Multiobjective Memetic Estimation of Distribution Algorithm Based on an Incremental Tournament Local Searcher

A novel hybrid multiobjective estimation of distribution algorithm is proposed in this study. It combines an estimation of distribution algorithm based on local linear embedding and an immune inspired algorithm. Pareto set to the continuous multiobjective optimization problems, in the decision space, is a piecewise continuous (m-1)-dimensional manifold, where m is the number of objectives. By this regularity, a local linear embedding based manifold algorithm is introduced to build the distribution model of promising solutions. Besides, for enhancing local search ability of the EDA, an immune inspired sparse individual clone algorithm (SICA) is introduced and combined with the EDA. The novel hybrid multiobjective algorithm, named HMEDA, is proposed accordingly. Compared with three other state-of-the-art multiobjective algorithms, this hybrid algorithm achieves comparable results in terms of convergence and diversity. Besides, the tradeoff proportions of EDA to SICA in HMEDA are studied. Finally, the scalability to the number of decision variables of HMEDA is investigated too.

In this paper, the problems of fuel cost and emission reduction based on multi-objective optimization are studied and solved. Various multi-objective optimization algorithms, such as the multi-objective ant lion optimization (MOALO), the multi-objective multiverse optimization (MOMVO), the multi-objective particle swarm optimization (MOPSO), the multi-objective thermal exchange optimization (MOTEO), and the multi-objective grasshopper optimization algorithm (MOGOA), are used to reduce the cost and emissions of generation fuel. With equality and inequality restrictions, the suggested work is carried out in an IEEE 30 bus system. To determine the lowest system-wide minimization of generating cost and emission, the results of several optimization strategies are compared. In terms of lowering fuel costs and emissions, the MOGOA performs better than any other multi-objective algorithms.

A novel scalable test problem suite for multimodal multiobjective optimization

Based on multi-objective optimization of discrete variable, a new multi-objective ant colony optimization algorithm based on discrete variable has been proposed in this paper. The improved multi-objective ant colony algorithm established two databases on the basis of P-ACO algorithm, including sets of feasible solutions and non-feasible solutions, and “the repeated solutions” was replaced with “the special solutions” to acquire the Pareto optimal front-end of the multi-objective problems. This algorithm is not only a better application in solving multi-objective problem in the discrete variables system, but also can be applied to the truss structure optimization successfully. The present paper proposes a multi-objective ant colony optimization algorithm based on discrete variable, which can provide a good performance in program design, arithmetic speed and generality of the proposed method. It is also simple and practical, and suitable for projects in the future.

Orthogonal simulated annealing for multiobjective optimization

Multi-objective optimization problems can be divided into continuous multi-objective optimization problems and discrete multi-objective optimization problems, and discrete multi-objective optimization is not universal. In practical applications, there are many discrete multi-objective optimization problems. The solution of different problems needs to design different evolutionary multi-objective algorithms according to their specific conditions. The threshold in the traditional multi-objective optimization of wireless network is a preset constant. It has relatively poor performance in the synthesis of images with different noise levels. An adaptive wireless network multi-objective optimization algorithm based on image synthesis is proposed. Based on the maximum inter class variance and maximum peak signal to noise ratio (SNR), an adaptive wireless network multi-objective optimization algorithm is established. The accuracy and noise immunity of image synthesis are also considered. In order to avoid the effect of threshold increase on algorithm efficiency, multi-objective optimization algorithm is introduced into the algorithm. Experiments show that the method proposed in this paper is accurate and robust and has good universality for the synthesis of different noise images.

Economic Environmental Dispatch (EED) problem is the most serious problem in power operations and management. Taking into consideration transmission losses, power balance constraint, and generator capacity constraint, the EED problem becomes a non convex optimization problem, which is a difficult task that cannot be solved with traditional techniques. Furthermore, with both the environmental issues and economic objectives, the EDD problem can be formulated as a constrained nonlinear multiobjective optimization problem. In the present work, an enhanced multiobjective particle swarm optimization algorithm (EMOPSO) is proposed and applied to solve the EED problem. The proposed approach EMOPSO extends the particle swarm optimization to deal with multiobjective continuous optimization problems, EMOPSO incorporates a crowding distance mechanism for leader selection and deletion in an external archive of non dominated solutions, this mechanism improves the diversity and uniformity of the pareto front. A mutation operator is used in the population to prevent the premature convergence of the algorithm. The simulations have been made on IEEE 30 bus test system with six generators. The results are satisfying, and show that the proposed EMOPSO method was capable of achieving better performance compared with other multiobjective algorithms in the literature.

The design of Renewable Energy Power Plants (REPPs) is crucial not only for the investments' performance and attractiveness measures, but also for the maximization of resource (source) usage (e.g. sun, water, and wind) and the minimization of raw materials (e.g. aluminum: Al, cadmium: Cd, iron: Fe, silicon: Si, and tellurium: Te) consumption. Hence, several appropriate and satisfactory Multi-Objective Problems (MOPs) are mandatory during the REPPs' design phases. MOPs related tasks can only be managed by very well organized knowledge acquisition on all REPPs' design equations and models. The proposed MOPs need to be solved with one or more multi-objective algorithm, such as Multi-Objective Evolutionary Algorithms (MOEAs). In this respect, the first aim of this research study is to start gathering knowledge on the REPPs' MOPs. The second aim of this study is to gather detailed information about all MOEAs and available free software tools for their development. The main contribution of this research is the initialization of a proposed multi-objective evolutionary algorithm knowledge acquisition system for renewable energy power plants (MOEAs-KAS-F-REPPs) (research and development loopwise process: develop, train, validate, improve, test, improve, operate, and improve). As a simple representative example of this knowledge acquisition system research with two selective and elective proposed standard objectives (as test objectives) and eight selective and elective proposed standard constraints (as test constraints) are generated and applied as a standardized MOP for a virtual small hydropower plant design and investment. The maximization of energy generation (MWh) and the minimization of initial investment cost (million €) are achieved by the Multi-Objective Genetic Algorithm (MOGA), the Niched Sharing Genetic Algorithm/Non-dominated Sorting Genetic Algorithm (NSGA-I), and the NSGA-II algorithms in the Scilab 6.0.0 as only three standardized MOEAs amongst all proposed standardized MOEAs on two desktop computer configurations (Windows 10 Home 1709 64 bits, Intel i5-7200 CPU @ 2.7 GHz, 8.00 GB RAM with internet connection and Windows 10 Pro, Intel(R) Core(TM) i5 CPU 650 @ 3.20 GHz, 6,00 GB RAM with internet connection). The algorithm run-times (computation time) of the current applications vary between 20.64 and 59.98 seconds.

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

MOGBO: A new Multiobjective Gradient-Based Optimizer for real-world structural optimization problems

Battle Royale Optimizer (BRO) is a recently proposed optimization algorithm that has added a new category named game-based optimization algorithms to the existing categorization of optimization algorithms. Both continuous and binary versions of this algorithm have already been proposed. Generally, optimization problems can be divided into single-objective and multi-objective problems. Although BRO has successfully solved single-objective optimization problems, no multi-objective version has been proposed for it yet. This gap motivated us to design and implement the multi-objective version of BRO (MOBRO). Although there are some multi-objective optimization algorithms in the literature, according to the no-free-lunch theorem, no optimization algorithm can efficiently solve all optimization problems. We applied the proposed algorithm to four benchmark datasets: CEC 2009, CEC 2018, ZDT, and DTLZ. We measured the performance of MOBRO based on three aspects: convergence, spread, and distribution, using three performance criteria: inverted generational distance, maximum spread, and spacing. We also compared its obtained results with those of three state-of-the-art optimization algorithms: the multi-objective Gray Wolf optimization algorithm (MOGWO), the multi-objective particle swarm optimization algorithm (MOPSO), the multi-objective artificial vulture's optimization algorithm (MOAVAO), the optimization algorithm for multi-objective problems (MAOA), and the multi-objective non-dominated sorting genetic algorithm III (NSGA-III). The obtained results approve that MOBRO outperforms the existing optimization algorithms in most of the benchmark suites and operates competitively with them in the others.

Multi-objective fuzzy Q-learning to solve continuous state-action problems

In the past few decades, multi-objective particle swarm optimization (PSO) has increasingly attracted attention from scientists. To obtain a set of more accurate and well-distributed solutions, many variations of multi-objective PSO algorithms have been proposed. However, for complicated multi-objective problems, existing multi-objective PSO algorithms are prone to falling into local optima because of their weak global search capability. In this study, a modified multi-objective particle swarm optimization algorithm based on levy flight and double-archive mechanism (MOPSO-LFDA) is proposed to alleviate this problem. On one hand, in the evolution process of the particles, levy flight is combined with PSO to avoid the algorithm falling into local optima. By expanding the search scope of the particles, levy flight can improve the global search ability of the particles and make them jump out of local optima with a high probability. On the other hand, when maintaining external archives, in addition to the primary external archive, a secondary external archive is created to avoid unnecessary removal of the particles that may be generated by traditional maintenance approaches. With the proposed double-archive mechanism, more useful particles can be kept, and thus the diversity of the solutions is increased. Moreover, in terms of accelerating the convergence rate, a novel leader selection strategy is presented, which selects particles closer to the boundary of the attainable objective set and with larger crowding distance as leaders in optimization. The proposed algorithm outperforms existing state-of-the-art multi-objective algorithms on benchmark test functions for its fast convergence and excellent accuracy.

The multi-joint robot manipulator has nonlinear and strong coupling characteristics. It’s motion planning can be obtained by multi-objective optimization control with minimum torque motion and position deviation. In this paper, NSGA-II and preference information based RV-NSGA-II multi-objective optimization algorithm are used to optimize the control of two link manipulator joints respectively. On the basis of the Kinetic model of two-link manipulator, the proportional, integral and differential coefficients of the PID controller can be online adjusted by the multi-objective optimization algorithm for the desired motion planning path, so that the motion of two link manipulator can be controlled. The optimization results show that the self-tuning PID controller of NSGA-II can effectively control the joints according to the established target, especially the proposed preference information based RV-NSGA-II multi-objective algorithm has less deviation on joint position control.

Evolutionary multi-objective optimization algorithms are generally employed to generate Pareto optimal solutions by exploring the search space. To enhance the performance, exploration by global search can be complemented with exploitation by combining it with local search. In this paper, we address the issues in integrating local search with global search such as: how to select individuals for local search; how deep the local search is performed; how to combine multiple objectives into single objective for local search. We introduce a Preferential Local Search mechanism to fine tune the global optimal solutions further and an adaptive weight mechanism for combining multi-objectives together. These ideas have been integrated into NSGA-II to arrive at a new memetic algorithm for solving multi-objective optimization problems. The proposed algorithm has been applied on a set of constrained and unconstrained multi-objective benchmark test suite. The performance was analyzed by computing different metrics such as Generational distance, Spread, Max spread, and HyperVolume Ratio for the test suite functions. Statistical test applied on the results obtained suggests that the proposed algorithm outperforms the state-of-art multi-objective algorithms like NSGA-II and SPEA2. To study the performance of our algorithm on a real-world application, Economic Emission Load Dispatch was also taken up for validation. The performance was studied with the help of measures such as Hypervolume and Set Coverage Metrics. Experimental results substantiate that our algorithm has the capability to solve real-world problems like Economic Emission Load Dispatch and is able to produce better solutions, when compared with NSGA-II, SPEA2, and traditional memetic algorithms with fixed local search steps.