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Summary: The portfolio optimization problem with cardinality constraint is usually solved by exact algorithms, heuristic algorithms, or combinations of them. We decompose the cardinality constraint mean‐variance model, and determine the assets and proportions by double roulette wheel selection (DRWS) and quadratic programming (QP), respectively. Then the accuracy of the solution is improved by a local search after we obtain the preliminary solution by combining DRWS and QP. Experimental results show that the proposed algorithm achieves better accuracy and more efficiency than the algorithms in the literature. Therefore, we can see that the algorithm designed according to the characteristics of specific problems can improve the computational efficiency, but the algorithm needs to be adjusted for different problems. [ABSTRACT FROM AUTHOR]

This paper proposes a novel metaheuristic optimizer, named Colony Search Optimization Algorithm (CSOA). The algorithm mimics the social behavior of early humans. Early humans expanded their settlements in search of more livable places to live. In CSOA, the worst solution is used to escape from local optima. And the number of these redundant solutions' updates is reduced to improve the performance of the algorithm. CSOA is tested with 26 mathematical optimization problems and 4 classical engineering optimization problems. The optimization results are compared with those of various optimization algorithms. The experimental results show that the CSOA is able to provide very competitive results on most of the tested problems. Then, a new effective method is provided for solving optimization problems. [ABSTRACT FROM AUTHOR]

The sine cosine algorithm's main idea is the sine and cosine-based vacillation outwards or towards the best solution. The first main contribution of this paper proposes an enhanced version of the SCA algorithm called as ESCA algorithm. The supremacy of the proposed algorithm over a set of state-of-the-art algorithms in terms of solution accuracy and convergence speed will be demonstrated by experimental tests. When these algorithms are transferred to the business sector, they must meet time requirements dependent on the industrial process. If these temporal requirements are not met, an efficient solution is to speed them up by designing parallel algorithms. The second major contribution of this work is the design of several parallel algorithms for efficiently exploiting current multicore processor architectures. First, one-level synchronous and asynchronous parallel ESCA algorithms are designed. They have two favors; retain the proposed algorithm's behavior and provide excellent parallel performance by combining coarse-grained parallelism with fine-grained parallelism. Moreover, the parallel scalability of the proposed algorithms is further improved by employing a two-level parallel strategy. Indeed, the experimental results suggest that the one-level parallel ESCA algorithms reduce the computing time, on average, by 87.4% and 90.8%, respectively, using 12 physical processing cores. The two-level parallel algorithms provide extra reductions of the computing time by 91.4%, 93.1%, and 94.5% with 16, 20, and 24 processing cores, including physical and logical cores. Comparison analysis is carried out on 30 unconstrained benchmark functions and three challenging engineering design problems. The experimental outcomes show that the proposed ESCA algorithm behaves outstandingly well in terms of exploration and exploitation behaviors, local optima avoidance, and convergence speed toward the optimum. The overall performance of the proposed algorithm is statistically validated using three non-parametric statistical tests, namely Friedman, Friedman aligned, and Quade tests. [ABSTRACT FROM AUTHOR]

This paper introduces the Human Evolutionary Optimization Algorithm (HEOA), a metaheuristic algorithm inspired by human evolution. HEOA divides the global search process into two distinct phases: human exploration and human development. Logistic Chaos Mapping is employed for initialization. In the human exploration phase, an initial global search is conducted, followed by the human development phase, in which the population is categorized into leaders, explorers, followers, and losers, each utilizing distinct search strategies. The convergence speed and search accuracy of HEOA are evaluated using 23 well-established test functions. Furthermore, the algorithm's applicability in engineering optimization is assessed with four engineering problems. A comparative analysis with ten other algorithms highlights HEOA's effectiveness, as evidenced by various performance metrics and statistical measures. Consistently, the results demonstrate that HEOA surpasses most current state-of-the-art algorithms in approximating optimal solutions for complex global optimization problems. The MATLAB code for HEOA is available at https://github.com/junbolian/HEOA.git. [ABSTRACT FROM AUTHOR]

The sine cosine algorithm’s main idea is the sine and cosine-based vacillation outwards or towards the best solution. The first main contribution of this paper proposes an enhanced version of the SCA algorithm called as ESCA algorithm. The supremacy of the proposed algorithm over a set of state-of-the-art algorithms in terms of solution accuracy and convergence speed will be demonstrated by experimental tests. When these algorithms are transferred to the business sector, they must meet time requirements dependent on the industrial process. If these temporal requirements are not met, an efficient solution is to speed them up by designing parallel algorithms. The second major contribution of this work is the design of several parallel algorithms for efficiently exploiting current multicore processor architectures. First, one-level synchronous and asynchronous parallel ESCA algorithms are designed. They have two favors; retain the proposed algorithm’s behavior and provide excellent parallel performance by combining coarse-grained parallelism with fine-grained parallelism. Moreover, the parallel scalability of the proposed algorithms is further improved by employing a two-level parallel strategy. Indeed, the experimental results suggest that the one-level parallel ESCA algorithms reduce the computing time, on average, by 87.4% and 90.8%, respectively, using 12 physical processing cores. The two-level parallel algorithms provide extra reductions of the computing time by 91.4%, 93.1%, and 94.5% with 16, 20, and 24 processing cores, including physical and logical cores. Comparison analysis is carried out on 30 unconstrained benchmark functions and three challenging engineering design problems. The experimental outcomes show that the proposed ESCA algorithm behaves outstandingly well in terms of exploration and exploitation behaviors, local optima avoidance, and convergence speed toward the optimum. The overall performance of the proposed algorithm is statistically validated using three non-parametric statistical tests, namely Friedman, Friedman aligned, and Quade tests.

Multi-objective problems with conflicting objectives cannot be effectively solved by aggregation-based methods. The answer to such problems is a Pareto optimal solution set. Due to the difficulty of solving multi-objective problems using multi-objective algorithms and the lack of enough expertise, researchers in different fields tend to aggregative objectives and use single-objective algorithms. This work is a seminal attempt to propose the use of multi-objective algorithms in the field of hand posture estimation. Hand posture estimation is a key step in hand gesture recognition, which is a part of an overall attempt to make human-computer interaction more like human face-to-face communication. Hand posture estimation is first formulated as a bi-objective problem. A modified version of Multi-Objective Particle Swarm Optimisation (MOPSO) is then proposed to approximate the Pareto optimal font of 50 different postures. The main motivation of integrating a new operator (called Evolutionary Population Dynamics — EPD) in MOPSO is due to the nature of hand posture estimation problems in which parameters should not be tuned in a same manner since they show varied impacts on the objectives. EPD allows randomising different parameters in a solution and provides different exploratory behaviours for the parameters of an optimisation algorithm rather than each individual solution. The MOPSO algorithm is equipped with a mechanism to randomly re-initialise poor particles around the optimal solutions in the archive. The improved MOPSO is tested on ZDT and CEC2009 test functions and compared with the standard MOPSO, NSGA-II, and MOEA/D. The results show that the proposed MOPSO (MOPSO+EPD) significantly outperforms MOPSO on the majority of test functions in terms of both convergence and coverage. MOPSO+EPD also approximates well-distributed Pareto optimal fronts for most of the postures considered in this work. The post analysis of the results is conducted to understand the relationship between the parameters and objectives of this problem (design principals) for the first time in the literature as well. [ABSTRACT FROM AUTHOR]

In order to down-weight or ignore unusual data and multicollinearity effects, some alternative robust estimators are introduced. Firstly, a ridge least trimmed squares approach is discussed. Then, based on a penalization scheme, a nonlinear integer programming problem is suggested. Because of complexity and difficulty, the proposed optimization problem is solved by a tabu search heuristic algorithm. Also, the robust generalized cross validation criterion is employed for selecting the optimal ridge parameter. Finally, a simulation case and two real-world data sets are computationally studied to support our theoretical discussions. [ABSTRACT FROM AUTHOR]

This paper proposes an optimisation algorithm called Grasshopper Optimisation Algorithm (GOA) and applies it to challenging problems in structural optimisation. The proposed algorithm mathematically models and mimics the behaviour of grasshopper swarms in nature for solving optimisation problems. The GOA algorithm is first benchmarked on a set of test problems including CEC2005 to test and verify its performance qualitatively and quantitatively. It is then employed to find the optimal shape for a 52-bar truss, 3-bar truss, and cantilever beam to demonstrate its applicability. The results show that the proposed algorithm is able to provide superior results compared to well-known and recent algorithms in the literature. The results of the real applications also prove the merits of GOA in solving real problems with unknown search spaces. [ABSTRACT FROM AUTHOR]

This paper proposes a novel nature-inspired meta-heuristic optimization algorithm, called Whale Optimization Algorithm (WOA), which mimics the social behavior of humpback whales. The algorithm is inspired by the bubble-net hunting strategy. WOA is tested with 29 mathematical optimization problems and 6 structural design problems. Optimization results prove that the WOA algorithm is very competitive compared to the state-of-art meta-heuristic algorithms as well as conventional methods. The source codes of the WOA algorithm are publicly available at http://www.alimirjalili.com/WOA.html [ABSTRACT FROM AUTHOR]

This paper proposes a novel nature-inspired algorithm called Ant Lion Optimizer (ALO). The ALO algorithm mimics the hunting mechanism of antlions in nature. Five main steps of hunting prey such as the random walk of ants, building traps, entrapment of ants in traps, catching preys, and re-building traps are implemented. The proposed algorithm is benchmarked in three phases. Firstly, a set of 19 mathematical functions is employed to test different characteristics of ALO. Secondly, three classical engineering problems (three-bar truss design, cantilever beam design, and gear train design) are solved by ALO. Finally, the shapes of two ship propellers are optimized by ALO as challenging constrained real problems. In the first two test phases, the ALO algorithm is compared with a variety of algorithms in the literature. The results of the test functions prove that the proposed algorithm is able to provide very competitive results in terms of improved exploration, local optima avoidance, exploitation, and convergence. The ALO algorithm also finds superior optimal designs for the majority of classical engineering problems employed, showing that this algorithm has merits in solving constrained problems with diverse search spaces. The optimal shapes obtained for the ship propellers demonstrate the applicability of the proposed algorithm in solving real problems with unknown search spaces as well. Note that the source codes of the proposed ALO algorithm are publicly available at http://www.alimirjalili.com/ALO.html . [ABSTRACT FROM AUTHOR]

Highlights: [•] A new meta-heuristic called Grey Wolf Optimizer inspired by grey wolves is proposed. [•] The GWO algorithm is benchmarked on 29 well-known test functions. [•] The results on the unimodal functions show the superior exploitation of GWO. [•] The exploration ability of GWO is confirmed by the results on multimodal functions. [•] The results on semi-real and real problems confirm the performance of GWO in practice. [ABSTRACT FROM AUTHOR]

In the field of robust optimization, the robustness of a solution is confirmed using a robustness indicator. In the literature, such an indicator uses explicit or implicit averaging techniques. One of the main drawbacks of the implicit averaging techniques is unreliability since they only use the sampled points generated by an optimization algorithm. In this paper, we propose a set of conditional operators for comparing solutions based on the number of sampled solutions in their neighbourhoods, thereby making reliable decisions during the process of robust optimization. This technique is integrated into the Particle Swarm Optimization (PSO) to update GBEST and PBESTs reliably, and the designed robust PSO algorithm is applied to a number of case studies. A set of extensive experiments shows that the proposed technique prevents an algorithm that relies on implicit averaging technique from making risky decisions and thus proven beneficial in finding robust solutions. [ABSTRACT FROM AUTHOR]