Set Of Multi-objective Optimization Problems Research Articles

Multiobjective Multitasking Optimization With Decomposition-Based Transfer Selection.

Multiobjective multitasking optimization (MTO) needs to solve a set of multiobjective optimization problems simultaneously, and tries to speed up their solution by transferring useful search experiences across tasks. However, the quality of transfer solutions will significantly impact the transfer effect, which may even deteriorate the optimization performance with an improper selection of transfer solutions. To alleviate this issue, this article suggests a new multiobjective multitasking evolutionary algorithm (MMTEA) with decomposition-based transfer selection, called MMTEA-DTS. In this algorithm, all tasks are first decomposed into a set of subproblems, and then the transfer potential of each solution can be quantified based on the performance improvement ratio of its associated subproblem. Only high-potential solutions are selected to promote knowledge transfer. Moreover, to diversify the transfer of search experiences, a hybrid transfer evolution method is designed in this article. In this way, more diverse search experiences are transferred from high-potential solutions across different tasks to speed up their convergence. Three well-known benchmark suites suggested in the competition of evolutionary MTO and one real-world problem suite are used to verify the effectiveness of MMTEA-DTS. The experiments validate its advantages in solving most of the test problems when compared to five recently proposed MMTEAs.

An ensemble learning-based multi-population evolutionary framework for multi-scenario multi-objective optimization problems

Multi-scenario multi-objective optimization problems (MSMOPs) are a topic of considerable interest in the field of optimization. The MSMOP contains a set of multi-objective optimization problems arising from varying operating conditions, with the goal of determining a set of communal compromise solutions. However, there are few universal methods available for MSMOPs. This paper presents a general method incorporating transfer learning for MSMOPs. First, a multi-scenario ensemble framework that transfers knowledge between scenarios is developed to combine arbitrary multi-objective evolutionary algorithms, where a scenario-based comprehensive evaluation indicator is developed for combination with base learners. Then, an adaptive decomposition-based multi-objective evolutionary algorithm with a bi-layer selection (EADaBS) is proposed and embedded within the framework as a base learner. EADaBS incorporates an adaptive fitness assignment in its first layer to facilitate exploration, and density measurement in its second layer to ensure exploitation. A rebalancing operator is also designed to aid the population towards the Pareto front. Finally, a multitude of experiments is conducted to verify the effectiveness and efficiency of the proposed algorithms. Two three-scenario multi-objective optimization problems are designed and utilized as test problems. The experimental results clearly demonstrate that the proposed framework outperforms existing state-of-the-art algorithms. In conclusion, this research provides new insights into the solution of MSMOPs.

Approximation Methods for Multiobjective Optimization Problems: A Survey

Algorithms for approximating the nondominated set of multiobjective optimization problems are reviewed. The approaches are categorized into general methods that are applicable under mild assumptions and, thus, to a wide range of problems, and into algorithms that are specifically tailored to structured problems. All in all, this survey covers 52 articles published within the last 41 years, that is, between 1979 and 2020. Summary of Contribution: In many problems in operations research, several conflicting objective functions have to be optimized simultaneously, and one is interested in finding Pareto optimal solutions. Because of the high complexity of finding Pareto optimal solutions and their usually very large number, however, the exact solution of such multiobjective problems is often very difficult, which motivates the study of approximation algorithms for multiobjective optimization problems. This research area uses techniques and methods from algorithmics and computing in order to efficiently determine approximate solutions to many well-known multiobjective problems from operations research. Even though approximation algorithms for multiobjective optimization problems have been investigated for more than 40 years and more than 50 research articles have been published on this topic, this paper provides the first survey of this important area at the intersection of computing and operations research.

Optimizing over the properly efficient set of convex multi-objective optimization problems

Optimizing over the efficient set of a multi-objective optimization problem is among the difficult problems in global optimization because of its nonconvexity, even in the linear case. In this paper, we consider only properly efficient solutions which are characterized through weighted sum scalarization. We propose a numerical method to tackle this problem when the objective functions and the feasible set of the multi-objective optimization problem are convex. This algorithm penalizes progressively iterates that are not properly efficient and uses a sequence of convex nonlinear subproblems that can be solved efficiently. The proposed algorithm is shown to perform well on a set of standard problems from the literature, as it allows to obtain optimal solutions in all cases.

Asymptotic Risk of Bézier Simplex Fitting

The B'ezier simplex fitting is a novel data modeling technique which utilizes geometric structures of data to approximate the Pareto set of multi-objective optimization problems. There are two fitting methods based on different sampling strategies. The inductive skeleton fitting employs a stratified subsampling from skeletons of a simplex, whereas the all-at-once fitting uses a non-stratified sampling which treats a simplex as a single object. In this paper, we analyze the asymptotic risks of those B'ezier simplex fitting methods and derive the optimal subsample ratio for the inductive skeleton fitting. It is shown that the inductive skeleton fitting with the optimal ratio has a smaller risk when the degree of a B'ezier simplex is less than three. Those results are verified numerically under small to moderate sample sizes. In addition, we provide two complementary applications of our theory: a generalized location problem and a multi-objective hyper-parameter tuning of the group lasso. The former can be represented by a B'ezier simplex of degree two where the inductive skeleton fitting outperforms. The latter can be represented by a B'ezier simplex of degree three where the all-at-once fitting gets an advantage.

An efficient multi-objective cuckoo search algorithm for design optimization

This paper adopts and investigates the non-dominated sorting approach for extending the single-objective Cuckoo Search (CS) into a multi-objective framework. The proposed approach uses an archive composed of primary and secondary population to select and keep the non-dominated solutions at each generation instead of pairwise analogy used in the original Multi-objective Cuckoo Search (MOCS). Our simulations show that such a low computational complexity approach can enrich CS to incorporate multi-objective needs instead of considering multiple eggs for cuckoos used in the original MOCS. The proposed MOCS is tested on a set of multi-objective optimization problems and two well-studied engineering design optimization problems. Compared to MOCS and some other available multi-objective algorithms such as NSGA-II, our approach is found to be competitive while benefiting simplicity. Moreover, the proposed approach is simpler and is capable of finding a wide spread of solutions with good coverage and convergence to true Pareto optimal fronts.

Immune optimization of task scheduling on multidimensional QoS constraints

Aiming at the sensitive issues of service quality in cloud computing, a task scheduling tactic with multidimensional QoS constraints is studied. Based on cluster service and user QoS preference, this article constructs an immune optimization model to make a description through formulas and quantify the performance constraints; the utility function of multidimensional QoS is given and then the immune optimization operation is performed with the antibodies. It is beneficial to increase the prediction accuracy of the equality evaluation, and the search for a Pareto optimal set of multiobjective optimization problems is implemented. Finally, the optimum node distribution structure with the highest utility value is obtained. It's shown that the approach gives sufficient consideration of multidimensional user QoS requirements. The results from the test show a significant improvement in average rate of equipment utilization, service time and response time compared to similar algorithms.

Multiobjective Dynamic Optimization of the Cell-Cast Process for Poly(methyl methacrylate)

During the normal operation of plastic sheet polymerization reactors, large monomer conversion and average molecular weight should be achieved. However, improving any one of these two operating objectives would result in worsening the remaining one, and vise versa. Because of physical constraints, it would not be possible to meet both operating objectives in similar extent. Therefore, trade-off solutions must be obtained from which the designer can pick up the one that best suits her/his design objectives. In this work we compute the whole set of trade-off solutions by solving a set of multiobjective optimization problems. In this work we select as the best trade-off solution, the point on the trade-off curve closest to the utopia region. We demonstrate that dynamic optimal warming temperature profiles improve the control on the weight-average molecular weight and monomer conversion simultaneously, and lead to a polymer sheet with better homogeneity characteristics, when trade-off solutions based on multiobjective optimization are used.

Application of AMGA in the Mixed Model Two-Sided Assembly Line Type I Balancing Problem

This paper searches mixed model two-sided assembly line type I balancing problem based on Y automobile manufacturing company. According to the characteristics and balance constraints of mixed model two-sided assembly line, the actual problem is abstracted as the mathematical model. The three minimal objectives are the station number, the balance index and the wait time. In this study, an advanced multi-objective genetic algorithm is proposed for analyzing and solving the satisfactory solution set of multi-objective optimization problem and example application shows its validity.

Characterizations of solution sets for parametric multiobjective optimization problems

In this article, we investigate the nonemptiness and compactness of the weak Pareto optimal solution set of a multiobjective optimization problem with functional constraints via asymptotic analysis. We then employ the obtained results to derive the necessary and sufficient conditions of the weak Pareto optimal solution set of a parametric multiobjective optimization problem. Our results improve and generalize some known results.

Generating equidistant representations in biobjective programming

In recent years, emphasis has been placed on generating quality representations of the nondominated set of multiobjective optimization problems. This paper presents two methods for generating discrete representations with equidistant points for biobjective problems with solution sets determined by convex, polyhedral cones. The Constraint Controlled-Spacing method is based on the epsilon-constraint method with an additional constraint to control the spacing of generated points. The Bilevel Controlled-Spacing method has a bilevel structure with the lower-level generating the nondominated points and the upper-level controlling the spacing, and is extended to multiobjective problems. Both methods are proven to produce (weakly) nondominated points and are demonstrated on a variety of test problems.

Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods

Obtaining a complete description of the efficient set of multiobjective optimization problems can be of invaluable help to the decision-maker when the objectives conflict and a solution has to be chosen. In this paper we present an interval branch-and-bound algorithm which aims at obtaining a tight outer approximation of the whole efficient set of nonlinear biobjective problems. The method enhances the performance of a previous rudimentary algorithm thanks to the use of new accelerating devices, namely, three new discarding tests. Some computational studies on a set of competitive location problems demonstrate the efficiency of the discarding tests, as well as the superiority of the new algorithm, both in time and in quality of the outer approximations of the efficient set, as compared to another method, an interval constraint-like algorithm, with the same aim. Furthermore, we also give some theoretical results of the method, which show its good properties, both in the limit (when the tolerances are set equal to zero and the algorithm does not stop) and when the algorithm stops after a finite number of steps (when we use positive tolerances). A key point in the approach is that, thanks to the use of interval analysis tools, it can be applied to nearly any biobjective problem.

An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method

This paper discusses methods for generating or approximating the Pareto set of multiobjective optimization problems by solving a sequence of constrained single-objective problems. The necessity of determining the constraint value a priori is shown to be a serious drawback of the original epsilon-constraint method. We therefore propose a new, adaptive scheme to generate appropriate constraint values during the run. A simple example problem is presented, where the running time (measured by the number of constrained single-objective sub-problems to be solved) of the original epsilon-constraint method is exponential in the problem size (number of decision variables), although the size of the Pareto set grows only linearly. We prove that––independent of the problem or the problem size––the time complexity of the new scheme is O( k m−1 ), where k is the number of Pareto-optimal solutions to be found and m the number of objectives. Simulation results for the example problem as well as for different instances of the multiobjective knapsack problem demonstrate the behavior of the method, and links to reference implementations are provided.