A Simplex Crossover based evolutionary algorithm including the genetic diversity as objective

In recent years, multi-objective evolutionary algorithms (MOEAs) have been widely used to handle various water resources problems. One challenge within MOEAs’ applications is a lack of understanding on how various operators alter a MOEA’s behavior to achieve its final performance (i.e., MOEAs are black-boxes to practitioners), and hence it is difficult to select the most appropriate operators to ensure the MOEA’s best performance for a given real-world problem. To address this issue, this study proposes the use of the run-time measure metrics to reveal the underlying searching behavior of the MOEA’s operators. The proposed methodology is demonstrated by the non-dominated sorting genetic algorithm II (NSGA-II, a widely used MOEA in water resources) with five commonly used crossover operators applied to six water distribution system design problems. Results show that the simulated binary crossover (SBX) and the simplex crossover (SPX) operators possess great ability in extending the front and finding Pareto-front solutions, respectively, while the naive crossover (NVX) strategy exhibits the overall worst performance in identifying optimal fronts. The obtained understanding on the operators’ searching behavior not only offers guidance for selecting appropriate operators for real-world water resources problems, but also builds fundamental knowledge for developing more advanced MOEAs in future.

An Enhanced multi-objective evolutionary optimization algorithm based on decomposition (E-MOEA-D) proposed for optimal placement of Distributed Generation (DG) and Electric Vehicle (EV) Fast Charging Station (FCS) in distribution system. The diversity of the evolutionary algorithm improves the convergence and diverse solution in the process of evolutionary optimization. The proposed algorithm is improved using enhanced diversity algorithm, which yield diverse candidate solutions in population. The optimal placement of DGs and FCS are formulated using three objective functions as i) Active power loss ii) Voltage deviation iii) DG cost. The proposed algorithm is simulated on IEEE-33 bus distribution system. The proposed algorithm is compared with other competitive multi-objective evolutionary algorithms such as decomposition based multi-objective evolutionary algorithm (MOEA-D) and Non-dominated sorting multi-objective evolutionary algorithm (NSGA-II).

Broad learning approach to Surrogate-Assisted Multi-Objective evolutionary fuzzy clustering algorithm based on reference points for color image segmentation

In multiobjective optimization, it is nontrivial for decision makers to articulate preferences without a priori knowledge, which is particularly true when the number of objectives becomes large. Depending on the shape of the Pareto front, optimal solutions such as knee points may be of interest. Although several multi- and many-objective optimization test suites have been proposed, little work has been reported focusing on designing multiobjective problems whose Pareto front contains complex knee regions. Likewise, few performance indicators dedicated to evaluate an algorithm's ability of accurately locating all knee points in high-dimensional objective space have been suggested. This paper proposes a set of multiobjective optimization test problems whose Pareto front consists of complex knee regions, aiming to assess the capability of evolutionary algorithms to accurately identify all knee points. Various features related to knee points have been taken into account in designing the test problems, including symmetry, differentiability, and degeneration. These features are also combined with other challenges in solving the optimization problems, such as multimodality, linkage between decision variables, nonuniformity, and scalability of the Pareto front. The proposed test problems are scalable to both decision and objective spaces. Accordingly, new performance indicators are suggested for evaluating the capability of optimization algorithms in locating the knee points. The proposed test problems, together with the performance indicators, offer a new means to develop and assess preference-based evolutionary algorithms for solving multi- and many-objective optimization problems.

Purpose: To evaluate the clinical effectiveness of a multiobjective evolutionary algorithm (MOEA) for IMRT plan generation.Methods: A MOEA was developed that generates a set of IMRT plans that approximates the clinical Pareto front in a time comparable to current commercial inverse planning systems. The stochastic nature of the algorithm permits the use of any objective function regardless of convexity. Selected plans generated by the MOEA were compared with those generated clinically using a commercial planning system (Pinnacle 8.0, Philips Electronics, N.V.). Cases of head & neck cancer and prostate cancer were planned for IMRT on both systems. MOEA plans were evaluated by comparing their performance in meeting and exceeding objectives used in generating plans using conventional methods. Characteristics of the MOEA‐generated solutions were compared using a range of commonly used objective functions. Results: Results are classified into three groups: (1) establishing the ability of the MOEA to approximate the clinical Pareto front and optimizing speed, (2) evaluating objective functions, and(3) comparing MOEA plans with current clinical IMRT methods. The effect of modifications and different objective functions on the algorithm were judged by assessing the fraction of plans generated with one algorithm that Pareto dominated those of another. Results of Aim (3) showed that plans selected from the MOEA performed better than the commercial algorithm. Conclusion:IMRT planning is inherently multiobjective and treatment planning decisions should be made using multiobjective systems. We describe an evolutionary algorithm that provides a set of plans that consistently contain multiple plans superior to those achieved using a conventional optimization algorithm and meets clinical requirements for speed and performance. Using mean dose objective for OARs and range objective for targets demonstrated better performance than using EUD. This work was supported by NIH RO1 CA112505.

Multi-objective evolutionary algorithms (MOEAs) of the state of the art are created with the only purpose of dealing with the number of objective functions in a multi-objective optimization problem (MOP) and treat the decision variables of a MOP as a whole. However, when dealing with MOPs with a large number of decision variables (more than 100) their efficacy decreases as the number of decision variables of the MOP increases. On the other hand, problem decomposition, in terms of decision variables, has been found to be extremely efficient and effective for solving large scale optimization problems. Nevertheless, most of the currently available approaches for large scale optimization rely on models based on cooperative coevolution or linkage learning methods that use multiple subpopulations or preliminary analysis, respectively, which is computationally expensive (in terms of function evaluations) when used within MOEAs. In this work, we study the effect of what we call operational decomposition, which is a novel framework based on coevolutionary concepts to apply MOEAs’s crossover operator without adding any extra cost. We investigate the improvements that NSGA-III can achieve when combined with our proposed coevolutionary operators. This new scheme is capable of improving efficiency of a MOEA when dealing with large scale MOPs having from 200 up to 1200 decision variables.

Multi-objective evolutionary algorithms (MOEAs) are currently a dynamic field of research that has attracted considerable attention. Mutation operators have been utilized by MOEAs as variation mechanisms. In particular, polynomial mutation (PLM) is one of the most popular variation mechanisms and has been utilized by many well-known MOEAs. In this paper, we revisit the PLM operator and we propose a fitness-guided version of the PLM. Experimental results obtained by non-dominated sorting genetic algorithm II and strength Pareto evolutionary algorithm 2 show that the proposed fitness-guided mutation operator outperforms the classical PLM operator, based on different performance metrics that evaluate both the proximity of the solutions to the Pareto front and their dispersion on it.

There can be a complicated mapping relation between decision variables and objective functions in multi-objective optimization problems (MOPs). It is uncommon that decision variables influence objective functions equally. Decision variables act differently in different objective functions. Hence, often, the mapping relation is unbalanced, which causes some redundancy during the search in a decision space. In response to this scenario, we propose a novel memetic (multi-objective) optimization strategy based on dimension reduction in decision space (DRMOS). DRMOS firstly analyzes the mapping relation between decision variables and objective functions. Then, it reduces the dimension of the search space by dividing the decision space into several subspaces according to the obtained relation. Finally, it improves the population by the memetic local search strategies in these decision subspaces separately. Further, DRMOS has good portability to other multi-objective evolutionary algorithms (MOEAs); that is, it is easily compatible with existing MOEAs. In order to evaluate its performance, we embed DRMOS in several state of the art MOEAs to facilitate our experiments. The results show that DRMOS has the advantage in terms of convergence speed, diversity maintenance, and portability when solving MOPs with an unbalanced mapping relation between decision variables and objective functions.

A fast sampling based evolutionary algorithm for million-dimensional multiobjective optimization

In this paper we propose a methodology based on an evolutionary multiobjective optimization algorithm for the problem of up-grading (expansion) the physical topology of transparent optical networks. The aim is to define the new topology layout and the specification of the new optical devices that should be deployed in an existing network in order to improve its performance, considering simultaneously the total installation cost (capital cost) and the total network blocking probability (performance criteria). To accomplish that, we propose a capital cost model for the network. We considered the following physical layer impairments: losses in optical devices, amplified spontaneous emission in optical amplifier and homodyne crosstalk in optical cross connect. The multiobjective optimization evolutionary algorithm used in the optimization process is the NSGA-II. Our proposed methodology can solve the expand physical topology design problem taking into account the physical layer impairments and the capital costs simultaneously. We also present a case study to show the effectiveness of our methodology.

Parallelism arises as an attractive option when Multi-Objective Evolutionary Algorithms (MOEAs) demand an intensive use of CPU or memory. The computational complexity of a MOEA depends on the scalability of its input parameters (i.e., the population size, number of decision variables, objectives, etc.) and on the computational cost of evaluating the objectives of the problem. Nonetheless, current research efforts have focused only on the second case. Therefore, in this chapter, we investigate the performance and behavior of S-PAMICRO, a recently proposed parallelization of SMS-EMOA that inhibits exponential execution time as the number of objectives increases. The idea behind S-PAMICRO is to divide the overall population into several semi-independent subpopulations each of which has very few individuals. Each subpopulation evolves a serial SMS-EMOA with an external archive for maintaining diversity. Our experimental results show that S-PAMICRO outperforms the standard island version of some state-of-the-art MOEAs in most instances of the many-objective Deb-Thiele-Laumanns-Zitzler (DTLZ) and Walking-Fish-Group (WFG) test suites.

Multicast transmission corresponds to send data to several destinations often involving requirements of Quality of Service (QoS) and Traffic Engineering (TE). This work investigates new evolutionary models to tackle Multicast Flow Routing in a Pareto multiobjective perspective. Two multiobjective evolutionary algorithms (SPEA and SPEA2) were applied as the underlying search of such models. QoS and TE requirements are also considered in the route calculus by optimizing four objectives - maximum link utilization, total cost, maximum end-to-end delay and hops count - attending a link capacity constraint. Besides, three heuristics for subtrees reconnection to be used on crossover and mutation operators are investigated. The first heuristic uses a shortest path algorithm to improve the convergence; the second one employs a random search to reconnect subtrees into a valid route and the third one mixes the other two combining the good skills of each one. The resultant evolutionary environments were evaluated using four multiobjective metrics: two for convergence and two for diversity. SPEA2 reached better results than SPEA on the vast majority cases. The design of crossover and mutation operators that provide more diversity lead to very good improvements on both multiobjective goals - convergence and diversity - being that the heuristic which combines random and shortest path reconnections and returned the best results.

Multi-Objective Evolutionary Algorithms (MOEA) have been succesfully applied to solve control problems. However, many improvements are still to be accomplished. In this paper a new approach is proposed: the Multi-Objective Pole Placement with Evolutionary Algorithms (MOPPEA). The design method is based upon using complex-valued chromosomes that contain information about closed-loop poles, which are then placed through an output feedback controller. Specific cross-over and mutation operators were implemented in simple but efficient ways. The performance is tested on a mixed multi-objective \(\mathcal{H}_{2}\)/\(\mathcal{H}_{\infty }\) control problem.

The selection mechanisms that are most commonly adopted by multi-objective evolutionary algorithms (MOEAs) are based on Pareto optimality. However, recent studies have provided theoretical and experimental evidence regarding the unsuitability of Pareto-based selection mechanisms when dealing with problems having four or more objectives. In this paper, we propose a novel MOEA designed for solving many-objective optimization problems. The selection mechanism of our approach is based on the transformation of a multi-objective optimization problem into a linear assignment problem, which is solved by the Kuhn–Munkres’ (Hungarian) algorithm. Our proposed approach is compared with respect to three state-of-the-art MOEAs, designed for solving many-objective optimization problems (i.e., problems having four or more objectives), adopting standard test problems and performance indicators taken from the specialized literature. Since one of our main aims was to analyze the scalability of our proposed approach, its validation was performed adopting test problems having from two to nine objective functions. Our preliminary experimental results indicate that our proposal is very competitive with respect to all the other MOEAs compared, obtaining the best results in several of the test problems adopted, but at a significantly lower computational cost.

Most of real-world optimization problems correspond to constrained multi-objective optimization problems (CMOPs). Multi-objective evolutionary algorithms (MOEAs) are useful to find out diverse Pareto-optimal solutions in CMOPs, and has been applied in various engineering fields. In order to expand the range of application of MOEAs further, we propose an improved evolutionary algorithm with parallel evaluation strategy (EAPES). In EAPES, feasible solutions and infeasible solution are separately stored in different populations, and infeasible solutions are evaluated in an unusual manner where not only feasible solutions but also useful infeasible solutions are used as parents to reproduce the populations for the next generation. Infeasible solutions are ranked based on a scalarizing function determined by objective function values and a total constraint violation value. This paper investigates the performance of the proposed EAPES to search for Pareto-optimal solutions compared to NSGA-II and the previous EAPES. The proposed EAPES with a well-tuned parameter is most capable to explore Pareto-optimal solutions with good diversity, spread, and convergence to the true Pareto front. The proposed EAPES assigns bad rank to the infeasible solutions that exist away from the true Pareto front, and does not store such solutions. Thus the proposed EAPES exhibits a higher searching capability than the previous EAPES by evaluating infeasible solutions in an appropriate balance between objective functions and total constraint violation. In addition, the results suggest that the proposed EAPES may exhibit high solution search performance even in more difficult CMOPs, which have more objective functions and/or more constraints.