Time Expanded Networks are powerful tools for the formulation of combinatorial optimization problems that simultaneously involve resource assignment and scheduling. However, in most cases, deriving algorithms from those formulations is difficult. This is due to the large size of the resulting models and to the fact that any heuristic reduction of this size is likely to induce significant discrepancies with the original problem. In this paper, we address this algorithmic issue while considering a multicommodity flow model that refers to an item relocation problem. We propose a Project-and-Lift decomposition scheme and focus here on the Lift issue. Addressing this issue requires turning a projected solution defined on the base network into a true solution that efficiently meets the temporal constraints. We propose several exact and heuristic approaches, and perform numerical experiments.
This paper studies the design of cost-sharing mechanisms for selfish concave bin packing. In our model, bins have unit-capacity, and the cost of each bin is determined by a concave function of its load. This cost is shared among the items packed in the bin according to a prescribed cost-sharing mechanism, while each item acts selfishly to minimize its own shared cost. We measure the efficiency loss of Nash equilibrium by the price of anarchy. For general concave cost functions f, we establish a tight instance-dependent bound f( s(I)/n) /f(1)s(I)/n . Since this bound can be arbitrarily large, no stable mechanism can guarantee a bounded price of anarchy in the general concave setting. We then focus on strictly concave cost functions and prove that every stable mechanism has a price of anarchy at least 4/3 . Finally, we analyze the proportional sharing mechanism, prove its stability, and show that its price of anarchy lies between 1.6424 and 2+√(10)/3(≈ 1.7208) .
Cold warehouses require inventory decisions that simultaneously account for product preservation, environmental control, and service-level requirements. However, most existing inventory models treat storage conditions as fixed parameters and do not jointly optimize inventory policies and environmental operating decisions. This paper develops a single-objective mixed-integer nonlinear programming (MINLP) model for cold-chain inventory management that minimizes total inventory cost while explicitly incorporating ordering, holding, shortage, temperature-adjustment, humidity-adjustment, and refrigerant-emission costs. The model allows storage temperature and humidity to be treated as decision variables and simultaneously determines the most appropriate inventory policy for each product from continuous-review and periodic-review alternatives under budget, capacity, and service-level constraints. Due to the computational complexity of the resulting MINLP, four solution approaches are investigated: Lagrangian Relaxation (LR), Genetic Algorithm (GA), Differential Evolution (DE), and a Hybrid GA–SFS algorithm. Computational experiments were performed on 30 benchmark instances, with each metaheuristic executed 20 independent runs. The results show that LR provides the best objective values but requires substantially higher computational effort. Statistical analysis indicates no significant difference among GA, DE, and Hybrid GA–SFS in terms of average objective value at the 5
The optimal day-ahead scheduling is the process of planning and determining one day in advance the most efficient charge schedule for multiple Electric Vehicles (EVs). The prevailing rule-based scheduling techniques were uncertain, which led to infeasible schedules when conditions varied from predictions. Therefore, a novel Lemming Aphids Optimization Algorithm (LeAdOA) is proposed for optimal day-ahead EV charge scheduling. Initially, the EV parking lot model is simulated in a cloud environment. Later, EV data is collected from relevant datasets. Next, EV charging behaviors are clustered using Deep Adaptive Fuzzy Clustering (DAFC). Later, Day-Ahead Market (DAM) prices are forecasted using a Quasi-Recurrent Neural Network (QRNN). The final step is to perform optimal day-ahead charge scheduling using LeAdOA with EV operating parameters and constraints, like an initial State of Charge (SOC) at arrival, required SOC at departure, charging power limits, discharging power limits, and total charging demand. LeAdOA integrates the Aphids Optimization Algorithm (AOA) and Artificial Lemming Algorithm (ALA) to manage EV charging and discharging in a cost-effective and energy-efficient manner. LeAdOA attained a fitness of 0.065, SOC of 40.376, and charging demand of 10.393 at iteration 910.
Let G be a graph of order n with m edges. Let λ _1^L ≥λ _2^L ≥…≥λ _n^L and ρ _1^Q ≥ρ _2^Q ≥…≥ρ _n^Q be the Laplacian eigenvalues and distance signless Laplacian eigenvalues of G, respectively. Let S^L_k(G) = ∑ _i=1^kλ _i^L and M_k^Q(G) = ∑ _i=1^kρ _i^Q . Brouwer conjectured that S^L_k(G) ≤ m + ( [ k+1; 2 ]) for any graph G and 1 ≤ k ≤ n. Similarly, in 2021, Alhevaz et al. proposed a Brouwer-type conjecture that M_k^Q(G) ≤ W(G) + ( [ k+2; 3 ]) for any graph G that is not a path and 1 ≤ k ≤ n , where W(G) is the Wiener index of G. They proved that this inequality holds for the graphs of diameter 1 or 2. Let Γ _n denote the family of graphs of order n with diameter 3 that contain a spanning tree of diameter 3. Let χ _n denote the family of graphs of order n with diameter 4 that contain a double starlike graph as a spanning subgraph. In this paper, we prove that the Brouwer-type inequality holds for any graph G in Γ _a+b+2 ( a+b ≥ 97 ) or χ _a+b+3 ( a+b ≥ 223 ), or some trees of diameter 4.
