Dynamic multi-objective optimisation (DMO) handles optimisation problems with multiple (often conflicting) objectives in varying environments. This paper proposes vector autoregressive evolution (VARE) consisting of vector autoregression (VAR) and environment-aware hypermutation (EAH) to address environmental changes in DMO. In light of mutual dependency between decision variables in Pareto-optimal solutions, VARE builds an efficient VAR model, capturing such mutual relationship while handling dense model parameterisation with dimensionality reduction, to predict the moving solutions in dynamic environments. Additionally, VARE introduces EAH to address the blindness of existing hypermutation strategies in increasing population diversity, for scenarios where predictive approaches are unsuitable, by making hypermutation aware of the significance of environmental changes in both decision and objective spaces. A seamless integration of VAR and EAH in an environment-adaptive manner makes VARE effective to handle a variety of dynamic environments and competitive with several popular DMO algorithms, as demonstrated in extensive empirical studies. Specially, the proposed algorithm is computationally much faster than popular transfer learning based approaches while producing significantly better results.

Most existing dynamic multi-objective evolutionary algorithms (DMOEAs) have been designed to handle dynamic multi-objective optimization problems (DMOPs) with regular environmental changes. However, they often overlook scenarios where environmental changes are irregular and less predictable. Recently, knowledge transfer has been proposed as a novel paradigm for solving DMOPs. Despite this, most transfer strategies only consider transferring knowledge obtained from the previous environment while ignoring significant differences that may exist between adjacent environments due to irregular changes. To address these issues, this paper proposes a novel knowledge transfer strategy based on a Gaussian mixture model (denoted as KTMM) for solving DMOPs with irregular changes. In particular, an adaptive Gaussian mixture model is designed to capture the knowledge of historical environments, which is then transferred to generate an initial population for the new environment. Additionally, a new method for controlling irregular changes is introduced into widely-used benchmarks to form the DMOP benchmark with irregular changes. Our proposed KTMM is compared with six state-of-the-art DMOEAs on several benchmark problems with irregular changes. Experimental results demonstrate the superiority of our proposed method in most test instances and in a real-world problem.

Summary Brain storm optimization (BSO) is a population‐based intelligence algorithm for optimization problems, which has attracted researchers' growing attention due to its simplicity and efficiency. An improved BSO, called CIBSO, is presented in this article. First of all, a new grouping method, in which the population is partitioned into chunks according to the fitness and recombined to groups, is developed to balance each group with same quality‐level. Afterwards, a new mutation strategy is designed in CIBSO and a learning mechanism is used to adaptively select appropriate strategy. Experiments on the CEC2014 test suite indicate that CIBSO is better or at least competitive performance against the compared BSO variants.

Unsustainable fishing, driven by bycatch and discards, harms marine ecosystems. Addressing this, we propose a Coordinate-Aware Mask R-CNN (CAM-RCNN) method to enhance fish detection in commercial trawls. Leveraging CoordConv and Group Normalization, our approach improves generalization and stability. To tackle class imbalance, a compound Dice and cross-entropy loss is employed, and image data are enhanced through multi-scale retinex and color restoration. Evaluating on two fishing datasets, CAM-RCNN excels in accuracy and generalization, achieving the best Average Precision (AP) for instance mask and BBOX prediction in both source (39.7%, 40.2%) and target domains (24.4%, 24.2%). This method promotes sustainable fishing by selectively capturing desired fish, reducing harm to non-target species.

In recent years, researchers have made significant progress in handling dynamic multiobjective optimization problems (DMOPs), particularly for environmental changes with predictable characteristics. However, little attention has been paid to DMOPs with stochastic changes. It may be difficult for existing dynamic multiobjective evolutionary algorithms (DMOEAs) to effectively handle this kind of DMOPs because most DMOEAs assume that environmental changes follow regular patterns and consecutive environments are similar. This article presents a Mahalanobis distance-based approach (MDA) to deal with DMOPs with stochastic changes. Specifically, we make an all-sided assessment of search environments via Mahalanobis distance on saved information to learn the relationship between the new environment and historical ones. Afterward, a change response strategy applies the learning to the new environment to accelerate the convergence and maintain the diversity of the population. Besides, the change degree is considered for all decision variables to alleviate the impact of stochastic changes on the evolving population. An MDA has been tested on stochastic DMOPs with two to four objectives. The results show that MDA performs significantly better than the other latest algorithms in this article, suggesting that MDA is effective for DMOPs with stochastic changes.

A mixed-integer programming (MIP) problem contains both constraints and integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts. In particular, the number of discontinuous feasible parts will drastically increase with the increase of the number of integer decision variables and/or the size of the candidate set of each integer decision variable. Due to the fact that the optimal solution is located in one of the discontinuous feasible parts, it is a challenging task to solve a MIP problem. This article presents a cutting and repulsion-based evolutionary framework (called CaR) to solve MIP problems. CaR includes two main strategies: 1) the cutting strategy and 2) the repulsion strategy. In the cutting strategy, an additional constraint is constructed based on the objective function value of the best individual found so far, the aim of which is to continuously cut unpromising discontinuous feasible parts. As a result, the probability of the population entering a wrong discontinuous feasible part can be decreased. In addition, in the repulsion strategy, once it has been detected that the population has converged to a discontinuous feasible part, the population will be reinitialized. Moreover, a repulsion function is designed to repulse the previously explored discontinuous feasible parts. Overall, the cutting strategy can significantly reduce the number of discontinuous feasible parts and the repulsion strategy can probe the remaining discontinuous feasible parts. Sixteen test problems developed in this article and two real-world cases are used to verify the effectiveness of CaR. The results demonstrate that CaR performs well in solving MIP problems.

The aim of multi-objective particle swarm optimizer (MOPSO) is to find an accurate and well-distributed approximation of the true Pareto Front (PF). The intrinsic character of PSO puts convergence first, which can cause great loss of population diversity. How to maintain the convergence and diversity simultaneously is an essential issue for MOPSO. In this paper, we propose a niche based multi-objective particle swarm optimizer (NMOPSO) to balance the convergence and diversity. First, a niche based on the Euclidean distance is constructed for each particle, then the leading particle is chosen out either from the niche or from the whole swarm. After that, two position update strategies are designed to update the position of each particle. The position update strategies provide two guiding models for leaders, one is utilizing the difference vector between the leader and the current particle, the other is directly taking some components of leaders. Three well-known test suites are employed to verify the performance of NMOPSO. Compared with three popular MOPSOs, simulation results show that NMOPSO performs better on most of test problems.

MOTIVATION: Flux balance analysis (FBA) based bilevel optimization has been a great success in redesigning metabolic networks for biochemical overproduction. To date, many computational approaches have been developed to solve the resulting bilevel optimization problems. However, most of them are of limited use due to biased optimality principle, poor scalability with the size of metabolic networks, potential numeric issues or low quantity of design solutions in a single run. RESULTS: Here, we have employed a network interdiction model free of growth optimality assumptions, a special case of bilevel optimization, for computational strain design and have developed a hybrid Benders algorithm (HBA) that deals with complicating binary variables in the model, thereby achieving high efficiency without numeric issues in search of best design strategies. More importantly, HBA can list solutions that meet users' production requirements during the search, making it possible to obtain numerous design strategies at a small runtime overhead (typically ∼1 h, e.g. studied in this article). AVAILABILITY AND IMPLEMENTATION: Source code implemented in the MATALAB Cobratoolbox is freely available at https://github.com/chang88ye/NIHBA. CONTACT: [email protected] or [email protected]. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems . However, the performance of these algorithms depends largely on problem characteristics. There is a need to improve these algorithms for wide applicability. References, often specified by the decision maker’s preference in different forms, are very effective to boost the performance of algorithms. This paper proposes a novel framework for effective use of references to strengthen algorithms. This framework considers references as search targets which can be adjusted based on the information collected during the search. The proposed framework is combined with new strategies, such as reference adaptation and adaptive local mating, to solve different types of problems. The proposed algorithm is compared with state-of-the-arts on a wide range of problems with diverse characteristics. The comparison and extensive sensitivity analysis demonstrate that the proposed algorithm is competitive and robust across different types of problems studied in this paper.

Dynamic multiobjective optimization (DMO) has gained increasing attention in recent years. Test problems are of great importance in order to facilitate the development of advanced algorithms that can handle dynamic environments well. However, many of the existing dynamic multiobjective test problems have not been rigorously constructed and analyzed, which may induce some unexpected bias when they are used for algorithmic analysis. In this paper, some of these biases are identified after a review of widely used test problems. These include poor scalability of objectives and, more important, problematic overemphasis of static properties rather than dynamics making it difficult to draw accurate conclusion about the strengths and weaknesses of the algorithms studied. A diverse set of dynamics and features is then highlighted that a good test suite should have. We further develop a scalable continuous test suite, which includes a number of dynamics or features that have been rarely considered in literature but frequently occur in real life. It is demonstrated with empirical studies that the proposed test suite is more challenging to the DMO algorithms found in the literature. The test suite can also test algorithms in ways that existing test suites cannot.

This paper proposes a new prediction-based dynamic multiobjective optimization (PBDMO) method, which combines a new prediction-based reaction mechanism and a popular regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA) for solving dynamic multiobjective optimization problems. Whenever a change is detected, PBDMO reacts effectively to it by generating three subpopulations based on different strategies. The first subpopulation is created by moving nondominated individuals using a simple linear prediction model with different step sizes. The second subpopulation consists of some individuals generated by a novel sampling strategy to improve population convergence as well as distribution. The third subpopulation comprises some individuals generated using a shrinking strategy based on the probability distribution of variables. These subpopulations are tailored to form a population for the new environment. The experimental results carried out on a variety of bi- and three-objective benchmark functions demonstrate that the proposed technique has competitive performance compared with some state-of-the-art algorithms.

Dynamic multiobjective optimisation deals with multiobjective problems whose objective functions, search spaces, or constraints are time-varying during the optimisation process. Due to wide presence in real-world applications, dynamic multiobjective problems (DMOPs) have been increasingly studied in recent years. Whilst most studies concentrated on DMOPs with only two objectives, there is little work on more objectives. This paper presents an empirical investigation of evolutionary algorithms for three-objective dynamic problems. Experimental studies show that all the evolutionary algorithms tested in this paper encounter performance degradedness to some extent. Amongst these algorithms, the multipopulation based change handling mechanism is generally more robust for a larger number of objectives, but has difficulty in deal with time-varying deceptive characteristics.

Multiobjective optimisation in dynamic environments is challenging due to the presence of dynamics in the problems in question. Whilst much progress has been made in benchmarks and algorithm design for dynamic multiobjective optimisation, there is a lack of work on the detectability of environmental changes and how this affects the performance of evolutionary algorithms. This is not intentionally left blank but due to the unavailability of suitable test cases to study. To bridge the gap, this work presents several scenarios where environmental changes are less likely to be detected. Our experimental studies suggest that the less detectable environments pose a big challenge to evolutionary algorithms.

Decomposition-based multiobjective evolutionary algorithms (MOEAs) have received increasing research interests due to their high performance for solving multiobjective optimization problems. However, scalarizing functions (SFs), which play a crucial role in balancing diversity and convergence in these kinds of algorithms, have not been fully investigated. This paper is mainly devoted to presenting two new SFs and analyzing their effect in decomposition-based MOEAs. Additionally, we come up with an efficient framework for decomposition-based MOEAs based on the proposed SFs and some new strategies. Extensive experimental studies have demonstrated the effectiveness of the proposed SFs and algorithm.

Dynamic multiobjective optimization (DMO) has received growing research interest in recent years since many real-world optimization problems appear to not only have multiple objectives that conflict with each other but also change over time. The time-varying characteristics of these DMO problems (DMOPs) pose new challenges to evolutionary algorithms. Considering the importance of a representative and diverse set of benchmark functions for DMO, in this paper, we propose a new benchmark generator that is able to tune a number of challenging characteristics, including mixed Pareto-optimal front (convexity-concavity), nonmonotonic and time-varying variable-linkages, mixed types of changes, and randomness in type change, which have rarely or not been considered or tested in the literature. A test suite of ten instances with different dynamic features is produced from the generator in this paper. Additionally, a few new performance measures are proposed to evaluate algorithms for DMOPs with different characteristics. Six representative multiobjective evolutionary algorithms from the literature are investigated based on the proposed DMO test suite and performance measures. The experimental results facilitate a better understanding of strengths and weaknesses of these compared algorithms for DMOPs.

This paper presents a new algorithm, called steady-state and generational evolutionary algorithm, which combines the fast and steadily tracking ability of steady-state algorithms and good diversity preservation of generational algorithms, for handling dynamic multiobjective optimization. Unlike most existing approaches for dynamic multiobjective optimization, the proposed algorithm detects environmental changes and responds to them in a steady-state manner. If a change is detected, it reuses a portion of outdated solutions with good distribution and relocates a number of solutions close to the new Pareto front based on the information collected from previous environments and the new environment. This way, the algorithm can quickly adapt to changing environments and thus is expected to provide a good tracking ability. The proposed algorithm is tested on a number of bi- and three-objective benchmark problems with different dynamic characteristics and difficulties. Experimental results show that the proposed algorithm is very competitive for dynamic multiobjective optimization in comparison with state-of-the-art methods.

While Pareto-based multiobjective optimization algorithms continue to show effectiveness for a wide range of practical problems that involve mostly two or three objectives, their limited application for many-objective problems, due to the increasing proportion of nondominated solutions and the lack of sufficient selection pressure, has also been gradually recognized. In this paper, we revive an early developed and computationally expensive strength Pareto-based evolutionary algorithm by introducing an efficient reference direction-based density estimator, a new fitness assignment scheme, and a new environmental selection strategy, for handling both multiobjective and many-objective problems. The performance of the proposed algorithm is validated and compared with some state-of-the-art algorithms on a number of test problems. Experimental studies demonstrate that the proposed method shows very competitive performance on both multiobjective and many-objective problems considered in this paper. Besides, our extensive investigations and discussions reveal an interesting finding, that is, diversity-first-and-convergence-second selection strategies may have great potential to deal with many-objective optimization.

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) decomposes a multiobjective optimization problem into a number of single-objective problems and solves them collaboratively. Since its introduction, MOEA/D has gained increasing research interest and has become a benchmark for validating new designed algorithms. Despite that, some recent studies have revealed that MOEA/D faces some difficulties to solve problems with complicated characteristics. In this paper, we study the influence of the penalty-based boundary intersection (PBI) approach, one of the most popular decomposition approaches used in MOEA/D, on individuals' convergence and diversity, showing that the fixed same penalty value for all the subproblems is not very sensible. Based on this observation, we propose to use adaptive penalty values to enhance the balance between population convergence and diversity. Experimental studies show that the proposed adaptive PBI can generally improve the performance of the original PBI when solving the problems considered in this paper.

The multiobjective evolutionary algorithm based on decomposition (MOEA/D) has been shown to be very efficient in solving multiobjective optimization problems (MOPs). In practice, the Pareto-optimal front (POF) of many MOPs has complex characteristics. For example, the POF may have a long tail and sharp peak and disconnected regions, which significantly degrades the performance of MOEA/D. This paper proposes an improved MOEA/D for handling such kind of complex problems. In the proposed algorithm, a two-phase strategy (TP) is employed to divide the whole optimization procedure into two phases. Based on the crowdedness of solutions found in the first phase, the algorithm decides whether or not to delicate computational resources to handle unsolved subproblems in the second phase. Besides, a new niche scheme is introduced into the improved MOEA/D to guide the selection of mating parents to avoid producing duplicate solutions, which is very helpful for maintaining the population diversity when the POF of the MOP being optimized is discontinuous. The performance of the proposed algorithm is investigated on some existing benchmark and newly designed MOPs with complex POF shapes in comparison with several MOEA/D variants and other approaches. The experimental results show that the proposed algorithm produces promising performance on these complex problems.

Quantum-behaved particle swarm optimization (QPSO) has shown to be an effective algorithm for solving global optimization problems that are of high complexity. This paper presents a new QPSO algorithm, denoted LI-QPSO, which employs a model-based linear interpolation method to strengthen the local search ability and improve the precision and convergence performance of the QPSO algorithm. In LI-QPSO, linear interpolation is used to approximate the objective function around a pre-chosen point with high quality in the search space. Then, local search is used to generate a promising trial point around this pre-chosen point, which is then used to update the worst personal best point in the swarm. Experimental results show that the proposed algorithm provides some significant improvements in performance on the tested problems.