A Novel Multiobjective Fireworks Algorithm and Its Applications to Imbalanced Distance Minimization Problems

Recently,multimodal multiobjective optimization problems(MMOPs)have received increasing attention.Their goal is to find a Pareto front and as many equivalent Pareto optimal solutions as possible.Although some evolutionary algorithms for them have been proposed,they mainly focus on the convergence rate in the decision space while ignoring solutions diversity.In this paper,we propose a new multiobjective fireworks algorithm for them,which is able to balance exploitation and exploration in the decision space.We first extend a latest single-objective fireworks algorithm to handle MMOPs.Then we make improvements by incorporating an adaptive strategy and special archive guidance into it,where special archives are established for each firework,and two strategies(i.e.,explosion and random strategies)are adaptively selected to update the positions of sparks generated by fireworks with the guidance of special archives.Finally,we compare the proposed algorithm with eight state-of-the-art multimodal multiobjective algorithms on all 22 MMOPs from CEC2019 and several imbalanced distance minimization problems.Experimental results show that the proposed algorithm is superior to compared algorithms in solving them.Also,its runtime is less than its peers'.

OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.

Lagrangian Relaxation Method for Multiobjective Optimization Methods: Solution Approaches

This paper introduces the Lagrangian relaxation method to solve multiobjective optimization problems. It is often required to use the appropriate technique to determine the Lagrangian multipliers in the relaxation method that leads to finding the optimal solution to the problem. Our analysis aims to find a suitable technique to generate Lagrangian multipliers, and later these multipliers are used in the relaxation method to solve Multiobjective optimization problems. We propose a search-based technique to generate Lagrange multipliers. In our paper, we choose a suitable and well-known scalarization method that transforms the original multiobjective into a scalar objective optimization problem. Later, we solve this scalar objective problem using Lagrangian relaxation techniques. We use Brute force techniques to sort optimum solutions. Finally, we analyze the results, and efficient methods are recommended.

GPS： a constraint-based gene position procurement in chromosome for solving large-scale multiobjective multiple knapsack problems

The multiple knapsack problem （MKP） forms a base for resolving many real-life problems. This has also been considered with multiple objectives in genetic algorithms （GAs） for proving its efficiency. GAs use self- adaptability to effectively solve complex problems with constraints, but in certain cases, self-adaptability fails by converging toward an infeasible region. This pitfall can be resolved by using different existing repairing techniques; however, this cannot assure convergence toward attaining the optimal solution. To overcome this issue, gene position-based suppression （GPS） has been modeled and embedded as a new phase in a classical GA. This phase works on the genes of a newly generated individual after the recombination phase to retain the solution vector within its feasible region and to im- prove the solution vector to attain the optimal solution. Genes holding the highest expressibility are reserved into a subset, as the best genes identified from the current individuals by re- placing the weaker genes from the subset. This subset is used by the next generated individual to improve the solution vec- tor and to retain the best genes of the individuals. Each gene＇s positional point and its genotype exposure for each region in an environment are used to fit the best unique genes. Further, suppression of expression in conflicting gene＇s relies on the requirement toward the level of exposure in the environment or in eliminating the duplicate genes from the environment.The MKP benchmark instances from the OR-library are taken for the experiment to test the new model. The outcome por- trays that GPS in a classical GA is superior in most of the cases compared to the other existing repairing techniques.

Higher-order Symmetric Duality in Multiobjective Programming Problems

In this paper, a pair of Mond-Weir type higher-order symmetric dual programs over arbitrary cones is formulated. The appropriate duality theorems, such as weak duality theorem, strong duality theorem and converse duality theorem, are established under higher-order （strongly） cone pseudoinvexity assumptions.

Scalarizations for Approximate Quasi Efficient Solutions in Multiobjective Optimization Problems

In this paper,by reviewing two standard scalarization techniques,a new necessary and sufficient condition for characterizing(ε,.ε)-quasi(weakly)efficient solutions of multiobjective optimization problems is presented.The proposed procedure for the computation of(ε,.ε)-quasi efficient solutions is given.Note that all of the provided results are established without any convexity assumptions on the problem under consideration.And our results extend several corresponding results in multiobjective optimization.

Uncertain multiobjective redundancy allocation problem of repairable systems based on artificial bee colony algorithm

Based on the uncertainty theory, this paper is devoted to the redundancy allocation problem in repairable parallel-series systems with uncertain factors, where the failure rate, repair rate and other relative coefficients involved are considered as uncertain variables. The availability of the system and the corresponding designing cost are considered as two optimization objectives. A crisp multiobjective optimization formulation is presented on the basis of uncertainty theory to solve this resultant problem. For solving this problem efficiently, a new multiobjective artificial bee colony algorithm is proposed to search the Pareto efficient set, which introduces rank value and crowding distance in the greedy selection strategy, applies fast non-dominated sort procedure in the exploitation search and inserts tournament selection in the onlooker bee phase. It shows that the proposed algorithm outperforms NSGA-II greatly and can solve multiobjective redundancy allocation problem efficiently. Finally, a numerical example is provided to illustrate this approach.

Optimal searching for a Helix target motion

This paper discusses a search problem for a Helix target motion in which any information of the target position is not available to the searchers. There exist three searchers start searching for the target from the origin. The purpose of this paper is to formulate a search model and finds the conditions under which the expected value of the first meeting time between one of the searchers and the target is finite. Also, the existence of the optimal search plan that minimizes the expected value of the first meeting time is shown. Furthermore,this optimal search plan is found. The effectiveness of this method is illustrated by using an example with numerical results.