On finding multiple pareto-optimal solutions using classical and evolutionary generating methods

In solving multi-objective optimization problems, evolutionary algorithms have been adequately applied to demonstrate that multiple and well-spread Pareto-optimal solutions can be found in a single simulation run. In this paper, we discuss and put together various different classical generating methods which are either quite well-known or are in oblivion due to publication in less accessible journals and some of which were even suggested before the inception of evolutionary methodologies. These generating methods specialize either in finding multiple Pareto-optimal solutions in a single simulation run or specialize in maintaining a good diversity by systematically solving a number of scalarizing problems. Most classical generating methodologies are classified into four groups mainly based on their working principles and one representative method from each group is chosen in the present study for a detailed discussion and for its performance comparison with a state-of-the-art evolutionary method. On visual comparisons of the efficient frontiers obtained for a number of two and three-objective test problems, the results bring out interesting insights about the strengths and weaknesses of these approaches. The results should motivate researchers to design hybrid multi-objective optimization algorithms which may be better than each of the individual methods

EMCSO: An Elitist Multi-Objective Cat Swarm Optimization

This paper introduces a novel multi-objective evolutionary algorithm based on cat swarm optimizationalgorithm (EMCSO) and its application to solve a multi-objective knapsack problem. The multi-objective optimizers try to find the closest solutions to true Pareto front (POF) where it will be achieved by finding the less-crowded non-dominated solutions. The proposed method applies cat swarm optimization (CSO), a swarm-based algorithm with ability of exploration and exploitation, to produce offspring solutions and uses thenon-dominated sorting method to findthe solutionsas close as to POFand crowding distance technique toobtain a uniform distribution among thenon-dominated solutions. Also, the algorithm is allowedto keep the elites of population in reproduction processand use an opposition-based learning method for population initialization to enhance the convergence speed.The proposed algorithm is tested on standard test functions (zitzler’ functions: ZDT) and its performance is compared with traditional algorithms and is analyzed based onperformance measures of generational distance (GD), inverted GD, spread,and spacing. The simulation results indicate that the proposed method gets the quite satisfactory results in comparison with other optimization algorithms for functions of ZDT1 and ZDT2. Moreover, the proposed algorithm is applied to solve multi-objective knapsack problem

A multi-objective genetic algorithm for the design of pressure swing adsorption

Pressure Swing Adsorption (PSA) is a cyclic separation process, more advantageous over other separation options for middle scale processes. Automated tools for the design of PSA processes would be beneficial for the development of the technology, but their development is a difficult task due to the complexity of the simulation of PSA cycles and the computational effort needed to detect the performance at cyclic steady state. We present a preliminary investigation of the performance of a custom multi-objective genetic algorithm (MOGA) for the optimisation of a fast cycle PSA operation, the separation of air for N2 production. The simulation requires a detailed diffusion model, which involves coupled nonlinear partial differential and algebraic equations (PDAEs). The efficiency of MOGA to handle this complex problem has been assessed by comparison with direct search methods. An analysis of the effect of MOGA parameters on the performance is also presented

Hybridization of multi-objective deterministic particle swarm with derivative-free local searches

The paper presents a multi-objective derivative-free and deterministic global/local hybrid algorithm for the efficient and effective solution of simulation-based design optimization (SBDO) problems. The objective is to show how the hybridization of two multi-objective derivative-free global and local algorithms achieves better performance than the separate use of the two algorithms in solving specific SBDO problems for hull-form design. The proposed method belongs to the class of memetic algorithms, where the global exploration capability of multi-objective deterministic particle swarm optimization is enriched by exploiting the local search accuracy of a derivative-free multi-objective line-search method. To the authors best knowledge, studies are still limited on memetic, multi-objective, deterministic, derivative-free, and evolutionary algorithms for an effective and efficient solution of SBDO for hull-form design. The proposed formulation manages global and local searches based on the hypervolume metric. The hybridization scheme uses two parameters to control the local search activation and the number of function calls used by the local algorithm. The most promising values of these parameters were identified using forty analytical tests representative of the SBDO problem of interest. The resulting hybrid algorithm was finally applied to two SBDO problems for hull-form design. For both analytical tests and SBDO problems, the hybrid method achieves better performance than its global and local counterparts

Adaptive Evolutionary Multitasking to Solve Inter-Domain Path Computation Under Node-Defined Domain Uniqueness Constraint: New Solution Encoding Scheme

In multi-domain networks, the efficiency of path computation becomes more and more important. The Inter-Domain Path Computation under Node-defined Domain Uniqueness Constraint (IDPC-NDU) is a recently investigated problem where its objective is to determine the effective routing path between two nodes that traverses every domain at most once. IDPC-NDU is NP-Hard, so the approximation approaches are suitable to deal with this problem for large instances. Multifactorial Evolutionary Algorithm (MFEA) is an emerging research topic in the field of evolutionary computation that can efficiently tackle multiple optimization problems at the same time. This study proposed an approach based on the combination of the Adaptive Multifactorial Evolutionary Algorithm (dMFEA-II) and Dijkstra algorithm for solving IDPC-NDU. The encoding and evaluating methods based on the permutation representation are also introduced, and the new individual representation is always to produce valid solutions. The proposed algorithm is evaluated on two types of instances. Simulation results demonstrate the superior performance of the proposed algorithm in comparison with the existing algorithms in terms of the quality of the solution

A Parallel General Purpose Multi-Objective Optimization Framework, with Application to Beam Dynamics

Particle accelerators are invaluable tools for research in the basic and applied sciences, in fields such as materials science, chemistry, the biosciences, particle physics, nuclear physics and medicine. The design, commissioning, and operation of accelerator facilities is a non-trivial task, due to the large number of control parameters and the complex interplay of several conflicting design goals. We propose to tackle this problem by means of multi-objective optimization algorithms which also facilitate a parallel deployment. In order to compute solutions in a meaningful time frame a fast and scalable software framework is required. In this paper, we present the implementation of such a general-purpose framework for simulation-based multi-objective optimization methods that allows the automatic investigation of optimal sets of machine parameters. The implementation is based on a master/slave paradigm, employing several masters that govern a set of slaves executing simulations and performing optimization tasks. Using evolutionary algorithms as the optimizer and OPAL as the forward solver, validation experiments and results of multi-objective optimization problems in the domain of beam dynamics are presented. The high charge beam line at the Argonne Wakefield Accelerator Facility was used as the beam dynamics model. The 3D beam size, transverse momentum, and energy spread were optimized

MaaSim: A Liveability Simulation for Improving the Quality of Life in Cities

Urbanism is no longer planned on paper thanks to powerful models and 3D simulation platforms. However, current work is not open to the public and lacks an optimisation agent that could help in decision making. This paper describes the creation of an open-source simulation based on an existing Dutch liveability score with a built-in AI module. Features are selected using feature engineering and Random Forests. Then, a modified scoring function is built based on the former liveability classes. The score is predicted using Random Forest for regression and achieved a recall of 0.83 with 10-fold cross-validation. Afterwards, Exploratory Factor Analysis is applied to select the actions present in the model. The resulting indicators are divided into 5 groups, and 12 actions are generated. The performance of four optimisation algorithms is compared, namely NSGA-II, PAES, SPEA2 and eps-MOEA, on three established criteria of quality: cardinality, the spread of the solutions, spacing, and the resulting score and number of turns. Although all four algorithms show different strengths, eps-MOEA is selected to be the most suitable for this problem. Ultimately, the simulation incorporates the model and the selected AI module in a GUI written in the Kivy framework for Python. Tests performed on users show positive responses and encourage further initiatives towards joining technology and public applications.Comment: 16 page