Surrogate-assisted evolutionary computation: Recent advances and future challenges

In artificial intelligence, evolutionary algorithms (EAs) have shown to be effective and robust in solving difficult optimization problems. EAs are generic populationbased metaheuristic optimization algorithms. The mechanisms used in EAs are inspired by biological evolution: reproduction, mutation, recombination, and selection. The development of EAs can be classified into two categories: single objective and multi-objective optimization. In this thesis, both single objective and multi-objective evolutionary algorithms have been studied. For single objective optimization, various niching techniques are integrated with differential evolution (DE) and particle swarm optimization (PSO) for multi-modal optimization. Multi-modal optimization deals with optimization tasks that involve finding all or most of the global/local peaks in one single run. EAs in their original forms are usually designed for locating one single global solution. To promote and maintain formation of multiple stable subpopulations within a single population, we introduced a neighborhood mutation technique to enhance DE with ability of handling multi-modal problems. We also proposed a locally informed PSO to tackle multi-modal optimization. Beside these, several existing niching techniques from the literature were modified and improved by us.

A two-archive model based evolutionary algorithm for multimodal multi-objective optimization problems

Engine mount tuning is a multi‐disciplinary exercise since it affects Idle‐shake, Road‐shake and power‐train noise response. Engine inertia is often used as a tuned absorber for controlling suspension resonance related road‐shake issues. Last but not least, vehicle ride and handling may also be affected by mount tuning. In this work, Torque‐Roll‐Axis (TRA) decoupling of the rigid powertrain was used as a starting point for mount tuning. Nodal point of flexible powertrain bending was used to define the envelop for transmission mount locations. The frequency corresponding to the decoupled roll mode of the rigid powertrain was then adjusted for idle‐shake and road‐shake response management.A TRA decoupling procedure, cast as a multi‐objective optimization problem, was applied to a body‐on‐frame sport‐utility vehicle powertrain system. In addition to a standard gradient based optimization algorithm, available in commercial finite element software, an evolutionary computation paradigm known as Evolutionary Strategies (ES) was used to solve the optimization problem. The primary advantages of evolutionary computation over gradient based algorithms are as follows: i) They are less likely to get trapped in local minima and less dependent on initial values of the design parameters and therefore able to handle multi‐modal optimization problems unlike gradient based algorithms, ii) They produce a population of viable solutions, unlike gradient based algorithms which yields a single solution. The second advantage is very attractive in a production environment since packaging and other multi‐disciplinary constraints often require multiple quality solutions for the same problem. The process outlined in this work was verified by exercising a full‐vehicle finite element model. The process produced a set of production feasible powertrain mount parameters for acceptable idle and road shake performance.

In the last two decades, the field of global optimization has become very active, and, in this regard, many deterministic and stochastic algorithms were developed for solving various optimization problems. Among them, swarm intelligence (SI) is a stochastic algorithm that is more flexible and robust and has had the ability to find an optimum solution for high-dimensional optimization and search problems. SI-based algorithms are mainly inspired by the social behavior of fish schooling or bird flocking. Among the SI-based algorithms, Bat algorithm (BA) is one of the recently developed evolutionary algorithms. It employs an echolocation behavior of microbats by varying pulse rates of emission and loudness to perform their search process. In this paper, a modified Bat algorithm (MBA) is developed. The main focus of the MBA is to further enhance the exploration and exploitation search abilities of the original Bat algorithm. The performance of the modified Bat algorithm (MBA) is examined over the benchmark functions designed for evolutionary algorithms competition in the special session of 2005 IEEE Congress on Evolutionary Computation. The used benchmark functions include the unimodal, multimodal, and hybrid benchmark functions with high dimensionality. Furthermore, the impact analysis with respect to different values of temperatures is conducted by executing the proposed algorithm twenty-five times independently by using each benchmark function with different random seeds.

Optimization problems arise in various fields of science, engineering, and industry. In many occasions, such optimization problems, particularly in the present scenario, involve a variety of decision variables and complex structured objectives, and constraints. Often, the classical or traditional optimization techniques face difficulty in solving such real world optimization problems in their original form. Due to deficiencies of classical optimization algorithms in solving large-scale, highly non-linear, and often non-differentiable problems, there is a need to develop efficient and robust computational algorithms, which can solve problems, numerically irrespective of their sizes. Taking inspiration from nature to develop computationally efficient algorithms is one way to deal with real world optimization problems. Broadly, one can put these algorithms in the field of computational sciences and in particular, to computational intelligence. Formally, computational intelligence (CI) is a set of nature-inspired computational methodologies and approaches to solve complex real world problems. The major constituents of CI are Fuzzy Systems (FS), Neural Networks (NN), and Swarm Intelligence (SI) and Evolutionary Computation (EC). Computational intelligence techniques are powerful, efficient, flexible, and reliable. Swarm Intelligence and Evolutionary Computation are two very useful components of computational intelligence that are primarily used to solve optimization problems. This book primarily concerns with various swarm and evolutionary optimization algorithms. This chapter provides a brief introduction to swarm and evolutionary algorithms.

Genetic algorithm based multi-objective reliability optimization in interval environment

Improved differential evolution algorithms for handling economic dispatch optimization with generator constraints

Single-objective continuous optimization can be challenging, especially when dealing with multimodal problems. This work sheds light on the effects that multi-objective optimization may have in the single-objective space. For this purpose, we examine the inner mechanisms of the recently developed sophisticated local search procedure SOMOGSA. This method solves multimodal single-objective continuous optimization problems based on first expanding the problem with an additional objective (e.g., a sphere function) to the bi-objective domain and subsequently exploiting local structures of the resulting landscapes. Our study particularly focuses on the sensitivity of this multiobjectivization approach w.r.t. (1) the parametrization of the artificial second objective, as well as (2) the position of the initial starting points in the search space. As SOMOGSA is a modular framework for encapsulating local search, we integrate Nelder–Mead local search as optimizer in the respective module and compare the performance of the resulting hybrid local search to its original single-objective counterpart. We show that the SOMOGSA framework can significantly boost local search by multiobjectivization. Hence, combined with more sophisticated local search and metaheuristics, this may help solve highly multimodal optimization problems in the future.

In a real life situation, due to the complexity of the industrial systems and non-linearity of their behavior, it is very difficult to achieve optimum performance of system for desired industrial goals using uncertain, vague and imprecise data. Herein, an approach has been proposed through which the behavior of the system is analyzed in the form of well- known six reliability indices by using triangular fuzzy numbers which allow the consideration of expert opinions, linguistic variables, operating conditions in reliability information. Using their behavior analysis a fuzzy multi-objective optimization problem (FMOOP) has been formulated. Due to the conflicting nature of the multiple objectives, the decision making is difficult and it leads to the Pareto optimal solutions instead of single optimal solutions. Many evolutionary algorithms (EAs) already exist in the literature for solving a multi-objective optimization problem (MOOP), and are termed as multi-objective evolutionary algorithms (MOEAs). Particle swarm optimization (PSO) is one of such MOEA which demonstrates the ability to identity a Pareto-optimal front efficiently. Here, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker (DM) and then PSO is applied to solve the resulting fuzzified MOOP. The presented approach is applied in order to solve the multi-objective series-parallel system reliability optimization problem for a crystallization unit of a urea plant.

Pareto-domination was adopted to handle not only trade-off between objective and constraints but also trade-off between convergence and diversity on solving a constrained optimisation problem (COP) in this paper like many other researchers. But there are some differences. This paper converts a COP into an equivalent dynamic constrained multi-objective optimisation problem (DCMOP) first, then dynamic version of non-dominated sorting genetic algorithm with decomposition (NSGA/D) is designed to solve the equivalent DCMOP, consequently solve the COP. A key issue for the NSGA/D working effectively is that the environmental change should not destroy the feasibility of the population. With a feasible population, the NSGA/D could solve well the DCMOP just as a MOEA usually can solve well an unconstrained MOP. Experimental results show that the NSGA/D outperforms or performs similarly to other state-of-the-art algorithms referred to in this paper, especially in global search.

Optimization problems in many industrial applications are very hard to solve. Many examples of them can be found in the design of aeronautical systems. In this field, the designer is frequently faced with the problem of considering not only a single design objective, but several of them, i.e., the designer needs to solve a Multi-Objective Optimization Problem (MOP). In aeronautical systems design, aerodynamics plays a key role in aircraft design, as well as in the design of propulsion system components, such as turbine engines. Thus, aerodynamic shape optimization is a crucial task, and has been extensively studied and developed. Multi-Objective Evolutionary Algorithms (MOEAs) have gained popularity in recent years as optimization methods in this area, mainly because of their simplicity, their ease of use and their suitability to be coupled to specialized numerical simulation tools. In this chapter, we will review some of the most relevant research on the use of MOEAs to solve multi-objective and/or multi-disciplinary aerodynamic shape optimization problems. In this review, we will highlight some of the benefits and drawbacks of the use of MOEAs, as compared to traditional design optimization methods. In the second part of the chapter, we will present a case study on the application of MOEAs for the solution of a multi-objective aerodynamic shape optimization problem.

Although various optimization methods for solving single-objective problems have been developed in the last few decades, these methods have lost their eligibility due to the fact that today’s engineering problems are toward multiple objective optimization problems, in real applications. For single-objective optimization problems, for example, in case of a minimization problem, this value is the decision vector giving the smallest objective that can be achieved within the specified constraints. Hence the minimum decision vector within all possible (feasible) solution vectors is the so-called optimal solution and/or optimal design. However, in multi-objective optimization problems, since a different objective value is generated against each decision vector, the superiority of the solutions over each other is determined by considering the trade-off among the objective values. Therefore, the solution of multi-objective optimization problems, unlike single-objective problems, is a set of vectors rather than a single decision vector. In multi-objective optimization problems, especially if there are intricate objectives, the computational cost of the problem increases. In other words, while synchronously trying to maximize one of the objectives and to minimize another one makes it difficult to find the global optimum design. One of the important techniques used in multi-objective optimization problems is Pareto optimality which enables to select the global optimum solution taking into account the trade-off among all objectives. In this context, using of derivative-based methods has decreased, but the use of metaheuristic methods has increased due to the rapid availability of global optimum solution. This is because the improvements in the field of optimization are progressing in proportion to technology and varying according to the needs. In this chapter, one of the recent metaheuristic optimization methods based on swarm intelligence that is so-called a Pareto-based bat algorithm inspired by the behavior of determining the direction and distance of an object using the echo of the sound called the echolocation of bats is used in order to obtain optimum solutions for multi-objective engineering design problems. In this regard, a four-bar planar truss, a real-sized welded steel beam as well as a multi-layer radar absorber are selected as multi-objective engineering design optimization problems. In case the obtained results (optimal designs) are examined, the potency and the reliability of the proposed multi-objective Pareto-based bat algorithm are demonstrated.

A Multiobjective Optimization Problem (MOP) requires the optimization of several objective functions simultaneously, usually in conflict with each other. One of the most efficient algorithms for solving MOPs is MOEA/D (Multiobjective Evolutionary Algorithm Based on Decomposition), which decomposes a MOP into single-objective optimization subproblems and solves them using information from neighboring subproblems. MOEA/D variants with other evolutionary operators have emerged over the years, improving their efficiency in various MOPs. Recently, the IWOA (Improved Whale Optimization Algorithm) was proposed, an optimization algorithm bioinspired by the whale hunting method hybridized with Differential Evolution, which presented excellent results in single-objective optimization problems. This work proposes the MOEA/D-IWOA algorithm, which associates characteristics of the evolutionary operators of the IWOA to MOEA/D. Computational experiments were accomplished to analyze the performance of the MOEA/D-IWOA in benchmark MOPs suites. The results were compared with those obtained by the MOEA/D, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Third Evolution Step of Generalized Differential Evolution (GDE3), Improving the Strength Pareto Evolutionary Algorithm (SPEA2), and Indicator-Based Evolutionary Algorithm (IBEA) algorithms in the Hypervolume and Inverted Generational Distance Plus (IGD+) indicators. The MOEA/D-IWOA proved to be competitive, with a good performance profile, in addition to presenting the best results in some POMs.

An important and challenging data mining application in marketing is to learn models for predicting potential customers who contribute large profit to a company under resource constraints. In this paper, we first formulate this learning problem as a constrained optimization problem and then converse it to an unconstrained Multi-objective Optimization Problem (MOP). A parallel Multi-Objective Evolutionary Algorithm (MOEA) on consumer-level graphics hardware is used to handle the MOP. We perform experiments on a real-life direct marketing problem to compare the proposed method with the parallel Hybrid Genetic Algorithm, the DMAX approach, and a sequential MOEA. It is observed that the proposed method is much more effective and efficient than the other approaches.

Pump management and reservoir management have many similarities, and therefore, should ideally be analyzed in an integrated way to plan effectively the daily operation of water distribution systems. Historically, these two management activities have been evolved as separate tasks in energy-efficiency (i.e., energy optimization) studies and are often carried out in an isolated way. The latter being most often associated directly with the concepts of multimodal and multi-objective optimization problems, whereas the former is usually considered as a single optimization problem to be solved. When some single optimization problems appear at part of the solution tied to a local (i.e., regional) search-space (i.e., objective space), this artificial integration (i.e., multi-modal and multi-objective optimization) can always obtain optimal solutions. Similarly when system constraints and load conditions are considered, a set of feasible and innovative optimal solutions can be obtained in order to continue the enhancement of energy consumption that turns into a significant reduction in the overall operational cost (i.e., a potential of 6.24% cost savings) without affecting the level of services provided to the clients in a safe and protected manner.