Dynamic Multi-objective Evolutionary Algorithm Research Articles

Combining mutual information and stable matching strategy for dynamic evolutionary multi-objective optimization

ABSTRACTIt is reasonable to assume that the changing of the optimization environment is smooth when considering a dynamic multi-objective optimization problem. Learning techniques are widely used to explore the dependence structure to facilitate population re-initialization in evolutionary search paradigms. The aim of the learning techniques is to discover knowledge from history information, thereby to track the movement of the optimal front quickly through good initialization when a change occurs. In this article, a new learning strategy is proposed, where the main ideas are (1) to use mutual information to identify the relationship between previously found approximated solutions; (2) to use a stable matching mechanism strategy to associate previously found optimal solutions bijectively; and (3) to re-initialize the new population based on a kinematics model. Controlled experiments were carried out systematically on some widely used test problems. Comparison against several state-of-the-art dynamic multi-objective evolutionary algorithms showed comparable performance in favour of the developed algorithm.

Dynamic multi-objective evolutionary algorithms for single-objective optimization

This paper proposes a new method for handling the difficulty of multi-modality for the single-objective optimization problem (SOP). The method converts a SOP to an equivalent dynamic multi-objective optimization problem (DMOP). A new dynamic multi-objective evolutionary algorithm (DMOEA) is implemented to solve the DMOP. The DMOP has two objectives: the original objective and a niche-count objective. The second objective aims to maintain the population diversity for handling the multi-modality difficulty during the search process. Experimental results show that the performance of the proposed algorithm is significantly better than the state-of-the-art competitors on a set of benchmark problems and real world antenna array problems.

A multi-stage dynamic soft scheduling algorithm for the uncertain steelmaking-continuous casting scheduling problem

The steelmaking-continuous casting (SCC) manufacturing system is usually regarded as a cornerstone as well as a bottleneck in a modern integrated steel company. In this study, we consider an uncertain scheduling problem that arises from the SCC manufacturing system where the processing times and arrival times are in intervals. To solve this problem, we propose a multi-stage dynamic soft scheduling (MDSS) algorithm based on an improved differential evolution. In the proposed algorithm, the uncertain SCC scheduling problem is decomposed into global and local scheduling problems. The global scheduling problem comprising cast units is solved by a dynamic multi-objective differential evolutionary algorithm based on decomposition where each solution is evaluated in the worst-case scenario. The local scheduling problem comprising charge units is solved by the knowledge-based differential evolutionary algorithm where all the solutions are sorted by the interval TOPSIS method. A modified critical ratio-based rule is also developed for real-time dispatching. Finally, computational results demonstrate that the MDSS algorithm outperforms previously described algorithms.

Constrained dynamic multi-objective evolutionary optimization for operational indices of beneficiation process

Operational indices optimization of beneficiation process is a dynamic optimization problem in nature. It is difficult to solve because the related dynamic models of operational indices cannot be achieved easily. Focusing on the operational indices optimization under uncertain environments in production process, this paper first formulates a constrained dynamic multi-objective optimization problem based on the collected data, which considers the changing factors in production and the constraints of operational and production indices, and takes the production indices as optimization objectives and the operational indices as decision variables. To solve the established constrained dynamic multi-objective problem, a prediction with modification mechanism based dynamic multi-objective evolutionary optimization algorithm is proposed. The algorithm first divides the population into several sub-populations and then predicts each sub-population center of new environment independently. New population is generated by Gaussian and uniform distribution based on the estimated centers to improve the convergence speed. At the same time, to ensure the population diversity, a modification strategy is adopted to detect which reference point has no individual associated and produces some individuals around it. The proposed algorithm is applied to solve the dynamic operational indices optimization problem and compared with a constrained and a modified unconstrained dynamic multi-objective optimization algorithm. The statistical results demonstrate the efficiency and effectiveness of the proposed algorithm to solve the real-world dynamic operational indices optimization problem.

Wide-band helical antenna designed by dynamic constrained multi-objective evolutionary algorithm

Dynamic Constrained Multi-Objective Evolutionary Algorithm DCMOEA is applied to optimise a wide-band helical antenna in this paper. The modelled antenna problem is a constrained two-objective optimisation problem CMOP. One objective is to maximise the right-hand circular polarisation gain RHCP gain over the required radiation range and frequency range. The other one is to minimise the height of the antenna. The constraints contain the requirements on RHCP gain, voltage standing wave ratio VSWR and axial ratio AR. The close-to-Pareto set obtained by DCMOEA satisfies the requirements. Users can choose preferred antennas from the set. One antenna in the set is chosen to compare with the antenna designed by a referred literature. The results show that it has a wider frequency band and higher gain results than the referred one.

A Benchmark Test Suite for Dynamic Evolutionary Multiobjective Optimization.

Growing trend of the dynamic multiobjective optimization research in the evolutionary computation community has increased the need for challenging and conceptually simple benchmark test suite to assess the optimization performance of an algorithm. This paper proposes a new dynamic multiobjective benchmark test suite which contains a number of component functions with clearly defined properties to assess the diversity maintenance and tracking ability of a dynamic multiobjective evolutionary algorithm (MOEA). Time-varying fitness landscape modality, tradeoff connectedness, and tradeoff degeneracy are considered as these properties rarely exist in the current benchmark test instances. Cross-problem comparative study is presented to analyze the sensitivity of a given algorithm to certain fitness landscape properties. To demonstrate the use of the proposed benchmark test suite, three evolutionary multiobjective algorithms, namely nondominated sorting genetic algorithm, decomposition-based MOEA, and recently proposed Kalman-filter-based prediction approach, are analyzed and compared. Besides, two problem-specific performance metrics are designed to assess the convergence and diversity performances, respectively. By applying the proposed test suite and performance metrics, microscopic performance details of these algorithms are uncovered to provide insightful guidance to the algorithm designer.

Evolutionary Dynamic Multiobjective Optimization Via Kalman Filter Prediction.

Evolutionary algorithms are effective in solving static multiobjective optimization problems resulting in the emergence of a number of state-of-the-art multiobjective evolutionary algorithms (MOEAs). Nevertheless, the interest in applying them to solve dynamic multiobjective optimization problems has only been tepid. Benchmark problems, appropriate performance metrics, as well as efficient algorithms are required to further the research in this field. One or more objectives may change with time in dynamic optimization problems. The optimization algorithm must be able to track the moving optima efficiently. A prediction model can learn the patterns from past experience and predict future changes. In this paper, a new dynamic MOEA using Kalman filter (KF) predictions in decision space is proposed to solve the aforementioned problems. The predictions help to guide the search toward the changed optima, thereby accelerating convergence. A scoring scheme is devised to hybridize the KF prediction with a random reinitialization method. Experimental results and performance comparisons with other state-of-the-art algorithms demonstrate that the proposed algorithm is capable of significantly improving the dynamic optimization performance.

New Dynamic Multi-Objective Constrained Optimization Evolutionary Algorithm

For dynamic multi-objective constrained optimization problem (DMCOP), it is important to find a sufficient number of uniformly distributed and representative dynamic Pareto optimal solutions. In this paper, the time period of the DMCOP is first divided into several random subperiods. In each random subperiod, the DMCOP is approximately regarded as a static optimization problem by taking the time subperiod fixed. Then, in order to decrease the amount of computation and improve the effectiveness of the algorithm, the dynamic multi-objective constrained optimization problem is further transformed into a dynamic bi-objective constrained optimization problem based on the dynamic mean rank variance and dynamic mean density variance of the evolution population. The evolution operators and a self-check operator which can automatically checkout the change of time parameter are introduced to solve the optimization problem efficiently. And finally, a dynamic multi-objective constrained optimization evolutionary algorithm is proposed. Also, the convergence analysis for the proposed algorithm is given. The computer simulations are made on four dynamic multi-objective optimization test functions and the results demonstrate that the proposed algorithm can effectively track and find the varying Pareto optimal solutions or the varying Pareto fronts with the change of time.

A dynamic multi-objective evolutionary algorithm using a change severity-based adaptive population management strategy

In addition to the need for simultaneously optimizing several competing objectives, many real-world problems are also dynamic in nature. These problems are called dynamic multi-objective optimization problems. Applying evolutionary algorithms to solve dynamic optimization problems has obtained great attention among many researchers. However, most of works are restricted to the single-objective case. In this work, we propose an adaptive hybrid population management strategy using memory, local search and random strategies, to effectively handle environment dynamicity for the multi-objective case where objective functions change over time. Moreover, the proposed strategy is based on a new technique that detects the change severity, according to which it adjusts the number of memory and random solutions to be used. This ensures, on the one hand, a high level of convergence and on the other hand, the required diversity. We propose a dynamic version of the Non dominated Sorting Genetic Algorithm II, within which we integrate the above-mentioned strategies. Empirical results show that our proposal based on the use of the adaptive strategy is able to handle dynamic environments and to track the Pareto front as it changes over time. Moreover, when confronted with several recently proposed dynamic algorithms, it has presented competitive and better results on most problems.

Dynamic Multiobjective Evolutionary Algorithm With Two Stages Evolution Operation

Multiobjective optimization problems occur in many situations and aspects of the engineering optimization field. In reality, many of the multiobjective optimization problems are dynamic in nature, i.e. their Pareto fronts change with the time or environment parameter; these optimization problems most often are called dynamic multiobjective optimization problem (DMOP). The major problems in solving DMOP are how to track and predict the Pareto optimization solutions and how to get the uniformly distributed Pareto fronts, which change with the time parameter. In this paper, a new dynamic multi-objective optimization evolutionary algorithm with two stages evolution operation is proposed for solving the kind of dynamic multiobjective optimization problem in which the Pareto optimal solutions change with time parameter continuously and slowly. At the first stage, when the time parameter has been changed, we use a new core distribution estimation algorithm to generate the new evolution population in the next env...

Integration of improved predictive model and adaptive differential evolution based dynamic multi-objective evolutionary optimization algorithm

A novel dynamic multi-objective optimization evolutionary algorithm is proposed in this paper to track the Pareto-optimal set of time-changing multi-objective optimization problems. In the proposed algorithm, to initialize the new population when a change is detected, a modified prediction model utilizng the historical optimal sets obtained in the last two times is adopted. Meantime, to improve both convergence and diversity, a self-adaptive differential evolution crossover operator is used. We conducted two experiments: the first one compares the proposed algorithm with the other three dynamic multiobjective evolutionary algorithms, and the second one investigates the performance of the two proposed operators. The statistical results indicate that the proposed algorithm has better conergence speed and diversity and it is very promising for dealing with dynamic environment.

An orthogonal predictive model-based dynamic multi-objective optimization algorithm

In this paper, a new dynamic multi-objective optimization evolutionary algorithm is proposed for tracking the Pareto-optimal set of time-changing multi-objective optimization problems effectively. In the proposed algorithm, to select individuals which are best suited for a new time from the historical optimal sets, an orthogonal predictive model is presented to predict the new individuals after the environment change is detected. Also, to converge to optimal front more quickly, an modified multi-objective optimization evolutionary algorithm based on decomposition is adopted. The proposed method has been extensively compared with other three dynamic multi-objective evolutionary algorithms over several benchmark dynamic multi-objective optimization problems. The experimental results indicate that the proposed algorithm achieves competitive results.

Memory Enhanced Dynamic Multi-Objective Evolutionary Algorithm Based on Decomposition

In addition to the need for satisfying several objectives, many real-world problems are also dynamic and require the optimization algorithm to continuously track the time-varying Pareto optimal set over time. This paper proposes a memory enhanced dynamic multi-objective evolutionary algorithm based on decomposition (denoted by dMOEAD-M). Specifically, the dMOEAD-M decomposes a dynamic multi-objective optimization problem into a number of dynamic scalar optimization subproblems and optimizes them simultaneously. An improved environment detection operator is presented. Also, a subproblem-based bunchy memory scheme, which allows evolutionary algorithm to store good solutions from old environments and reuse them as necessary, is designed to respond to the environment change. Simulation results on eight benchmark problems show that the proposed dMOEAD-M not only runs at a faster speed, more memory capabilities, and a better robustness, but is also able to find a much better spread of solutions and converge better near the

High-gain wide-band dual-circular-polarised antenna design using dynamic constrained multi-objective evolutionary algorithm

A high-gain wide-band dual-circular-polarised antenna is designed using a dynamic constrained multi-objective evolutionary algorithm (DCMOEA) in this paper. This antenna design is a constrained optimisation problem (COP). It has many constraints. Then we shall face two challenges to solve the problem. One is that it has huge local optima. The other is that feasible solutions are hard to find, or even no feasible solution exists in the problem. The DCMOEA in this paper has the potential capacity in solving such problem since multi-objective evolutionary algorithm can compromise conflict between global search and convergence rate. Then it is adopted to solve a COP after a COP is converted into an equivalent dynamic constrained multiobjective optimisation problem (DCMOP). The antenna design of NASAs TDRS-C communications satellite is employed to test this technique. A satisfactory antenna is found.

Particle Dynamic Multi-objective Evolutionary Algorithm Based on Graphic Process Unit

Particle Dynamic Multi-objective Evolutionary Algorithm Based on Graphic Process Unit

Intelligent Online Path Planning for UAVs in Adversarial Environments

Online path planning (OPP) for unmanned aerial vehicles (UAVs) is a basic issue of intelligent flight and is indeed a dynamic multi-objective optimization problem (DMOP). In this paper, an OPP framework is proposed in the sense of model predictive control (MPC) to continuously update the environmental information for the planner. For solving the DMOP involved in the MPC we propose a dynamic multi-objective evolutionary algorithm based on linkage and prediction (LP-DMOEA). Within this algorithm, the historical Pareto sets are collected and analysed to enhance the performance. For intelligently selecting the best path from the output of the OPP, the Bayesian network and fuzzy logic are used to quantify the bias to each optimization objective. The DMOEA is validated on three benchmark problems characterized by different changing types in decision and objective spaces. Moreover, the simulation results show that the LP-DMOEA overcomes the restart method for OPP. The decision-making method for solution selection can assess the situation in an adversarial environment and accordingly adapt the path planner.

A predictive gradient strategy for multiobjective evolutionary algorithms in a fast changing environment

An essential feature of a dynamic multiobjective evolutionary algorithm (MOEA) is to converge quickly to the Pareto-optimal Set before it changes. In cases where the behavior of the dynamic problem follows a certain trend, convergence can be accelerated by anticipating the characteristics of future changes in the problem. A prediction model is usually used to exploit past information and estimate the location of the new Pareto-optimal Set. In this work, we propose the novel approach of tracking and predicting the changes in the location of the Pareto Set in order to minimize the effects of a landscape change. The predicted direction and magnitude of the next change, known as the predictive gradient, is estimated based on the history of previously discovered solutions using a weighted average approach. Solutions updated with the predictive gradient will remain in the vicinity of the new Pareto-optimal Set and help the rest of the population to converge. The prediction strategy is simple to implement, making it suitable for fast-changing problems. In addition, a new memory technique is introduced to exploit any periodicity in the dynamic problem. The memory technique selects only the more promising stored solutions for retrieval in order to reduce the number of evaluations used. Both techniques are incorporated into a variant of the multi-objective evolutionary gradient search (MO-EGS) and two other MOEAs for dynamic optimization and results indicate that they are effective at improving performance on several dynamic multiobjective test problems.

Dynamic multiobjective evolutionary algorithm: adaptive cell-based rank and density estimation

This paper proposes a new evolutionary approach to multiobjective optimization problems - the dynamic multiobjective evolutionary algorithm (DMOEA). In DMOEA, a novel cell-based rank and density estimation strategy is proposed to efficiently compute dominance and diversity information when the population size varies dynamically. In addition, a population growing and declining strategies are designed to determine if an individual will survive or be eliminated based on some qualitative indicators. Meanwhile, an objective space compression strategy is devised to continuously refine the quality of the resulting Pareto front. By examining the selected performance metrics on three recently designed benchmark functions, DMOEA is found to be competitive with or even superior to five state-of-the-art MOEAs in terms of maintaining the diversity of the individuals along the tradeoff surface, tending to extend the Pareto front to new areas, and finding a well-approximated Pareto optimal front. Moreover, DMOEA is evaluated by using different parameter settings on the chosen test functions to verify its robustness of converging to an optimal population size, if it exists. Simulations show that DMOEA has the potential of autonomously determining the optimal population size, which is found insensitive to the initial population size chosen.