problems (MOPs) are very common in practice. To solve MOPs, many kinds of multi-objective evolutionary algorithms (MOEAs) are proposed. However, different MOEAs have different performances for different MOPs. Therefore, it is a time-consuming task to choose a suitable MOEA for a given problem. To pursue a competitive performance for various kinds of MOPs, in this paper, we propose a framework named hyper multi-objective evolutionary algorithm (HMOEA). In this framework, more than one MOEAs are employed, which is more adaptive to different problems. In HMOEA, the population will be randomly divided into several groups. In each group, a selected MOEA will be implemented. Therefore in the framework, the number of groups is equal to the number of the employed MOEAs. The size of each group, namely the size of sub-population in each group, is adjusted according to the corresponding MOEA’s performance. If a MOEA performs well, its corresponding group will have a large size group, which means the MOEA obtains more computational resources. On the contrary, if a MOEA has a poor performance in current generation, its corresponding group will obtain only a few individuals. Although a MOEA does not perform very well in current generation, the framework will not abandon this MOEA, but provide it a group that has predefined small size. The reason is that an involvement of different MOEAs will increase the diversity of algorithms in the hyper framework, which is helpful for HMOEA to avoid local optima and also can help HMOEA be adaptive to different phases in the whole optimization process. To compare MOEAs’ performances, coverage rate (CR) metric is used to evaluate the quality of MOEA and therefore decides the size of group for each MOEA. In numerical experiments, ZDT benchmarks are employed to test the proposed hyper framework. Several classic MOEAs are also used in comparisons. According to the comparison results, HMOEA can achieve very competitive performances, which demonstrates that the design is feasible and effective to solve MOPs.

Species-Based Genetic Algorithm for Multiobjective Optimization Problems

Species-Based Genetic Algorithm for Multiobjective Optimization Problems

Optimization of airport bus timetable in cultivation period considering passenger dynamic airport choice under conditions of uncertainty

An airport bus service, which is newly introduced in a multi-airport region, commonly leads to a gradually increasing market share of airports until a new state of equilibrium is reached. With the goal of speeding up and enlarging the increase in market share, this paper proposes a timetable optimization model by incorporating reactions of airport-loyal passengers to bus service quality. The simulation part of the model, which uses cumulative prospect theory to formulate discrete airport choices, results in predicted passenger demand needed in the optimization part. Then a genetic algorithm for multi-objective optimization problems called NSGA-II is applied to solve the model. To illustrate the model, the “Lukou airport-Wuxi” airport bus in China is taken as an example. The results show that the optimized timetables shorten the cultivation period and impel the market share to grow rapidly.

A double-module immune algorithm for multi-objective optimization problems

Multi-objective optimization problems (MOPs) have become a research hotspot, as they are commonly encountered in scientific and engineering applications. When solving some complex MOPs, it is quite difficult to locate the entire Pareto-optimal front. To better settle this problem, a novel double-module immune algorithm named DMMO is presented, where two evolutionary modules are embedded to simultaneously improve the convergence speed and population diversity. The first module is designed to optimize each objective independently by using a sub-population composed with the competitive individuals in this objective. Differential evolution crossover is performed here to enhance the corresponding objective. The second one follows the traditional procedures of immune algorithm, where proportional cloning, recombination and hyper-mutation operators are operated to concurrently strengthen the multiple objectives. The performance of DMMO is validated by 16 benchmark problems, and further compared with several multi-objective algorithms, such as NSGA-II, SPEA2, SMSEMOA, MOEA/D, SMPSO, NNIA and MIMO. Experimental studies indicate that DMMO performs better than the compared targets on most of test problems and the advantages of double modules in DMMO are also analyzed.

A Hybrid Evolutionary Immune Algorithm for Multiobjective Optimization Problems

In recent years, multiobjective immune algorithms (MOIAs) have shown promising performance in solving multiobjective optimization problems (MOPs). However, basic MOIAs only use a single hypermutation operation to evolve individuals, which may induce some difficulties in tackling complicated MOPs. In this paper, we propose a novel hybrid evolutionary framework for MOIAs, in which the cloned individuals are divided into several subpopulations and then evolved using different evolutionary strategies. An example of this hybrid framework is implemented, in which simulated binary crossover and differential evolution with polynomial mutation are adopted. A fine-grained selection mechanism and a novel elitism sharing strategy are also adopted for performance enhancement. Various comparative experiments are conducted on 28 test MOPs and our empirical results validate the effectiveness and competitiveness of our proposed algorithm in solving MOPs of different types.

An Efficient Hybrid Algorithm for Multiobjective Optimization Problems with Upper and Lower Bounds in Engineering

Generally, the inconvenience of establishing the mathematical optimization models directly and the conflicts of preventing simultaneous optimization among several objectives lead to the difficulty of obtaining the optimal solution of a practical engineering problem with several objectives. So in this paper, a generate-first-choose-later method is proposed to solve the multiobjective engineering optimization problems, which can set the number of Pareto solutions and optimize repeatedly until the satisfactory results are obtained. Based on Frisch’s method, Newton method, and weighed sum method, an efficient hybrid algorithm for multiobjective optimization models with upper and lower bounds and inequality constraints has been proposed, which is especially suitable for the practical engineering problems based on surrogate models. The generate-first-choose-later method with this hybrid algorithm can calculate the Pareto optimal set, show the Pareto front, and provide multiple designs for multiobjective engineering problems fast and accurately. Numerical examples demonstrate the effectiveness and high efficiency of the hybrid algorithm. In order to prove that the generate-first-choose-later method is rapid and suitable for solving practical engineering problems, an optimization problem for crash box of vehicle has been handled well.

Generalized decomposition and cross entropy methods for many-objective optimization

Decomposition-based algorithms for multi-objective optimization problems have increased in popularity in the past decade. Although convergence to the Pareto optimal front (PF) for such algorithms can often be superior to that of Pareto-based alternatives, the problem of effectively distributing Pareto optimal solutions in a high-dimensional space has not been solved. In this work, we introduce a novel concept which we call generalized decomposition. Generalized decomposition provides a framework with which the decision maker (DM) can guide the underlying search algorithm toward specific regions of interest, or the entire Pareto front, with the desired distribution of Pareto optimal solutions. The method simplifies many-objective problems by unifying the three performance objectives of an a posteriori multi-objective optimizer – convergence to the PF, evenly distributed Pareto optimal solutions and coverage of the entire front – to only one, that of convergence. A framework, established on generalized decomposition, and an estimation of distribution algorithm (EDA) based on low-order statistics, namely the cross-entropy method, is created to illustrate the benefits of the proposed concept for many-objective problems. The algorithm – MACE-gD – is shown to be highly competitive with the existing best-in-class decomposition-based algorithm (MOEA/D) and a more elaborate EDA method (RM-MEDA).