When some parameters of a constrained optimization problem (COP) are uncertain, this gives rise to a predict-then-optimize (PtO) problem, comprising two stages: the prediction of the unknown parameters from contextual information and the subsequent optimization using those predicted parameters. Decision-focused learning (DFL) implements the first stage by training a machine learning (ML) model to optimize the quality of the decisions made using the predicted parameters. When the predicted parameters occur in the constraints, they can lead to infeasible solutions. Therefore, it is important to simultaneously manage both feasibility and decision quality. We develop a DFL framework for predicting constraint parameters in a generic COP. While prior works typically assume that the underlying optimization problem is a linear program (LP) or integer LP (ILP), our approach makes no such assumption. We derive two novel loss functions based on maximum likelihood estimation (MLE): the first one penalizes infeasibility (by penalizing predicted parameters that lead to infeasible solutions), while the second one penalizes suboptimal decisions (by penalizing predicted parameters that make the true optimal solution infeasible). We introduce a single tunable parameter to form a weighted average of the two losses, allowing decision-makers to balance suboptimality and feasibility. We experimentally demonstrate that adjusting this parameter provides decision-makers control over this trade-off. Moreover, across several COP instances, we show that adjusting the tunable parameter allows a decision-maker to prioritize either suboptimality or feasibility, outperforming the performance of existing baselines in either objective.

The widespread acceptance of empirically derived codal provisions and equations in civil engineering stands in stark contrast to the skepticism facing machine learning (ML) models, despite their shared statistical foundations. This paper examines this philosophical tension through the lens of structural engineering and explores how integrating ML challenges traditional engineering philosophies and professional identities. Recent efforts have documented how ML enhances predictive accuracy, optimizes designs, and analyzes complex behaviors. However, one might also raise concerns about the diminishing role of human intuition and the interpretability of algorithms. To showcase this rarely explored front, this paper presents how ML can be successfully integrated into various engineering problems by means of formulation via deduction, induction, and abduction. Then, this paper identifies three principal paradoxes that could arise when adopting ML: analysis paralysis (increased prediction accuracy leading to a reduced understanding of physical mechanisms), infeasible solutions (optimization resulting in unconventional designs that challenge engineering intuition), and the Rashomon effect (where contradictions in explainability methods and physics arise). This paper concludes by addressing these paradoxes and arguing the need to rethink epistemological shifts in engineering and engineering education and methodologies to harmonize traditional principles with ML.

Integer linear programming (ILP) models a wide range of practical combinatorial optimization problems and has significant impacts in industry and management sectors. This work proposes new characterizations of ILP with the concept of boundary solutions. Motivated by the new characterizations, we develop an efficient local search solver, which is the first local search solver for general ILP validated on a large heterogeneous problem dataset. We propose a new local search framework that switches between three modes, namely Search, Improve, and Restore modes. We design tailored operators adapted to different modes, thus improving the quality of the current solution according to different situations. For the Search and Restore modes, we propose an operator named tight move, which adaptively modifies variables' values, trying to make some constraint tight. For the Improve mode, an efficient operator lift move is proposed to improve the quality of the objective function while maintaining feasibility. Putting these together, we develop a local search solver for integer linear programming called Local-ILP. Experiments conducted on the MIPLIB dataset show the effectiveness of our solver in solving large-scale hard integer linear programming problems within a reasonably short time. Local-ILP is competitive and complementary to the state-of-the-art commercial solver Gurobi and significantly outperforms the state-of-the-art non-commercial solver SCIP. Moreover, our solver establishes new records for 6 MIPLIB open instances. The theoretical analysis of our algorithm is also presented, which shows our algorithm could avoid visiting unnecessary regions and also maintain good connectivity of targeted solutions.

The goal of constrained multiobjective evolutionary optimization is to obtain a set of well-converged and welldistributed feasible solutions. To complete this goal, there should be a tradeoff among feasibility, diversity, and convergence. However, it is nontrivial to balance these three elements simultaneously by using a single tradeoff model since the importance of each element varies in different evolutionary phases. As an alternative, we adapt different tradeoff models in different phases and propose a novel algorithm called ATM-R. In the infeasible phase, ATM-R takes the tradeoff between diversity and feasibility into account, aiming to move the population toward feasible regions from diverse search directions. In the semi-feasible phase, ATM-R promotes the transition from "the tradeoff between feasibility and diversity" to "the tradeoff between diversity and convergence", which can facilitate the discovering of enough feasible regions and speed up the search for the feasible Pareto optima in succession. In the feasible phase, the tradeoff between diversity and convergence is considered to attain a set of well-converged and well-distributed feasible solutions. It is worth noting that the merits of reference points are leveraged in ATM-R to accomplish these tradeoff models. Also, in ATM-R, a multiphase mating selection strategy is developed to generate promising solutions beneficial to different evolutionary phases. Systemic experiments on a wide range of benchmark test functions demonstrate that ATM-R is effective and competitive, compared against five state-of-the-art constrained multiobjective optimization evolutionary algorithms.

We argue that results produced by a heuristic optimisation algorithm cannot be considered reproducible unless the algorithm fully specifies what should be done with solutions generated outside the domain, even in the case of simple box constraints. Currently, in the field of heuristic optimisation, such specification is rarely mentioned or investigated due to the assumed triviality or insignificance of this question. Here, we demonstrate that, at least in algorithms based on Differential Evolution, this choice induces notably different behaviours - in terms of performance, disruptiveness and population diversity. This is shown theoretically (where possible) for standard Differential Evolution in the absence of selection pressure and experimentally for the standard and state-of-the-art Differential Evolution variants on special test function $f_0$ and BBOB benchmarking suite, respectively. Moreover, we demonstrate that the importance of this choice quickly grows with problem's dimensionality. Different Evolution is not at all special in this regard - there is no reason to presume that other heuristic optimisers are not equally affected by the aforementioned algorithmic choice. Thus, we urge the field of heuristic optimisation to formalise and adopt the idea of a new algorithmic component in heuristic optimisers, which we call here a strategy of dealing with infeasible solutions. This component needs to be consistently (a) specified in algorithmic descriptions to guarantee reproducibility of results, (b) studied to better understand its impact on algorithm's performance in a wider sense and (c) included in the (automatic) algorithmic design. All of these should be done even for problems with box constraints.

Consequently, any optimisation algorithm, including nonlinear optimisation heuristics, should be able to deal with such constraints by means of a constraint handling method. Such a method deals with infeasible solution (IS) candidates x R D by means of a suitable approach, involving concepts such as, e.g., ignoring or repairing them. In nonlinear optimisation heuristics inspired by nature, the infeasible components of a solution are generated by the mutation operator, which is expected to help explore regions of the search space outside the scope of the crossover operator and then converge towards solution candidates for which f is minimised or maximised. Intuitively, this search process is disrupted and thus lacks the ability to adapt itself to the properties of the objective function f when it generates many infeasible solutions during the course of the search. In this paper, we present an empirical investigation of the proportion of infeasible solutions generated for various variants and parameter settings of Differential Evolution. The algorithm variants under consideration are introduced in Section 2 while the adopted methods of dealing with generated infeasible solutions, as well as the experimental setup, are introduced in Section 3. The results are discussed in Section 4 and conclusions are drawn in Section 5. 2. Differential evolution Originally intended for a simple fitting problem [36, 31], Differential Evolution (DE) has soon become an established metaheuristic method for general-purpose real-valued optimisation, finding its place among other optimisation methods for real-world applications in engineering, robotics and other fields [35, 30, 41]. Besides the effectiveness of the DE optimisation framework, its success is attributed to the simplicity of its algorithmic structure. As can be seen from the pseudocode in Algorithm 1, it requires tuning only three parameters: the population size N (i.e., number of candidate solutions), the scaling factor F (i.e., a prefixed scalar multiplier in the range p0,2s involved in the mutation process) and the crossover rate C

Many science and engineering applications require finding solutions to planning and optimization problems by satisfying a set of constraints. These constraint problems (CPs) are typically NP-complete and can be formalized as constraint satisfaction problems (CSPs) or constraint optimization problems (COPs). Evolutionary algorithms (EAs) are good solvers for optimization problems ubiquitous in various problem domains, however traditional operators for EAs are 'blind' to constraints or generally use problem dependent objective functions; as they do not exploit information from the constraints in search for solutions. A variation of EA, Intelligent constraint handling evolutionary algorithm (ICHEA), has been demonstrated to be a versatile constraints-guided EA for continuous constrained problems in our earlier works in (Sharma and Sharma, 2012) where it extracts information from constraints and exploits it in the evolutionary search to make the search more efficient. In this paper ICHEA has been demonstrated to solve benchmark exam timetabling problems, a classic COP. The presented approach demonstrates competitive results with other state-of-the-art approaches in EAs in terms of quality of solutions. ICHEA first uses its inter-marriage crossover operator to satisfy all the given constraints incrementally and then uses combination of traditional and enhanced operators to optimize the solution. Generally CPs solved by EAs are problem dependent penalty based fitness functions. We also proposed a generic preference based solution model that does not require a problem dependent fitness function, however currently it only works for mutually exclusive constraints.

Recurrent neural networks (RNNs) are a powerful approach for time series prediction. However, their performance is strongly affected by their architecture and hyperparameter settings. The architecture optimization of RNNs is a time-consuming task, where the search space is typically a mixture of real, integer and categorical values. To allow for shrinking and expanding the size of the network, the representation of architectures often has a variable length. In this paper, we propose to tackle the architecture optimization problem with a variant of the Bayesian Optimization (BO) algorithm. To reduce the evaluation time of candidate architectures the Mean Absolute Error Random Sampling (MRS), a training-free method to estimate the network performance, is adopted as the objective function for BO. Also, we propose three fixed-length encoding schemes to cope with the variable-length architecture representation. The result is a new perspective on accurate and efficient design of RNNs, that we validate on three problems. Our findings show that 1) the BO algorithm can explore different network architectures using the proposed encoding schemes and successfully designs well-performing architectures, and 2) the optimization time is significantly reduced by using MRS, without compromising the performance as compared to the architectures obtained from the actual training procedure.

This paper addresses the Traveling Salesman Problem with Drone (TSP-D), in which a truck and drone are used to deliver parcels to customers. The objective of this problem is to either minimize the total operational cost (min-cost TSP-D) or minimize the completion time for the truck and drone (min-time TSP-D). This problem has gained a lot of attention in the last few years since it is matched with the recent trends in a new delivery method among logistics companies. To solve the TSP-D, we propose a hybrid genetic search with dynamic population management and adaptive diversity control based on a split algorithm, problem-tailored crossover and local search operators, a new restore method to advance the convergence and an adaptive penalization mechanism to dynamically balance the search between feasible/infeasible solutions. The computational results show that the proposed algorithm outperforms existing methods in terms of solution quality and improves best known solutions found in the literature. Moreover, various analyses on the impacts of crossover choice and heuristic components have been conducted to analysis further their sensitivity to the performance of our method.

A minimum dominating set in a graph is a minimum set of vertices such that every vertex of the graph either belongs to it, or is adjacent to one vertex of this set. This mathematical object is of high relevance in a number of applications related to social networks analysis, design of wireless networks, coding theory, and data mining, among many others. When vertex weights are given, minimizing the total weight of the dominating set gives rise to a problem variant known as the minimum weight dominating set problem. To solve this problem, we introduce a hybrid matheuristic combining a tabu search with an integer programming solver. The latter is used to solve subproblems in which only a fraction of the decision variables, selected relatively to the search history, are left free while the others are fixed. Moreover, we introduce an adaptive penalty to promote the exploration of intermediate infeasible solutions during the search, enhance the algorithm with perturbations and node elimination procedures, and exploit richer neighborhood classes. Extensive experimental analyses on a variety of instance classes demonstrate the good performance of the algorithm, and the contribution of each component in the success of the search is analyzed.