Algorithm For Multi-objective Problems Research Articles

Multi-objective generalized normal distribution optimization: a novel algorithm for multi-objective problems

AbstractThis study introduces the Multi-objective Generalized Normal Distribution Optimization (MOGNDO) algorithm, an advancement of the Generalized Normal Distribution Optimization (GNDO) algorithm, now adapted for multi-objective optimization tasks. The GNDO algorithm, previously known for its effectiveness in single-objective optimization, has been enhanced with two key features for multi-objective optimization. The first is the addition of an archival mechanism to store non-dominated Pareto optimal solutions, ensuring a detailed record of the best outcomes. The second enhancement is a new leader selection mechanism, designed to strategically identify and select the best solutions from the archive to guide the optimization process. This enhancement positions MOGNDO as a cutting-edge solution in multi-objective optimization, setting a new benchmark for evaluating its performance against leading algorithms in the field. The algorithm's effectiveness is rigorously tested across 35 varied case studies, encompassing both mathematical and engineering challenges, and benchmarked against prominent algorithms like MOPSO, MOGWO, MOHHO, MSSA, MOALO, MOMVO, and MOAOS. Utilizing metrics such as Generational Distance (GD), Inverted Generational Distance (IGD), and Maximum Spread (MS), the study underscores MOGNDO's ability to produce Pareto fronts of high quality, marked by exceptional precision and diversity. The results affirm MOGNDO's superior performance and versatility, not only in theoretical tests but also in addressing complex real-world engineering problems, showcasing its high convergence and coverage capabilities. The source codes of the MOGNDO algorithm are publicly available at https://nimakhodadadi.com/algorithms-%2B-codes.

Integral Global Optimality Conditions and an Algorithm for Multiobjective Problems

In this work, we propose integral global optimality conditions for multiobjective problems not necessarily differentiable. The integral characterization, already known for single objective problems, are extended to multiobjective problems by weighted sum and Chebyshev weighted scalarizations. Using this last scalarization, we propose an algorithm for obtaining an approximation of the weak Pareto front whose effectiveness is illustrated by solving a collection of multiobjective test problems.

Identifying efficient solutions via simulation: myopic multi-objective budget allocation for the bi-objective case

Simulation optimisation offers great opportunities in the design and optimisation of complex systems. In the presence of multiple objectives, there is usually no single solution that performs best on all objectives. Instead, there are several Pareto-optimal (efficient) solutions with different trade-offs which cannot be improved in any objective without sacrificing performance in another objective. For the case where alternatives are evaluated on multiple stochastic criteria, and the performance of an alternative can only be estimated via simulation, we consider the problem of efficiently identifying the Pareto-optimal designs out of a (small) given set of alternatives. We present a simple myopic budget allocation algorithm for multi-objective problems and propose several variants for different settings. In particular, this myopic method only allocates one simulation sample to one alternative in each iteration. This paper shows how the algorithm works in bi-objective problems under different settings. Empirical tests show that our algorithm can significantly reduce the necessary simulation budget.

An experimental analysis of a new two-stage crossover operator for multiobjective optimization

Evolutionary algorithms for multiobjective problems utilize three types of operations for progressing toward the higher fitness regions of the search space. Each type of operator contributes in a different way toward the achievement of the common goal. The mutation operation is responsible for diversity maintenance, while the selection operation favors the survival of the fittest. In this paper we focus our attention on the crossover operator. The crossover operator by default is responsible for the search effort and as such deserves our special attention. In particular, we propose a two-stage crossover (TSX) operator for more efficient exploration of the search space. The performance of the proposed TSX operator is assessed in comparison with the simulated binary crossover operator with the assistance of three well-known multiobjective evolutionary algorithms, namely the NSGAII, the SPEA2 and the MOCELL, for the solution of the DTLZ1---7 set of test functions. We also compare the proposed TSX with other popular reproduction operators like the differential evolution and the particle swarm optimization. Finally, we examine the efficacy of the TSX operator in handling problems having five objectives. It is shown with the assistance of the Deb, Thiele, Laumanns and Zitzler set of test functions that the TSX operator can substantially improve the results generated by three popular performance metrics for most of the cases.

Multiobjective firefly algorithm for continuous optimization

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.

Multiobjective Optimization Using Compromise Programming and an Immune Algorithm

The m-AINet is a modified version of the artificial immune network algorithm for single-objective and multimodal optimization (opt-AINet), with constraint-handling capability and improvements aiming to reduce the computational effort required by the original algorithm. In this paper we extend this algorithm for multiobjective problems by using the compromise programming approach to aggregate the objectives in the evaluation step. We adopt a compromise programming formulation that is theoretically able to map the whole Pareto front. The proposed multiobjective m-AINet is tested on the design of a loudspeaker with two objectives, showing promising results.

Fuzzy Control Algorithm for Multi-Objective Problems by Using Orthogonal Array and its Application to an AMB System

Abstract A new fuzzy logic control design algorithm suitable for multi-objective control problem is proposed based on the concept of orthogonal array, widely used for design of experiments in statistics and industrial engineering. The essence of the algorithm is to introduce an N-th order certainty factor for each rule defined from its F-value, in order to effectively exclude the less confident rules and rate the rules. The proposed algorithm with multi-objective decision table is found to be capable of detection of inconsistency and the rule classification, reduction and modification. It is also shown that the algorithm can be successfully applied to a simple numerical example and the fuzzy controller design of a rigid rotor-active magnetic bearing system with model uncertainties and harmonic disturbances.